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   "source": [
    "![(book cover)](https://covers.oreillystatic.com/images/0636920167433/cat.gif \"(book cover)\")\n",
    "# \"Programming Quantum Computers\" by O'Reilly Media -  [book info](http://shop.oreilly.com/product/0636920167433.do)  - [all code samples](https://oreilly-qc.github.io)\n",
    "\n",
    "## Code samples for Chapter 5\n",
    "These code samples were written by Mariia Mykhailova."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 5-1: Integer increment-by-one operation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Example 5-1, part 1: Integer increment-by-one operation (circuit implementation)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
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      "application/json": "[\"CircuitIncrement\",\"CircuitIncrementAndDecrement\"]",
      "text/html": [
       "<ul><li>CircuitIncrement</li><li>CircuitIncrementAndDecrement</li></ul>"
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      "text/plain": [
       "CircuitIncrement, CircuitIncrementAndDecrement"
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   "source": [
    "// Example 5-1: Integer increment-by-one operation (circuit implementation)\n",
    "\n",
    "open Microsoft.Quantum.Diagnostics;\n",
    "\n",
    "// Circuit implementation of modular increment operation\n",
    "operation CircuitIncrement (register : Qubit[]) : Unit is Adj {\n",
    "    for i in Length(register) - 1 .. -1 .. 0 {\n",
    "        Controlled X(register[0 .. i - 1], register[i]);\n",
    "    }\n",
    "}\n",
    "\n",
    "operation CircuitIncrementAndDecrement () : Unit {\n",
    "    // allocate the qubit register\n",
    "    use register = Qubit[4];\n",
    "    // initialize the inputs\n",
    "    X(register[0]);\n",
    "    H(register[2]);\n",
    "    T(register[2]);\n",
    "\n",
    "    DumpMachine(());\n",
    "    // note that at this point non-zero amplitudes are at the basis states |1❭ and |5❭\n",
    "\n",
    "    Message(\"Increment (circuit implementation)\");\n",
    "    CircuitIncrement(register);\n",
    "    DumpMachine(());\n",
    "    // note that after incrementing the same amplitudes shifted to the basis states |5❭ and |6❭\n",
    "\n",
    "    // decrement is an adjoint of increment, so we don't need to implement it separately\n",
    "    Message(\"Decrement (curcuit implementation)\");\n",
    "    Adjoint CircuitIncrement(register);\n",
    "    DumpMachine(());\n",
    "\n",
    "    // make sure the qubits are back to the |0❭ state\n",
    "    ResetAll(register);\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note the use of `%config` below: setting `dump.truncateSmallAmplitudes` to `true` hides the basis states of a state vector with near-zero measurement probabilities."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": false
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   "outputs": [
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       "                                <td>$\\left|5\\right\\rangle$</td>\r\n",
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       "|1⟩\t0.7071067811865476 + 0𝑖\n",
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      "Increment (circuit implementation)\r\n"
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      "Decrement (curcuit implementation)\r\n"
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       "|1⟩\t0.7071067811865476 + 0𝑖\n",
       "|5⟩\t0.5000000000000001 + 0.5000000000000001𝑖"
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       "()"
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   ],
   "source": [
    "%config dump.truncateSmallAmplitudes=true\n",
    "%simulate CircuitIncrementAndDecrement"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Example 5-1, part 2: Integer increment-by-one operation (using library operation)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
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       "<ul><li>LibraryIncrementAndDecrement</li></ul>"
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      "text/plain": [
       "LibraryIncrementAndDecrement"
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     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "// Example 5-1: Integer increment-by-one operation (using library operation)\n",
    "\n",
    "open Microsoft.Quantum.Arithmetic;\n",
    "open Microsoft.Quantum.Diagnostics;\n",
    "\n",
    "operation LibraryIncrementAndDecrement () : Unit {\n",
    "    // allocate the qubit register\n",
    "    use register = Qubit[4];\n",
    "    // initialize the inputs\n",
    "    X(register[0]);\n",
    "    H(register[2]);\n",
    "    T(register[2]);\n",
    "\n",
    "    DumpMachine(());\n",
    "    // note that at this point non-zero amplitudes are at the basis states |1❭ and |5❭\n",
    "\n",
    "    // Increment the register using library implementation of the increment from Microsoft.Quantum.Arithmetic\n",
    "    Message(\"Increment (library implementation)\");\n",
    "    IncrementByInteger(1, LittleEndian(register));\n",
    "    DumpMachine();\n",
    "\n",
    "    Message(\"Decrement (library implementation)\");\n",
    "    IncrementByInteger(-1, LittleEndian(register));\n",
    "    DumpMachine();\n",
    "\n",
    "    // make sure the qubits are back to the |0❭ state\n",
    "    ResetAll(register);\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true
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   "outputs": [
    {
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       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">0, 1, 2, 3</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (little endian)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
       "                            </tr>\r\n",
       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|1\\right\\rangle$</td>\r\n",
       "                                <td>$0.7071 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
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       "                                    <p id=\"round-3a54f2e7-8346-4133-a9e8-881b9aa0215a\"> \r\n",
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       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
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       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|5\\right\\rangle$</td>\r\n",
       "                                <td>$0.5000 + 0.5000 i$</td>\r\n",
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       "                                \r\n",
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       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
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       "|1⟩\t0.7071067811865476 + 0𝑖\n",
       "|5⟩\t0.5000000000000001 + 0.5000000000000001𝑖"
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     "text": [
      "Increment (library implementation)\r\n"
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       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">0, 1, 2, 3</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (little endian)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
       "                            </tr>\r\n",
       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|2\\right\\rangle$</td>\r\n",
       "                                <td>$0.7071  -0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
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       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
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       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|6\\right\\rangle$</td>\r\n",
       "                                <td>$0.5000 + 0.5000 i$</td>\r\n",
       "                                \r\n",
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       "                                    num = num.toFixed(4);\r\n",
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       "                                <td style=\"transform: rotate(44.99999999999999deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
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       "                            \r\n",
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       "|2⟩\t0.7071067811865482 + -2.465190328815662E-32𝑖\n",
       "|6⟩\t0.5000000000000007 + 0.5000000000000006𝑖"
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     "text": [
      "Decrement (library implementation)\r\n"
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       "\r\n",
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       "                        <thead>\r\n",
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       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">0, 1, 2, 3</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (little endian)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
       "                            </tr>\r\n",
       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|1\\right\\rangle$</td>\r\n",
       "                                <td>$0.7071 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
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       "                                <td style=\"transform: rotate(4.497983566394931E-15deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
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       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|5\\right\\rangle$</td>\r\n",
       "                                <td>$0.5000 + 0.5000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
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       "                                <td style=\"transform: rotate(44.999999999999986deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
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      "text/plain": [
       "|1⟩\t0.707106781186549 + 5.551115123125777E-17𝑖\n",
       "|5⟩\t0.5000000000000014 + 0.5000000000000011𝑖"
      ]
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     "data": {
      "application/json": "{\"@type\":\"tuple\"}",
      "text/plain": [
       "()"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%simulate LibraryIncrementAndDecrement"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 5-2: Adding two quantum integers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "application/json": "{\"LastUpdated\":\"2021-04-03T23:53:19.9108448-07:00\",\"IsCompleted\":true,\"Description\":\"Adding package Microsoft.Quantum.Numerics\",\"Subtask\":\"done\"}",
      "text/plain": [
       "Adding package Microsoft.Quantum.Numerics: done!"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/json": "[\"Microsoft.Quantum.Standard::0.15.2101125897\",\"Microsoft.Quantum.Standard.Visualization::0.15.2101125897\",\"Microsoft.Quantum.Numerics::0.15.2101125897\"]",
      "text/html": [
       "<ul><li>Microsoft.Quantum.Standard::0.15.2101125897</li><li>Microsoft.Quantum.Standard.Visualization::0.15.2101125897</li><li>Microsoft.Quantum.Numerics::0.15.2101125897</li></ul>"
      ],
      "text/plain": [
       "Microsoft.Quantum.Standard::0.15.2101125897, Microsoft.Quantum.Standard.Visualization::0.15.2101125897, Microsoft.Quantum.Numerics::0.15.2101125897"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%package Microsoft.Quantum.Numerics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/json": "[\"QuantumAddition\"]",
      "text/html": [
       "<ul><li>QuantumAddition</li></ul>"
      ],
      "text/plain": [
       "QuantumAddition"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "// Example 5-2: Adding two quantum integers\n",
    "\n",
    "open Microsoft.Quantum.Diagnostics;\n",
    "\n",
    "// Open namespace which defines arithmetic operations\n",
    "open Microsoft.Quantum.Arithmetic;\n",
    "\n",
    "operation QuantumAddition () : Unit {\n",
    "    use (a, b) = (Qubit[4], Qubit[2]);\n",
    "    // Initialize the inputs\n",
    "    X(a[0]);\n",
    "    H(a[2]);\n",
    "    T(a[2]);\n",
    "    Message(\"Register a\");\n",
    "    DumpRegister((), a);\n",
    "    // At this point non-zero amplitudes of register a are at the basis states |1❭ and |5❭\n",
    "\n",
    "    X(b[0]);\n",
    "    H(b[1]);\n",
    "    T(b[1]);\n",
    "    Message(\"Register b\");\n",
    "    DumpRegister((), b);\n",
    "    // At this point non-zero amplitudes of register b are at the basis states |1❭ and |3❭\n",
    "\n",
    "    // The library operation AddI will add the first parameter to the second one\n",
    "    AddI(LittleEndian(b), LittleEndian(a));\n",
    "\n",
    "    // Note that now the registers a and b are entangled, so you can not look at just the state of the register b.\n",
    "    Message(\"State of the system after computing a += b\");\n",
    "    DumpMachine();\n",
    "    // The output of this operation is a bit tricky to decipher, since it represents both registers a and b.\n",
    "    // Register a is the lowest 4 bits of the overall state, and register b is the highest 2 bits.\n",
    "    // Thus, the non-zero amplitude 0.5 of the basis state |18❭ corresponds to the little-endian bit mask 010010,\n",
    "    // which can be split up into registers a and b as 0100 10, \n",
    "    // which in turn is converted to decimal numbers 2 and 1:\n",
    "    // the first number is the basis state of register a, storing the sum of basis states |1❭ and |1❭,\n",
    "    // and the second number is the input state of register b (|1❭).\n",
    "    // The amplitude of this state is a product of the amplitudes of the basis states |1❭ and |1❭ that were added, 1/sqrt(2) * 1/sqrt(2).\n",
    "    // The rest of the states can be traced in a similar way.\n",
    "\n",
    "    // Make sure the qubits are back to the |0❭ state\n",
    "    ResetAll(a + b);\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Register a\r\n"
     ]
    },
    {
     "data": {
      "application/json": "{\"div_id\":\"dump-machine-div-c4eb0b05-5768-4d2f-8e37-655519e6c93b\",\"qubit_ids\":[0,1,2,3],\"n_qubits\":4,\"amplitudes\":[{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.7071067811865475,\"Imaginary\":0.0,\"Magnitude\":0.7071067811865475,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.5,\"Imaginary\":0.5,\"Magnitude\":0.7071067811865476,\"Phase\":0.7853981633974483},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0}]}",
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       "\r\n",
       "                    <table style=\"table-layout: fixed; width: 100%\">\r\n",
       "                        <thead>\r\n",
       "                            \r\n",
       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">0, 1, 2, 3</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (little endian)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
       "                            </tr>\r\n",
       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|1\\right\\rangle$</td>\r\n",
       "                                <td>$0.7071 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
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       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
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       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|5\\right\\rangle$</td>\r\n",
       "                                <td>$0.5000 + 0.5000 i$</td>\r\n",
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       "                                \r\n",
       "                                <td style=\"transform: rotate(45deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
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      "text/plain": [
       "|1⟩\t0.7071067811865475 + 0𝑖\n",
       "|5⟩\t0.5 + 0.5𝑖"
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     "text": [
      "Register b\r\n"
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       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">4, 5</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (little endian)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
       "                            </tr>\r\n",
       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|1\\right\\rangle$</td>\r\n",
       "                                <td>$0.5000 + 0.5000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
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       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|3\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.7071 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
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       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
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       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
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       "                    </table>"
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       "|1⟩\t0.4999999999999999 + 0.4999999999999999𝑖\n",
       "|3⟩\t1.7431527984210487E-32 + 0.7071067811865476𝑖"
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     "text": [
      "State of the system after computing a += b\r\n"
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      "application/json": "{\"div_id\":\"dump-machine-div-19696b75-0b95-4e09-aae0-6efa3d57c394\",\"qubit_ids\":[0,1,2,3,4,5],\"n_qubits\":6,\"amplitudes\":[{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.5000000000000001,\"Imaginary\":0.0,\"Magnitude\":0.5000000000000001,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.35355339059327384,\"Imaginary\":0.35355339059327384,\"Magnitude\":0.5000000000000001,\"Phase\":0.7853981633974483},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.35355339059327384,\"Imaginary\":0.35355339059327384,\"Magnitude\":0.5000000000000001,\"Phase\":0.7853981633974483},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":1.232595164407831E-32,\"Imaginary\":0.5000000000000002,\"Magnitude\":0.5000000000000002,\"Phase\":1.5707963267948966},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0}]}",
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       "\r\n",
       "                    <table style=\"table-layout: fixed; width: 100%\">\r\n",
       "                        <thead>\r\n",
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       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">0, 1, 2, 3, 4, 5</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (little endian)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
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       "                        </thead>\r\n",
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       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|18\\right\\rangle$</td>\r\n",
       "                                <td>$0.5000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
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       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|22\\right\\rangle$</td>\r\n",
       "                                <td>$0.3536 + 0.3536 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
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       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|52\\right\\rangle$</td>\r\n",
       "                                <td>$0.3536 + 0.3536 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"25.00000000000001\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-631301fb-3d83-471b-8e2f-71ab5932a0c4\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 25.00000000000001;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-631301fb-3d83-471b-8e2f-71ab5932a0c4\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(45deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|56\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.5000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"25.00000000000002\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-52fce04d-245a-44a6-8b31-36cd39876d35\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 25.00000000000002;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-52fce04d-245a-44a6-8b31-36cd39876d35\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(90deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
      ],
      "text/plain": [
       "|18⟩\t0.5000000000000001 + 0𝑖\n",
       "|22⟩\t0.35355339059327384 + 0.35355339059327384𝑖\n",
       "|52⟩\t0.35355339059327384 + 0.35355339059327384𝑖\n",
       "|56⟩\t1.232595164407831E-32 + 0.5000000000000002𝑖"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/json": "{\"@type\":\"tuple\"}",
      "text/plain": [
       "()"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%simulate QuantumAddition"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 5-3: Some interesting arithmetic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/json": "[\"AddBSquared\"]",
      "text/html": [
       "<ul><li>AddBSquared</li></ul>"
      ],
      "text/plain": [
       "AddBSquared"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "// Example 5-3: Some interesting arithmetic\n",
    "\n",
    "open Microsoft.Quantum.Diagnostics;\n",
    "open Microsoft.Quantum.Arithmetic;\n",
    "\n",
    "operation AddBSquared () : Unit {\n",
    "    use (a, b) = (Qubit[4], Qubit[2]);\n",
    "    // Initialize the inputs\n",
    "    X(a[0]);\n",
    "    H(a[2]);\n",
    "    T(a[2]);\n",
    "    Message(\"Register a\");\n",
    "    DumpRegister((), a);\n",
    "    // At this point non-zero amplitudes of register a are at the basis states |1❭ and |5❭\n",
    "\n",
    "    X(b[0]);\n",
    "    H(b[1]);\n",
    "    T(b[1]);\n",
    "    Message(\"Register b\");\n",
    "    DumpRegister((), b);\n",
    "    // At this point non-zero amplitudes of register b are at the basis states |1❭ and |3❭\n",
    "\n",
    "    // Allocate extra qubits to hold the value of b² temporarily;\n",
    "    // note that the register has to have twice the number of qubits in register b.\n",
    "    use anc = Qubit[4];\n",
    "    within {\n",
    "        // Compute anc = b * b\n",
    "        SquareI(LittleEndian(b), LittleEndian(anc));\n",
    "    } apply {\n",
    "        // Compute a += anc\n",
    "        AddI(LittleEndian(anc), LittleEndian(a));\n",
    "    }\n",
    "    \n",
    "    // Note that now the registers a and b are entangled, so you can not look at just the state of the register b.\n",
    "    Message(\"State of the system after computing a += b * b\");\n",
    "    DumpMachine();\n",
    "    // The output of this operation can be deciphered in a same way as the previous one:\n",
    "    // basis states |18❭ and |22❭ remain unchanged, since they correspond to the number 1 written in register b;\n",
    "    // basis state |58❭ corresponds to little-endian binary 010111, which represents b = 3 and a + b * b = 1 + 3² = 10,\n",
    "    // and basis state |62❭ is binary 011111, which is b = 3 and a + b * b = 5 + 3² = 14. \n",
    "\n",
    "    // Make sure the qubits are back to the |0❭ state\n",
    "    ResetAll(a + b);\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Register a\r\n"
     ]
    },
    {
     "data": {
      "application/json": "{\"div_id\":\"dump-machine-div-86e405bf-216e-4f6f-b8d5-178ed1650e01\",\"qubit_ids\":[0,1,2,3],\"n_qubits\":4,\"amplitudes\":[{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.7071067811865475,\"Imaginary\":0.0,\"Magnitude\":0.7071067811865475,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.5,\"Imaginary\":0.5,\"Magnitude\":0.7071067811865476,\"Phase\":0.7853981633974483},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0}]}",
      "text/html": [
       "\r\n",
       "                    <table style=\"table-layout: fixed; width: 100%\">\r\n",
       "                        <thead>\r\n",
       "                            \r\n",
       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">0, 1, 2, 3</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (little endian)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
       "                            </tr>\r\n",
       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|1\\right\\rangle$</td>\r\n",
       "                                <td>$0.7071 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"49.999999999999986\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-3854dba3-aa75-4ec6-8cef-68ff3ae78b2b\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 49.999999999999986;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-3854dba3-aa75-4ec6-8cef-68ff3ae78b2b\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|5\\right\\rangle$</td>\r\n",
       "                                <td>$0.5000 + 0.5000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"50.000000000000014\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-ad74a50d-79c2-4c2c-8af2-607bfac159c1\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 50.000000000000014;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-ad74a50d-79c2-4c2c-8af2-607bfac159c1\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(45deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
      ],
      "text/plain": [
       "|1⟩\t0.7071067811865475 + 0𝑖\n",
       "|5⟩\t0.5 + 0.5𝑖"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Register b\r\n"
     ]
    },
    {
     "data": {
      "application/json": "{\"div_id\":\"dump-machine-div-d2fbf841-97c4-4d5e-8457-78d78ca7220b\",\"qubit_ids\":[4,5],\"n_qubits\":2,\"amplitudes\":[{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.4999999999999999,\"Imaginary\":0.4999999999999999,\"Magnitude\":0.7071067811865475,\"Phase\":0.7853981633974483},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":1.7431527984210487E-32,\"Imaginary\":0.7071067811865476,\"Magnitude\":0.7071067811865476,\"Phase\":1.5707963267948966}]}",
      "text/html": [
       "\r\n",
       "                    <table style=\"table-layout: fixed; width: 100%\">\r\n",
       "                        <thead>\r\n",
       "                            \r\n",
       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">4, 5</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (little endian)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
       "                            </tr>\r\n",
       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|1\\right\\rangle$</td>\r\n",
       "                                <td>$0.5000 + 0.5000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"49.999999999999986\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-a050252f-8a31-425f-a587-70d18ad05e38\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 49.999999999999986;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-a050252f-8a31-425f-a587-70d18ad05e38\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(45deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|3\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.7071 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"50.000000000000014\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-71341a71-bc10-4682-99e8-04b5c0cf1144\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 50.000000000000014;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-71341a71-bc10-4682-99e8-04b5c0cf1144\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(90deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
      ],
      "text/plain": [
       "|1⟩\t0.4999999999999999 + 0.4999999999999999𝑖\n",
       "|3⟩\t1.7431527984210487E-32 + 0.7071067811865476𝑖"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "State of the system after computing a += b * b\r\n"
     ]
    },
    {
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       "                        <thead>\r\n",
       "                            \r\n",
       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">0, 1, 2, 3, 4, 5, 6, 7, 8, 9</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (little endian)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
       "                            </tr>\r\n",
       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|18\\right\\rangle$</td>\r\n",
       "                                <td>$0.5000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"25.00000000000001\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-a755ccc3-de0d-4092-8b4b-2c73959c4e0e\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 25.00000000000001;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-a755ccc3-de0d-4092-8b4b-2c73959c4e0e\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|22\\right\\rangle$</td>\r\n",
       "                                <td>$0.3536 + 0.3536 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"25.00000000000001\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-81cac7fe-e1fe-4037-96d9-fe64930eb6c8\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 25.00000000000001;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-81cac7fe-e1fe-4037-96d9-fe64930eb6c8\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(45deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|58\\right\\rangle$</td>\r\n",
       "                                <td>$0.3536 + 0.3536 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"25.00000000000001\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-2ae69a7b-02b2-4405-b807-8c885489a1fc\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 25.00000000000001;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-2ae69a7b-02b2-4405-b807-8c885489a1fc\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(45deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|62\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.5000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"25.00000000000002\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-8a927457-bdb1-4079-a5fb-70c305af64cc\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 25.00000000000002;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-8a927457-bdb1-4079-a5fb-70c305af64cc\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(90deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
      ],
      "text/plain": [
       "|18⟩\t0.5000000000000001 + 0𝑖\n",
       "|22⟩\t0.35355339059327384 + 0.35355339059327384𝑖\n",
       "|58⟩\t0.35355339059327384 + 0.35355339059327384𝑖\n",
       "|62⟩\t1.232595164407831E-32 + 0.5000000000000002𝑖"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/json": "{\"@type\":\"tuple\"}",
      "text/plain": [
       "()"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%simulate AddBSquared"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 5-4: Quantum-conditional execution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/json": "[\"QuantumConditionalExecution\"]",
      "text/html": [
       "<ul><li>QuantumConditionalExecution</li></ul>"
      ],
      "text/plain": [
       "QuantumConditionalExecution"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "// Example 5-4: Quantum-conditional execution\n",
    "\n",
    "open Microsoft.Quantum.Diagnostics;\n",
    "open Microsoft.Quantum.Arithmetic;\n",
    "\n",
    "operation QuantumConditionalExecution () : Unit {\n",
    "    use (a, b) = (Qubit[3], Qubit[3]);\n",
    "    // Initialize the inputs\n",
    "    X(a[0]);\n",
    "    H(a[2]);\n",
    "    Message(\"Register a\");\n",
    "    DumpRegister((), a);\n",
    "    // At this point non-zero amplitudes of register a are at the basis states |1❭ and |5❭\n",
    "\n",
    "    X(b[0]);\n",
    "    H(b[1]);\n",
    "    T(b[1]);\n",
    "    Message(\"Register b\");\n",
    "    DumpRegister((), b);\n",
    "    // At this point non-zero amplitudes of register b are at the basis states |1❭ and |3❭\n",
    "\n",
    "    // a -= 3\n",
    "    IncrementByInteger(-3, LittleEndian(a));\n",
    "\n",
    "    // if (a < 0) then b++;\n",
    "    (Controlled IncrementByInteger)([a[2]], (1, LittleEndian(b)));\n",
    "\n",
    "    // a += 3\n",
    "    IncrementByInteger(3, LittleEndian(a));\n",
    "\n",
    "    // Note that now the registers a and b are entangled, so you can not look at just the state of the register b.\n",
    "    Message(\"State of the system after the computation\");\n",
    "    DumpMachine();\n",
    "\n",
    "    // Make sure the qubits are back to the |0❭ state\n",
    "    ResetAll(a + b);\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Register a\r\n"
     ]
    },
    {
     "data": {
      "application/json": "{\"div_id\":\"dump-machine-div-110b2009-d386-43e1-90d9-6743d65d1c13\",\"qubit_ids\":[0,1,2],\"n_qubits\":3,\"amplitudes\":[{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.7071067811865476,\"Imaginary\":0.0,\"Magnitude\":0.7071067811865476,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.7071067811865476,\"Imaginary\":0.0,\"Magnitude\":0.7071067811865476,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0}]}",
      "text/html": [
       "\r\n",
       "                    <table style=\"table-layout: fixed; width: 100%\">\r\n",
       "                        <thead>\r\n",
       "                            \r\n",
       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">0, 1, 2</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (little endian)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
       "                            </tr>\r\n",
       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|1\\right\\rangle$</td>\r\n",
       "                                <td>$0.7071 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"50.000000000000014\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-a214df4d-0df4-48cf-8d20-980cea04d00d\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 50.000000000000014;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-a214df4d-0df4-48cf-8d20-980cea04d00d\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|5\\right\\rangle$</td>\r\n",
       "                                <td>$0.7071 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"50.000000000000014\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-cec06e09-b3fe-4766-aeba-325be5e307b9\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 50.000000000000014;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-cec06e09-b3fe-4766-aeba-325be5e307b9\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
      ],
      "text/plain": [
       "|1⟩\t0.7071067811865476 + 0𝑖\n",
       "|5⟩\t0.7071067811865476 + 0𝑖"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Register b\r\n"
     ]
    },
    {
     "data": {
      "application/json": "{\"div_id\":\"dump-machine-div-7dd9fd8a-1fb5-4521-aab7-68c3ec360a0c\",\"qubit_ids\":[3,4,5],\"n_qubits\":3,\"amplitudes\":[{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.7071067811865475,\"Imaginary\":0.0,\"Magnitude\":0.7071067811865475,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.5,\"Imaginary\":0.5,\"Magnitude\":0.7071067811865476,\"Phase\":0.7853981633974483},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0}]}",
      "text/html": [
       "\r\n",
       "                    <table style=\"table-layout: fixed; width: 100%\">\r\n",
       "                        <thead>\r\n",
       "                            \r\n",
       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">3, 4, 5</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (little endian)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
       "                            </tr>\r\n",
       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|1\\right\\rangle$</td>\r\n",
       "                                <td>$0.7071 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"49.999999999999986\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-1cb05aa7-01ca-44a6-835b-6b7f784811fb\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 49.999999999999986;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-1cb05aa7-01ca-44a6-835b-6b7f784811fb\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|3\\right\\rangle$</td>\r\n",
       "                                <td>$0.5000 + 0.5000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"50.000000000000014\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-da890022-a46d-48f7-a473-c882ab3faeea\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 50.000000000000014;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-da890022-a46d-48f7-a473-c882ab3faeea\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(45deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
      ],
      "text/plain": [
       "|1⟩\t0.7071067811865475 + 0𝑖\n",
       "|3⟩\t0.5 + 0.5𝑖"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "State of the system after the computation\r\n"
     ]
    },
    {
     "data": {
      "application/json": 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       "\r\n",
       "                    <table style=\"table-layout: fixed; width: 100%\">\r\n",
       "                        <thead>\r\n",
       "                            \r\n",
       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">0, 1, 2, 3, 4, 5</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (little endian)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
       "                            </tr>\r\n",
       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|13\\right\\rangle$</td>\r\n",
       "                                <td>$0.5000  -0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"25.000000000000146\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-e22025e6-5d8b-4490-aba1-4f5a3d815557\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 25.000000000000146;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-e22025e6-5d8b-4490-aba1-4f5a3d815557\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(-3.093754127345297E-15deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|17\\right\\rangle$</td>\r\n",
       "                                <td>$0.5000  -0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"25.000000000000146\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-d32540b6-625d-46dc-aade-3b237e41e040\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 25.000000000000146;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-d32540b6-625d-46dc-aade-3b237e41e040\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(-4.3949009417559266E-15deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|29\\right\\rangle$</td>\r\n",
       "                                <td>$0.3536 + 0.3536 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"25.000000000000135\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-4c4077eb-80e6-4359-9176-7d4ed4451bcd\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 25.000000000000135;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-4c4077eb-80e6-4359-9176-7d4ed4451bcd\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(45deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|33\\right\\rangle$</td>\r\n",
       "                                <td>$0.3536 + 0.3536 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"25.000000000000135\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-1457ac3f-7284-49d5-976e-fcfdd56192f1\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 25.000000000000135;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-1457ac3f-7284-49d5-976e-fcfdd56192f1\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(45deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
      ],
      "text/plain": [
       "|13⟩\t0.5000000000000014 + -2.699809788466976E-17𝑖\n",
       "|17⟩\t0.5000000000000014 + -3.835274586632034E-17𝑖\n",
       "|29⟩\t0.35355339059327473 + 0.3535533905932747𝑖\n",
       "|33⟩\t0.35355339059327473 + 0.3535533905932747𝑖"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/json": "{\"@type\":\"tuple\"}",
      "text/plain": [
       "()"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%simulate QuantumConditionalExecution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 5-5: Phase-encoding the result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/json": "[\"PhaseEncoding\"]",
      "text/html": [
       "<ul><li>PhaseEncoding</li></ul>"
      ],
      "text/plain": [
       "PhaseEncoding"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "// Example 5-5: Phase-encoding the result\n",
    "\n",
    "open Microsoft.Quantum.Diagnostics;\n",
    "open Microsoft.Quantum.Arithmetic;\n",
    "\n",
    "operation PhaseEncoding () : Unit {\n",
    "    use (a, b) = (Qubit[3], Qubit[2]);\n",
    "    // Initialize the inputs\n",
    "    H(a[0]);\n",
    "    H(a[1]);\n",
    "    Message(\"Register a\");\n",
    "    DumpRegister((), a);\n",
    "    // At this point non-zero amplitudes of register a are at the basis states |0❭, |1❭, |2❭, and |3❭\n",
    "\n",
    "    X(b[0]);\n",
    "    H(b[1]);\n",
    "    Message(\"Register b\");\n",
    "    DumpRegister((), b);\n",
    "    // At this point non-zero amplitudes of register b are at the basis states |1❭ and |3❭\n",
    "\n",
    "    Message(\"Complete state of the system\");\n",
    "    DumpMachine(());\n",
    "\n",
    "    // a -= 3\n",
    "    IncrementByInteger(-3, LittleEndian(a));\n",
    "\n",
    "    // if (a < 0) and b == 1 then flip the phase\n",
    "    (ControlledOnInt(1, Z))(b, a[2]);\n",
    "\n",
    "    // a += 3\n",
    "    IncrementByInteger(3, LittleEndian(a));\n",
    "\n",
    "    // Note that now the registers a and b are entangled, so you can not look at just the state of the register b.\n",
    "    Message(\"State of the system after the computation\");\n",
    "    DumpMachine(());\n",
    "\n",
    "    // Make sure the qubits are back to the |0❭ state\n",
    "    ResetAll(a + b);\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Register a\r\n"
     ]
    },
    {
     "data": {
      "application/json": "{\"div_id\":\"dump-machine-div-6fda55da-0e5f-49b1-b93d-e7c6dead1d72\",\"qubit_ids\":[0,1,2],\"n_qubits\":3,\"amplitudes\":[{\"Real\":0.5,\"Imaginary\":0.0,\"Magnitude\":0.5,\"Phase\":0.0},{\"Real\":0.5,\"Imaginary\":0.0,\"Magnitude\":0.5,\"Phase\":0.0},{\"Real\":0.5,\"Imaginary\":0.0,\"Magnitude\":0.5,\"Phase\":0.0},{\"Real\":0.5,\"Imaginary\":0.0,\"Magnitude\":0.5,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0}]}",
      "text/html": [
       "\r\n",
       "                    <table style=\"table-layout: fixed; width: 100%\">\r\n",
       "                        <thead>\r\n",
       "                            \r\n",
       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">0, 1, 2</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (little endian)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
       "                            </tr>\r\n",
       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|0\\right\\rangle$</td>\r\n",
       "                                <td>$0.5000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"25\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-b6580600-6a3e-4a19-aa8d-0e9e7bd0b3d0\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 25;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-b6580600-6a3e-4a19-aa8d-0e9e7bd0b3d0\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|1\\right\\rangle$</td>\r\n",
       "                                <td>$0.5000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"25\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-85ded114-99dd-4a7d-9d8b-edeb4bb82801\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 25;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-85ded114-99dd-4a7d-9d8b-edeb4bb82801\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|2\\right\\rangle$</td>\r\n",
       "                                <td>$0.5000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"25\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-d6af0034-7063-4573-a2c5-cd5a3edf8903\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 25;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-d6af0034-7063-4573-a2c5-cd5a3edf8903\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|3\\right\\rangle$</td>\r\n",
       "                                <td>$0.5000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"25\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-148c5154-4be2-4d27-9781-78af83f77a63\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 25;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-148c5154-4be2-4d27-9781-78af83f77a63\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
      ],
      "text/plain": [
       "|0⟩\t0.5 + 0𝑖\n",
       "|1⟩\t0.5 + 0𝑖\n",
       "|2⟩\t0.5 + 0𝑖\n",
       "|3⟩\t0.5 + 0𝑖"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Register b\r\n"
     ]
    },
    {
     "data": {
      "application/json": "{\"div_id\":\"dump-machine-div-0c44ce91-82fe-4941-bd8a-f57693e63217\",\"qubit_ids\":[3,4],\"n_qubits\":2,\"amplitudes\":[{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.7071067811865476,\"Imaginary\":0.0,\"Magnitude\":0.7071067811865476,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.7071067811865476,\"Imaginary\":0.0,\"Magnitude\":0.7071067811865476,\"Phase\":0.0}]}",
      "text/html": [
       "\r\n",
       "                    <table style=\"table-layout: fixed; width: 100%\">\r\n",
       "                        <thead>\r\n",
       "                            \r\n",
       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">3, 4</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (little endian)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
       "                            </tr>\r\n",
       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|1\\right\\rangle$</td>\r\n",
       "                                <td>$0.7071 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"50.000000000000014\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-fbf6ff36-f8c4-41a6-9dc7-a7a67d9e0981\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 50.000000000000014;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-fbf6ff36-f8c4-41a6-9dc7-a7a67d9e0981\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|3\\right\\rangle$</td>\r\n",
       "                                <td>$0.7071 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"50.000000000000014\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-aa437330-41ed-455f-aa4e-8c84bd9d7da2\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 50.000000000000014;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-aa437330-41ed-455f-aa4e-8c84bd9d7da2\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
      ],
      "text/plain": [
       "|1⟩\t0.7071067811865476 + 0𝑖\n",
       "|3⟩\t0.7071067811865476 + 0𝑖"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Complete state of the system\r\n"
     ]
    },
    {
     "data": {
      "application/json": "{\"div_id\":\"dump-machine-div-5c7885d4-2f5f-4b68-86f9-36db3355b6e5\",\"qubit_ids\":[0,1,2,3,4],\"n_qubits\":5,\"amplitudes\":[{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.35355339059327384,\"Imaginary\":0.0,\"Magnitude\":0.35355339059327384,\"Phase\":0.0},{\"Real\":0.35355339059327384,\"Imaginary\":0.0,\"Magnitude\":0.35355339059327384,\"Phase\":0.0},{\"Real\":0.35355339059327384,\"Imaginary\":0.0,\"Magnitude\":0.35355339059327384,\"Phase\":0.0},{\"Real\":0.35355339059327384,\"Imaginary\":0.0,\"Magnitude\":0.35355339059327384,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.35355339059327384,\"Imaginary\":0.0,\"Magnitude\":0.35355339059327384,\"Phase\":0.0},{\"Real\":0.35355339059327384,\"Imaginary\":0.0,\"Magnitude\":0.35355339059327384,\"Phase\":0.0},{\"Real\":0.35355339059327384,\"Imaginary\":0.0,\"Magnitude\":0.35355339059327384,\"Phase\":0.0},{\"Real\":0.35355339059327384,\"Imaginary\":0.0,\"Magnitude\":0.35355339059327384,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0}]}",
      "text/html": [
       "\r\n",
       "                    <table style=\"table-layout: fixed; width: 100%\">\r\n",
       "                        <thead>\r\n",
       "                            \r\n",
       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">0, 1, 2, 3, 4</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (little endian)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
       "                            </tr>\r\n",
       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|8\\right\\rangle$</td>\r\n",
       "                                <td>$0.3536 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"12.500000000000005\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-79814730-66aa-4edd-b23e-6f694477bfef\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 12.500000000000005;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-79814730-66aa-4edd-b23e-6f694477bfef\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|9\\right\\rangle$</td>\r\n",
       "                                <td>$0.3536 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"12.500000000000005\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-b426a1c3-38ed-43a1-a77a-0045f246ab56\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 12.500000000000005;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-b426a1c3-38ed-43a1-a77a-0045f246ab56\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|10\\right\\rangle$</td>\r\n",
       "                                <td>$0.3536 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"12.500000000000005\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-278bd217-25eb-43f3-9308-7b37fd98a21b\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 12.500000000000005;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-278bd217-25eb-43f3-9308-7b37fd98a21b\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|11\\right\\rangle$</td>\r\n",
       "                                <td>$0.3536 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"12.500000000000005\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-efafdd0b-7f66-4efc-b9e6-d509119f222d\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 12.500000000000005;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-efafdd0b-7f66-4efc-b9e6-d509119f222d\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|24\\right\\rangle$</td>\r\n",
       "                                <td>$0.3536 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"12.500000000000005\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-ce419a72-a1e9-414d-a305-3cace9c509c0\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 12.500000000000005;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-ce419a72-a1e9-414d-a305-3cace9c509c0\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|25\\right\\rangle$</td>\r\n",
       "                                <td>$0.3536 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"12.500000000000005\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-312c66ea-6d39-4352-b251-60c27ab66bc9\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 12.500000000000005;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-312c66ea-6d39-4352-b251-60c27ab66bc9\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|26\\right\\rangle$</td>\r\n",
       "                                <td>$0.3536 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"12.500000000000005\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-2f4f5a88-259b-41d0-9d0f-fa1e0f3647df\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 12.500000000000005;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-2f4f5a88-259b-41d0-9d0f-fa1e0f3647df\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|27\\right\\rangle$</td>\r\n",
       "                                <td>$0.3536 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"12.500000000000005\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-9cfbb63d-4dfb-4082-b96d-cb2c703a433e\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 12.500000000000005;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-9cfbb63d-4dfb-4082-b96d-cb2c703a433e\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
      ],
      "text/plain": [
       "|8⟩\t0.35355339059327384 + 0𝑖\n",
       "|9⟩\t0.35355339059327384 + 0𝑖\n",
       "|10⟩\t0.35355339059327384 + 0𝑖\n",
       "|11⟩\t0.35355339059327384 + 0𝑖\n",
       "|24⟩\t0.35355339059327384 + 0𝑖\n",
       "|25⟩\t0.35355339059327384 + 0𝑖\n",
       "|26⟩\t0.35355339059327384 + 0𝑖\n",
       "|27⟩\t0.35355339059327384 + 0𝑖"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "State of the system after the computation\r\n"
     ]
    },
    {
     "data": {
      "application/json": "{\"div_id\":\"dump-machine-div-970b7fd6-18e7-43ed-8fff-af7bd7c2337e\",\"qubit_ids\":[0,1,2,3,4],\"n_qubits\":5,\"amplitudes\":[{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":-0.3535533905932743,\"Imaginary\":1.962615573354723E-17,\"Magnitude\":0.3535533905932743,\"Phase\":3.141592653589793},{\"Real\":-0.3535533905932744,\"Imaginary\":6.364057111333954E-17,\"Magnitude\":0.3535533905932744,\"Phase\":3.141592653589793},{\"Real\":-0.35355339059327445,\"Imaginary\":2.2007207689896168E-17,\"Magnitude\":0.35355339059327445,\"Phase\":3.141592653589793},{\"Real\":0.35355339059327423,\"Imaginary\":-4.738173134917614E-17,\"Magnitude\":0.35355339059327423,\"Phase\":-1.340157741654465E-16},{\"Real\":-9.139614672896846E-17,\"Imaginary\":-7.513730696480505E-17,\"Magnitude\":1.1831682270423964E-16,\"Phase\":-2.4535171243956184},{\"Real\":6.125951915699059E-17,\"Imaginary\":-1.3302951015241183E-16,\"Magnitude\":1.4645674876473376E-16,\"Phase\":-1.1392485237494245},{\"Real\":7.513730696480505E-17,\"Imaginary\":-6.364057111333954E-17,\"Magnitude\":9.846693449861922E-17,\"Phase\":-0.70274418852118},{\"Real\":-7.513730696480503E-17,\"Imaginary\":6.125951915699059E-17,\"Magnitude\":9.694505446524352E-17,\"Phase\":2.457591238204659},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.3535533905932742,\"Imaginary\":-3.3503943541361674E-17,\"Magnitude\":0.3535533905932742,\"Phase\":-9.476346269835218E-17},{\"Real\":0.35355339059327434,\"Imaginary\":-1.9626155733547217E-17,\"Magnitude\":0.35355339059327434,\"Phase\":-5.551115123125782E-17},{\"Real\":0.3535533905932743,\"Imaginary\":4.7381731349176125E-17,\"Magnitude\":0.3535533905932743,\"Phase\":1.3401577416544645E-16},{\"Real\":0.35355339059327434,\"Imaginary\":4.738173134917614E-17,\"Magnitude\":0.35355339059327434,\"Phase\":1.3401577416544645E-16},{\"Real\":-4.7381731349176125E-17,\"Imaginary\":3.3503943541361674E-17,\"Magnitude\":5.803053246755755E-17,\"Phase\":2.5261129449194057},{\"Real\":8.129419882081693E-18,\"Imaginary\":1.9626155733547217E-17,\"Magnitude\":2.124319788771534E-17,\"Phase\":1.1780972450961744},{\"Real\":-3.3503943541361674E-17,\"Imaginary\":-4.7381731349176125E-17,\"Magnitude\":5.803053246755755E-17,\"Phase\":-2.186276035465284},{\"Real\":8.129419882081696E-18,\"Imaginary\":-4.738173134917614E-17,\"Magnitude\":4.8074067159589126E-17,\"Phase\":-1.4008778720678363}]}",
      "text/html": [
       "\r\n",
       "                    <table style=\"table-layout: fixed; width: 100%\">\r\n",
       "                        <thead>\r\n",
       "                            \r\n",
       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">0, 1, 2, 3, 4</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (little endian)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
       "                            </tr>\r\n",
       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|8\\right\\rangle$</td>\r\n",
       "                                <td>$-0.3536 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"12.500000000000036\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-8030f186-9469-4c7c-9ae3-4f12d6f55f91\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 12.500000000000036;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-8030f186-9469-4c7c-9ae3-4f12d6f55f91\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(180deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|9\\right\\rangle$</td>\r\n",
       "                                <td>$-0.3536 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"12.500000000000044\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-47977eaf-5147-498b-b8d2-de15b1d355b2\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 12.500000000000044;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-47977eaf-5147-498b-b8d2-de15b1d355b2\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(180deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|10\\right\\rangle$</td>\r\n",
       "                                <td>$-0.3536 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"12.50000000000005\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-1931076d-e2db-4ce6-a0fd-86da192402c5\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 12.50000000000005;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-1931076d-e2db-4ce6-a0fd-86da192402c5\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(180deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|11\\right\\rangle$</td>\r\n",
       "                                <td>$0.3536  -0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"12.500000000000034\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-bd4fcf2b-0a3c-4a84-8877-9aae52115aea\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 12.500000000000034;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-bd4fcf2b-0a3c-4a84-8877-9aae52115aea\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(-7.678538247858457E-15deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|24\\right\\rangle$</td>\r\n",
       "                                <td>$0.3536  -0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"12.50000000000003\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-55633442-2b7a-4b29-8123-e866e1918043\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 12.50000000000003;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-55633442-2b7a-4b29-8123-e866e1918043\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(-5.429546464660987E-15deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|25\\right\\rangle$</td>\r\n",
       "                                <td>$0.3536  -0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"12.50000000000004\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-9bdbaacb-a5db-426d-8f83-371a54608421\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 12.50000000000004;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-9bdbaacb-a5db-426d-8f83-371a54608421\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(-3.1805546814635164E-15deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|26\\right\\rangle$</td>\r\n",
       "                                <td>$0.3536 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"12.500000000000036\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-d6a3a5d6-6a0c-424a-9dfb-9aced1762495\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 12.500000000000036;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-d6a3a5d6-6a0c-424a-9dfb-9aced1762495\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(7.678538247858454E-15deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|27\\right\\rangle$</td>\r\n",
       "                                <td>$0.3536 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"12.50000000000004\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-e4c46cd8-913d-48e9-93a0-e3c9c364fb7c\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 12.50000000000004;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-e4c46cd8-913d-48e9-93a0-e3c9c364fb7c\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(7.678538247858454E-15deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
      ],
      "text/plain": [
       "|8⟩\t-0.3535533905932743 + 1.962615573354723E-17𝑖\n",
       "|9⟩\t-0.3535533905932744 + 6.364057111333954E-17𝑖\n",
       "|10⟩\t-0.35355339059327445 + 2.2007207689896168E-17𝑖\n",
       "|11⟩\t0.35355339059327423 + -4.738173134917614E-17𝑖\n",
       "|24⟩\t0.3535533905932742 + -3.3503943541361674E-17𝑖\n",
       "|25⟩\t0.35355339059327434 + -1.9626155733547217E-17𝑖\n",
       "|26⟩\t0.3535533905932743 + 4.7381731349176125E-17𝑖\n",
       "|27⟩\t0.35355339059327434 + 4.738173134917614E-17𝑖"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/json": "{\"@type\":\"tuple\"}",
      "text/plain": [
       "()"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%simulate PhaseEncoding"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 5-6: Logic using CNOT gates"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "application/json": "[\"CNOTLogic\"]",
      "text/html": [
       "<ul><li>CNOTLogic</li></ul>"
      ],
      "text/plain": [
       "CNOTLogic"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "// Example 5-6: Logic using CNOT gates\n",
    "\n",
    "open Microsoft.Quantum.Diagnostics;\n",
    "open Microsoft.Quantum.Measurement;\n",
    "\n",
    "operation CNOTLogic () : Unit {\n",
    "    Message(\"c = ~c\");\n",
    "    use (a, b, c) = (Qubit(), Qubit(), Qubit());\n",
    "    Message($\"Input: c = {M(c)}\");\n",
    "    X(c);\n",
    "    Message($\"Output: c = {M(c)}\");\n",
    "    Reset(c);\n",
    "    \n",
    "    // ------------------------------------------------------\n",
    "    Message(\"\");\n",
    "    Message(\"if (b) then c = ~c\");\n",
    "    // initialize input\n",
    "    X(b);\n",
    "    Message($\"Input: b = {M(b)}, c = {M(c)}\");\n",
    "\n",
    "    CNOT(b, c);\n",
    "    Message($\"Output: b = {M(b)}, c = {M(c)}\");\n",
    "\n",
    "    ResetAll([b, c]);\n",
    "    \n",
    "    // ------------------------------------------------------\n",
    "    Message(\"\");\n",
    "    Message(\"if (a and b) then c = ~c\");\n",
    "    // initialize input\n",
    "    X(a);\n",
    "    X(b);\n",
    "    Message($\"Input: a = {M(a)}, b = {M(b)}, c = {M(c)}\");\n",
    "\n",
    "    (Controlled X)([a, b], c);\n",
    "    Message($\"Output: a = {M(a)}, b = {M(b)}, c = {M(c)}\");\n",
    "\n",
    "    ResetAll([a, b, c]);\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "c = ~c\n",
      "Input: c = Zero\n",
      "Output: c = One\n",
      "\n",
      "if (b) then c = ~c\n",
      "Input: b = One, c = Zero\n",
      "Output: b = One, c = One\n",
      "\n",
      "if (a and b) then c = ~c\n",
      "Input: a = One, b = One, c = Zero\n",
      "Output: a = One, b = One, c = One\n"
     ]
    },
    {
     "data": {
      "application/json": "{\"@type\":\"tuple\"}",
      "text/plain": [
       "()"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%simulate CNOTLogic"
   ]
  }
 ],
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