{
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   "source": [
    "# 14 - Quantum Phase Estimation\n",
    "\n",
    "Estimate the eigenvalue of a unitary operator.\n",
    "\n",
    "**Concepts:** Phase estimation, inverse QFT, eigenvalues"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ce09b30c",
   "metadata": {},
   "outputs": [],
   "source": [
    "import quantsdk as qs\n",
    "import math"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c9c2a4fb",
   "metadata": {},
   "source": [
    "## Phase Estimation for T Gate\n",
    "\n",
    "The T gate has eigenvalue $e^{i\\pi/4}$, so the phase is $\\phi = 1/8$.\n",
    "\n",
    "With 3 counting qubits we can represent $\\phi = 0.001_2 = 1/8$ exactly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "59405cd1",
   "metadata": {},
   "outputs": [],
   "source": [
    "n_count = 3  # counting qubits\n",
    "circuit = qs.Circuit(n_count + 1, name=\"QPE-T\")\n",
    "\n",
    "# Prepare eigenstate |1> on target qubit\n",
    "circuit.x(n_count)\n",
    "\n",
    "# Hadamard on counting qubits\n",
    "for i in range(n_count):\n",
    "    circuit.h(i)\n",
    "\n",
    "# Controlled-U^(2^k) operations (textbook convention: qubit 0 = MSB)\n",
    "# T gate: phase = pi/4, so T^(2^k) = Phase(pi/4 * 2^k)\n",
    "for k in range(n_count):\n",
    "    power = n_count - 1 - k  # qubit 0 gets highest power\n",
    "    angle = math.pi / 4 * (2 ** power)\n",
    "    circuit.cp(k, n_count, angle)\n",
    "\n",
    "# Inverse QFT on counting qubits\n",
    "circuit.swap(0, 2)\n",
    "circuit.h(0)\n",
    "circuit.cp(0, 1, -math.pi / 2)\n",
    "circuit.h(1)\n",
    "circuit.cp(0, 2, -math.pi / 4)\n",
    "circuit.cp(1, 2, -math.pi / 2)\n",
    "circuit.h(2)\n",
    "\n",
    "# Measure counting qubits\n",
    "for i in range(n_count):\n",
    "    circuit.measure(i)\n",
    "\n",
    "result = qs.run(circuit, shots=1000, seed=42)\n",
    "print(f\"QPE for T gate (phase = 1/8):\")\n",
    "print(f\"Result: {result.counts}\")\n",
    "print(f\"Most likely: {result.most_likely}\")\n",
    "\n",
    "# Convert binary to phase\n",
    "measured = result.most_likely\n",
    "phase = int(measured, 2) / (2 ** n_count)\n",
    "print(f\"Estimated phase: {phase} (expected: 0.125 = 1/8)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2b5d652d",
   "metadata": {},
   "source": [
    "## Phase Estimation for S Gate\n",
    "\n",
    "S gate: eigenvalue $e^{i\\pi/2}$, phase $\\phi = 1/4$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "42d83cba",
   "metadata": {},
   "outputs": [],
   "source": [
    "n_count = 3\n",
    "circuit = qs.Circuit(n_count + 1, name=\"QPE-S\")\n",
    "\n",
    "circuit.x(n_count)\n",
    "for i in range(n_count):\n",
    "    circuit.h(i)\n",
    "\n",
    "# S gate: phase = pi/2\n",
    "for k in range(n_count):\n",
    "    power = n_count - 1 - k\n",
    "    angle = math.pi / 2 * (2 ** power)\n",
    "    circuit.cp(k, n_count, angle)\n",
    "\n",
    "# Inverse QFT\n",
    "circuit.swap(0, 2)\n",
    "circuit.h(0)\n",
    "circuit.cp(0, 1, -math.pi / 2)\n",
    "circuit.h(1)\n",
    "circuit.cp(0, 2, -math.pi / 4)\n",
    "circuit.cp(1, 2, -math.pi / 2)\n",
    "circuit.h(2)\n",
    "\n",
    "for i in range(n_count):\n",
    "    circuit.measure(i)\n",
    "\n",
    "result = qs.run(circuit, shots=1000, seed=42)\n",
    "measured = result.most_likely\n",
    "phase = int(measured, 2) / (2 ** n_count)\n",
    "print(f\"QPE for S gate: measured={measured}, phase={phase} (expected: 0.25)\")"
   ]
  }
 ],
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