{
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   "source": [
    "# Metrics in pyGSTi\n",
    "PyGSTi contains implementation of common ways to compare quantum processes and models.  You may just want to `import pygsti` just for this functionality, as many of the functions below act on standard NumPy arrays.  Here are some of the most common functions (this tutorial is <font style=\"color:red\">under construction, and we plan to expand it in future releases.  We apologize for it's current brevity</font>.\n",
    "\n",
    "Let's begin by getting some gate (process) matrices for several simple 1-qubit operations.  Note that `Gx`, `Gy` and `Gi` below are superoperator matrices in the Pauli basis - they're $4 \\times 4$ *real* matrices.  We do this for a standard model (see the [standard module tutorial](../objects/advanced/StandardModules.ipynb)) and a version of this model with slightly rotated gates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   1.0000        0        0        0\n",
      "        0   1.0000        0        0\n",
      "        0        0  -0.0998  -0.9950\n",
      "        0        0   0.9950  -0.0998\n",
      "\n"
     ]
    }
   ],
   "source": [
    "import pygsti.tools as tls\n",
    "import pygsti.report.reportables as rptbls\n",
    "from pygsti.construction import std1Q_XYI as std\n",
    "import numpy as np\n",
    "\n",
    "mdl = std.target_model()\n",
    "Gx = mdl['Gx'].todense()\n",
    "Gy = mdl['Gy'].todense()\n",
    "Gi = mdl['Gi'].todense()\n",
    "\n",
    "mdl_overrot = mdl.rotate( (0.1,0,0) )\n",
    "Gx_overrot = mdl_overrot['Gx'].todense()\n",
    "Gy_overrot = mdl_overrot['Gy'].todense()\n",
    "Gi_overrot = mdl_overrot['Gi'].todense()\n",
    "\n",
    "tls.print_mx(Gx_overrot)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Process matrix comparisons\n",
    "### Fidelities"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0024979173609871452"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rptbls.entanglement_infidelity(Gx, Gx_overrot, 'pp')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0016652782406580968"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rptbls.avg_gate_infidelity(Gx, Gx_overrot, 'pp')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0024979173609871452"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rptbls.eigenvalue_entanglement_infidelity(Gx, Gx_overrot, 'pp')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0016652782406580968"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rptbls.eigenvalue_avg_gate_infidelity(Gx, Gx_overrot, 'pp')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Diamond distance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.04997916855345197"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rptbls.half_diamond_norm(Gx, Gx_overrot, 'pp')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.07496875390601751"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rptbls.eigenvalue_diamondnorm(Gx, Gx_overrot, 'pp')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Unitarity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0000000000000002"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tls.unitarity(Gx_overrot)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Jamiolkowski trace distance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.04997916927067833"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rptbls.jt_diff(Gx, Gx_overrot, 'pp')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## State comparisons\n",
    "\n",
    "### State fidelity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rhoA = tls.ppvec_to_stdmx(mdl['rho0'].todense())\n",
    "rhoB = np.array( [ [0.9,   0],\n",
    "                   [ 0,  0.1]], complex)\n",
    "tls.fidelity(rhoA, rhoB)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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