Tomography notebook

examples/superoperator_tools.ipynb

@@ -601,6 +601,67 @@
     "print(choi_is_cptp(AD_choi))"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Project an unphysical state to the closest physical state"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from forest.benchmarking.operator_tools.project_state_matrix import project_state_matrix_to_physical"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "True"
+      ]
+     },
+     "execution_count": 6,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# Test the method. Example from fig 1 of maximum likelihood minimum effort \n",
+    "# https://doi.org/10.1103/PhysRevLett.108.070502\n",
+    "\n",
+    "eigs = np.diag(np.array(list(reversed([3.0/5, 1.0/2, 7.0/20, 1.0/10, -11.0/20]))))\n",
+    "phys = project_state_matrix_to_physical(eigs)\n",
+    "np.allclose(phys, np.diag([0, 0, 1.0/5, 7.0/20, 9.0/20]))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from forest.benchmarking.plotting import hinton\n",
+    "\n",
+    "rho_unphys = np.random.uniform(-1, 1, (2, 2)) \\\n",
+    "    * np.exp(1.j * np.random.uniform(-np.pi, np.pi, (2, 2)))\n",
+    "rho_phys = project_state_matrix_to_physical(rho_unphys)\n",
+    "\n",
+    "fig, (ax1, ax2) = plt.subplots(1, 2)\n",
+    "hinton(rho_unphys, ax=ax1)\n",
+    "hinton(rho_phys, ax=ax2)\n",
+    "ax1.set_title('Unphysical')\n",
+    "ax2.set_title('Physical projection')\n",
+    "fig.tight_layout()"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},