Add a more general tutorial showing how to handle Clifford gates

docs/tutorials/simulate_kicked_ising.ipynb → docs/tutorials/02_simulate_127Q_kicked_ising.ipynb

@@ -5,15 +5,15 @@
    "id": "df27beb5-e42d-4fa8-a47b-cbd4b7fd61a4",
    "metadata": {},
    "source": [
-    "### Simulating quantum systems with Pauli propagation\n",
+    "### Simulating 127-qubit kicked-Ising model\n",
     "\n",
     "In this tutorial we will use the ``pauli-prop`` package to classically simulate the time dynamics of a 127-qubit kicked Ising model on a heavy-hex lattice and approximate the single-site magnetization, $\\langle Z_{62} \\rangle$. The Hamiltonian considered is:\n",
     "\n",
     "$H = -J\\sum\\limits_{\\langle i,j \\rangle} Z_iZ_j + h\\sum\\limits_iX_i$\n",
     "\n",
     "where $J>0$ describes the coupling of nearest-neighbor spins, $i<j$, and $h$ is the global transverse field. A first-order Trotter decomposition of the time-evolved operator will be implemented as a quantum circuit, $U$, over $20$ Trotter steps. The coupling constant, $J$, will be fixed at $J=-\\frac{\\pi}{2}$ such that $U$ is Clifford any time $h\\mod\\frac{\\pi}{2}=0$.\n",
     "\n",
-    "In this tutorial, we will:\n",
+    "Workflow:\n",
     "\n",
     "- Create quantum circuits implementing the Trotterized Ising model\n",
     "    - Vary $h$ between Clifford points, $0.0$ and $\\frac{\\pi}{2}$.\n",
@@ -107,7 +107,7 @@
     "approx_evs = []\n",
     "for circuit in circuits:\n",
     "    st = time.time()\n",
-    "    propagated_obs, _ = propagate_through_circuit(observable, circuit, 100_000, 1e-5, frame=\"h\")\n",
+    "    propagated_obs = propagate_through_circuit(observable, circuit, 100_000, 1e-5, frame=\"h\")[0]\n",
     "    times.append(time.time() - st)\n",
     "    approx_evs.append(float(propagated_obs.coeffs[~propagated_obs.paulis.x.any(axis=1)].sum()))\n",
     "print(f\"Finshed {len(circuits)} simulations in {sum(times):.0f}s\")"