From 4f27c79c2a7f13d77bd4b1aa41a09dff154bbc01 Mon Sep 17 00:00:00 2001 From: Elyes Ben Lassoued Date: Sat, 7 Nov 2026 15:57:53 -0500 Subject: [PATCH] [docs] Add two-spin Heisenberg model example notebook --- examples/heisenberg_two_spin_dynamics.ipynb | 651 ++++++++++++++++++++ 1 file changed, 651 insertions(+) create mode 100644 examples/heisenberg_two_spin_dynamics.ipynb diff --git a/examples/heisenberg_two_spin_dynamics.ipynb b/examples/heisenberg_two_spin_dynamics.ipynb new file mode 100644 index 0000000..b35fbf7 --- /dev/null +++ b/examples/heisenberg_two_spin_dynamics.ipynb @@ -0,0 +1,651 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "bc63e704", + "metadata": {}, + "source": [ + "# **Heisenberg Model: Two-Spin Dynamics**" + ] + }, + { + "cell_type": "markdown", + "id": "c041288d", + "metadata": {}, + "source": [ + "The Heisenberg Hamiltonian describes spins on a lattice whose neighbours are coupled equally along x, y and z. Depending on the sign of the coupling $J$, the interaction is ferromagnetic ($J > 0$, spins prefer to align) or antiferromagnetic ($J < 0$, spins prefer to anti-align). Trapped-ion quantum computers provide a natural platform to simulate this model, so let's first emulate it with OQD's analog tools, starting with two spins:\n", + "\n", + "$$H = -J \\, \\mathbf{S}_0 \\cdot \\mathbf{S}_1 = -\\frac{J\\hbar^2}{4}\\left( X_0 X_1 + Y_0 Y_1 + Z_0 Z_1 \\right), \\qquad \\mathbf{S}_i = \\frac{\\hbar}{2}\\boldsymbol{\\sigma}_i .$$\n", + "\n", + "From here on we set $\\hbar = 1$ and $J = 1$, so time is measured in units of $1/J$, and the Hamiltonian becomes\n", + "\n", + "$$H = -\\frac{1}{4}\\left( X_0 X_1 + Y_0 Y_1 + Z_0 Z_1 \\right).$$" + ] + }, + { + "cell_type": "markdown", + "id": "3ea20ad7", + "metadata": {}, + "source": [ + "## **Setup**" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "eaa64247", + "metadata": {}, + "outputs": [], + "source": [ + "# Importing dependencies\n", + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "from oqd_analog_emulator.qutip_backend import QutipBackend\n", + "from oqd_core.backend.metric import EntanglementEntropyVN, Expectation\n", + "from oqd_core.backend.task import Task, TaskArgsAnalog\n", + "from oqd_core.interface.analog.operation import AnalogCircuit, AnalogGate\n", + "from oqd_core.interface.analog.operator import PauliI, PauliX, PauliY, PauliZ" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "3b40ca54", + "metadata": {}, + "outputs": [], + "source": [ + "# Defining Pauli operators and the Heisenberg Hamiltonian\n", + "X, Y, Z, I = PauliX(), PauliY(), PauliZ(), PauliI() # noqa: E741\n", + "\n", + "# Heisenberg Hamiltonian with J = 1\n", + "J = 1.0\n", + "H = -J / 4 * (X @ X + Y @ Y + Z @ Z)" + ] + }, + { + "cell_type": "markdown", + "id": "510d678c", + "metadata": {}, + "source": [ + "## **Experiment 1: |↑↑⟩ is an eigenstate**" + ] + }, + { + "cell_type": "markdown", + "id": "2ccd568b", + "metadata": {}, + "source": [ + "For two aligned spins, the Hamiltonian only multiplies the state by its energy:\n", + "\n", + "$$H|\\uparrow\\uparrow\\rangle = -\\frac{J}{4}\\,|\\uparrow\\uparrow\\rangle,$$\n", + "\n", + "so $|\\uparrow\\uparrow\\rangle$ is an eigenstate of $H$. Time evolution then only adds a global phase, and all expectation values should stay constant. Let's test this!\n", + "\n", + "> **Note:** The emulator always starts in $|00\\rangle = |\\uparrow\\uparrow\\rangle$, so no state preparation is needed." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "5137883d", + "metadata": {}, + "outputs": [], + "source": [ + "# Start in |00⟩ = |↑↑⟩, evolve under H for t = 10, then measure in the Z basis\n", + "circuit = AnalogCircuit()\n", + "circuit.evolve(duration=10, gate=AnalogGate(hamiltonian=H))\n", + "circuit.measure()" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "a3212533", + "metadata": {}, + "outputs": [], + "source": [ + "# Expectation values to track: one metric per Pauli string\n", + "metrics = {\n", + " \"XX\": Expectation(operator=X @ X),\n", + " \"YY\": Expectation(operator=Y @ Y),\n", + " \"ZZ\": Expectation(operator=Z @ Z),\n", + " \"Z0\": Expectation(operator=Z @ I), # Z on qubit 0\n", + " \"Z1\": Expectation(operator=I @ Z), # Z on qubit 1\n", + "}" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "7d9b5e04", + "metadata": {}, + "outputs": [], + "source": [ + "# Bundle the circuit with the emulation settings, then run it\n", + "args = TaskArgsAnalog(\n", + " n_shots=1000, # number of measurement samples of the final state\n", + " metrics=metrics, # expectation values tracked during the evolution\n", + " dt=0.01, # time step at which metrics are recorded\n", + ")\n", + "task = Task(program=circuit, args=args)\n", + "results = QutipBackend().run(task=task)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "ea2c23bb", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Visualizing the results\n", + "\n", + "t = np.array(results.times)\n", + "\n", + "markers = [\"o\", \"s\", \"^\", \"v\", \"D\"]\n", + "for i, (name, values) in enumerate(results.metrics.items()):\n", + " plt.plot(\n", + " t,\n", + " values,\n", + " label=name,\n", + " marker=markers[i],\n", + " markevery=(i * 20, 100),\n", + " linestyle=\"none\",\n", + " )\n", + "\n", + "plt.xlabel(\"t (units of 1/J)\")\n", + "plt.ylabel(\"expectation value\")\n", + "plt.title(r\"$|\\uparrow\\uparrow\\rangle$: all expectation values stay constant\")\n", + "plt.legend()\n", + "plt.grid()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "d842823e", + "metadata": {}, + "source": [ + "As predicted, all expectation values stay constant. What about the energy and the total $Z$? Both are conserved for *any* initial state, so checking them is a good test that the emulation is consistent. We build both from the separate metrics:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "0c54fca5", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Total Z conserved? True\n", + "Energy conserved? True\n", + "Counts: {'00': 1000}\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Convert the metric results into NumPy arrays\n", + "XX = np.array(results.metrics[\"XX\"])\n", + "YY = np.array(results.metrics[\"YY\"])\n", + "ZZ = np.array(results.metrics[\"ZZ\"])\n", + "Z0 = np.array(results.metrics[\"Z0\"])\n", + "Z1 = np.array(results.metrics[\"Z1\"])\n", + "\n", + "# Build the energy and total Z from the separate metrics\n", + "E = -J / 4 * (XX + YY + ZZ)\n", + "total_Z = Z0 + Z1\n", + "\n", + "# Consistency checks: both should stay at their initial value\n", + "print(\"Total Z conserved?\", np.allclose(total_Z, total_Z[0]))\n", + "print(\"Energy conserved?\", np.allclose(E, E[0]))\n", + "\n", + "# |00⟩ is an eigenstate, so every shot should return 00\n", + "print(\"Counts:\", results.counts)\n", + "\n", + "plt.plot(t, E, label=\"Energy\")\n", + "plt.plot(t, total_Z, label=\"Total Z\")\n", + "plt.xlabel(\"t (units of 1/J)\")\n", + "plt.ylabel(\"expectation value\")\n", + "plt.grid()\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "8c70352a", + "metadata": {}, + "source": [ + "## **Experiment 2: Dynamics of the |↑↓⟩ state** " + ] + }, + { + "cell_type": "markdown", + "id": "73cb1f70", + "metadata": {}, + "source": [ + "\n", + "Unlike the $|\\uparrow\\uparrow\\rangle$ state, the $|\\uparrow\\downarrow\\rangle$ state is not an eigenstate of the Heisenberg Hamiltonian, and would show time-dependent expectation values $\\langle Z_0 \\rangle$ and $\\langle Z_1 \\rangle$.\n", + "\n", + "One can determine this by writing $|\\uparrow\\downarrow\\rangle$ in the triplet and singlet basis of the Hamiltonian, time evolving each of the terms and calculating the expectation values. Working this out, one would see that\n", + "\n", + "$$\\langle Z_0 \\rangle = \\cos(Jt), \\qquad \\langle Z_1 \\rangle = -\\cos(Jt).$$\n", + "\n", + "Let's see if this agrees with our emulation!\n", + "\n", + "**Preparing the state.** As we mentioned, our emulator always starts in the $|\\uparrow\\uparrow\\rangle$ state, so we first need to prepare the $|\\uparrow\\downarrow\\rangle$ state using analog pulses. In other words, we time evolve under different Hamiltonians for different times to get to the state that we want. For example, to get to $|\\uparrow\\downarrow\\rangle$ from $|\\uparrow\\uparrow\\rangle$, we time evolve under the $I \\otimes X$ operator for $t = \\pi/2$:\n", + "\n", + "$$e^{-i(I \\otimes X)\\pi/2}\\,|\\uparrow\\uparrow\\rangle = -i\\,|\\uparrow\\downarrow\\rangle .$$\n", + "\n", + "The factor $-i$ is a global phase, so it has no effect on any measurement.\n", + "\n", + "> **Note:** Here $t$ is measured from the start of the Heisenberg evolution. The emulator's `results.times` also includes the preparation step, so we shift the time axis by $\\pi/2$ before comparing." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "d0afc326", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Counts: {'01': 1000}\n", + "Prepared |↑↓⟩? True\n" + ] + } + ], + "source": [ + "# Check the preparation alone: flipping qubit 1 should give |↑↓⟩ = \"01\"\n", + "t_prep = np.pi / 2\n", + "\n", + "prep_circuit = AnalogCircuit()\n", + "prep_circuit.evolve(duration=t_prep, gate=AnalogGate(hamiltonian=I @ X))\n", + "prep_circuit.measure()\n", + "\n", + "prep_task = Task(program=prep_circuit, args=TaskArgsAnalog(n_shots=1000))\n", + "prep_results = QutipBackend().run(task=prep_task)\n", + "\n", + "print(\"Counts:\", prep_results.counts)\n", + "print(\"Prepared |↑↓⟩?\", prep_results.counts == {\"01\": 1000})" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "66479ad4", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Prepare |↑↓⟩ (flip qubit 1), then evolve under the Heisenberg Hamiltonian\n", + "t_prep = np.pi / 2\n", + "\n", + "circuit = AnalogCircuit()\n", + "circuit.evolve(duration=t_prep, gate=AnalogGate(hamiltonian=I @ X))\n", + "circuit.evolve(duration=10, gate=AnalogGate(hamiltonian=H))\n", + "circuit.measure()\n", + "\n", + "# One metric per Pauli string\n", + "metrics = {\n", + " \"XX\": Expectation(operator=X @ X),\n", + " \"YY\": Expectation(operator=Y @ Y),\n", + " \"ZZ\": Expectation(operator=Z @ Z),\n", + " \"Z0\": Expectation(operator=Z @ I), # Z on qubit 0\n", + " \"Z1\": Expectation(operator=I @ Z), # Z on qubit 1\n", + " \"EntropyVN0\": EntanglementEntropyVN(qreg=[0]), # von Neumann entropy of qubit 0\n", + "}\n", + "\n", + "# Emulation settings\n", + "args = TaskArgsAnalog(n_shots=1000, metrics=metrics, dt=0.01)\n", + "task = Task(program=circuit, args=args)\n", + "results = QutipBackend().run(task=task)\n", + "\n", + "# Keep only the Heisenberg part, and restart its clock at t = 0\n", + "t_all = np.array(results.times)\n", + "after_prep = t_all > t_prep\n", + "t = t_all[after_prep] - t_prep\n", + "\n", + "Z0 = np.array(results.metrics[\"Z0\"])[after_prep]\n", + "Z1 = np.array(results.metrics[\"Z1\"])[after_prep]\n", + "\n", + "plt.plot(t, Z0, label=r\"$\\langle Z_0 \\rangle$\")\n", + "plt.plot(t, Z1, label=r\"$\\langle Z_1 \\rangle$\")\n", + "plt.plot(t, np.cos(J * t), \"k--\", label=r\"$\\pm\\cos(Jt)$\")\n", + "plt.plot(t, -np.cos(J * t), \"k--\")\n", + "plt.xlabel(\"t (units of 1/J)\")\n", + "plt.ylabel(\"expectation value\")\n", + "plt.title(r\"$|\\uparrow\\downarrow\\rangle$: the spins swap back and forth\")\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "481c3e93", + "metadata": {}, + "source": [ + "To quantify entanglement, we can compute the von Neumann entropy of a qubit. For qubit 0, the von Neumann entropy is defined as\n", + "\n", + "$$S = -\\mathrm{Tr}\\left(\\rho_0 \\ln \\rho_0\\right), \\qquad \\rho_0 = \\mathrm{Tr}_1 |\\psi\\rangle\\langle\\psi| ,$$\n", + "\n", + "where $\\rho_0$ is the reduced density matrix of qubit 0. This tells us how entangled the state is: $S = 0$ for a product state and $S = \\ln 2$ for a maximally entangled one. For the $|\\uparrow\\downarrow\\rangle$ state, we would expect the state to start as not entangled, then slowly become more entangled, reaching maximal entanglement at $Jt = \\pi/2$, and disentangle again at $Jt = \\pi$, when the swap is complete. The theoretical formula is:\n", + "\n", + "$$S(t) = -p \\ln p - (1-p) \\ln(1-p), \\qquad p = \\cos^2(Jt/2).$$\n", + "\n", + "We already added the entanglement entropy metric to our experiment, so we just need to plot it now." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "ae18467a", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "S0 = np.array(results.metrics[\"EntropyVN0\"])[after_prep]\n", + "\n", + "# Theory: S(t) = -p ln p - (1 - p) ln(1 - p), with p = cos²(Jt/2)\n", + "p = np.clip(np.cos(J * t / 2) ** 2, 1e-12, 1 - 1e-12) # avoid ln(0)\n", + "S_theory = -p * np.log(p) - (1 - p) * np.log(1 - p)\n", + "\n", + "plt.plot(t, S0, label=\"emulation\")\n", + "plt.plot(t, S_theory, \"k--\", label=\"theory\")\n", + "plt.axhline(np.log(2), color=\"gray\", linestyle=\":\", label=r\"$\\ln 2$\")\n", + "plt.xlabel(\"t (units of 1/J)\")\n", + "plt.ylabel(\"entanglement entropy of qubit 0\")\n", + "plt.title(\"Entanglement peaks halfway through each swap\")\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "282ca627", + "metadata": {}, + "source": [ + "To conclude our experiment let's run our consistency checks making sure that the energy, as well as the total Z are conserved." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "ac8c5b5b", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Total Z conserved? True\n", + "Energy conserved? True\n", + "Counts: {'10': 916, '01': 84}\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Restrict our Expectation values after the state preparation as usual.\n", + "\n", + "XX = np.array(results.metrics[\"XX\"])[after_prep]\n", + "YY = np.array(results.metrics[\"YY\"])[after_prep]\n", + "ZZ = np.array(results.metrics[\"ZZ\"])[after_prep]\n", + "\n", + "E = -J / 4 * (XX + YY + ZZ)\n", + "total_Z = Z0 + Z1\n", + "\n", + "# Consistency checks: both should stay at their initial value\n", + "print(\"Total Z conserved?\", np.allclose(total_Z, total_Z[0]))\n", + "print(\"Energy conserved?\", np.allclose(E, E[0]))\n", + "\n", + "print(\"Counts:\", results.counts)\n", + "\n", + "plt.plot(t, E, label=\"Energy\")\n", + "plt.plot(t, total_Z, label=\"Total Z\")\n", + "plt.xlabel(\"t (units of 1/J)\")\n", + "plt.ylabel(\"expectation value\")\n", + "plt.grid()\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "ce01cf97", + "metadata": {}, + "source": [ + "## **Experiment 3: Preparing the Singlet and Triplet States**\n", + "\n", + "A strong capability of the analog emulator is that it lets us experiment with which sequence of analog pulses prepares a given state. On real quantum hardware, this matters because we can only apply the interactions and fields the device physically provides, each for a chosen duration, so preparing a target state means finding the right pulse sequence. Testing sequences on an emulator first saves valuable hardware time.\n", + "\n", + "We have already seen how to prepare $|\\uparrow\\downarrow\\rangle$ from $|\\uparrow\\uparrow\\rangle$. Now, starting again from $|\\uparrow\\uparrow\\rangle$, let's prepare the triplet state $T_0$ and the singlet state $S$, which are both eigenstates of the Heisenberg Hamiltonian:\n", + "\n", + "$$T_0 = \\frac{|\\uparrow\\downarrow\\rangle + |\\downarrow\\uparrow\\rangle}{\\sqrt{2}}, \\qquad S = \\frac{|\\uparrow\\downarrow\\rangle - |\\downarrow\\uparrow\\rangle}{\\sqrt{2}} .$$\n", + "\n", + "After preparing each one, we keep evolving under the Heisenberg Hamiltonian and check that they really are eigenstates: all expectation values should stay frozen. To tell them apart, we measure the spin correlation $\\langle \\mathbf{S}_0 \\cdot \\mathbf{S}_1 \\rangle$, which is $+1/4$ for $T_0$ and $-3/4$ for $S$.\n", + "\n", + "To prepare $T_0$ and $S$, we use a sequence of three pulses:\n", + "\n", + "1. **Flip qubit 1** with $I \\otimes X$ for $t = \\pi/2$: $|\\uparrow\\uparrow\\rangle \\to |\\uparrow\\downarrow\\rangle$.\n", + "2. **Evolve under the Heisenberg Hamiltonian** until $Jt = \\pi/2$. The swap is halfway done, giving an equal superposition $(|\\uparrow\\downarrow\\rangle + i|\\downarrow\\uparrow\\rangle)/\\sqrt{2}$, but with the wrong relative phase ($i$).\n", + "3. **Fix the phase with a $Z$ field on qubit 0** for a time $\\tau$. This multiplies the relative phase by $e^{2i\\tau}$ without changing the amplitudes, so the phase becomes $i\\,e^{2i\\tau} = e^{i(\\pi/2 + 2\\tau)}$:\n", + " - $\\tau = \\pi/4$ gives phase $-1$, the singlet $S$;\n", + " - $\\tau = 3\\pi/4$ gives phase $+1$, the triplet $T_0$.\n", + "\n", + "Finally, we keep evolving under the Heisenberg Hamiltonian. Since both states are eigenstates, everything should stay frozen: $\\langle Z_0 \\rangle = \\langle Z_1 \\rangle = 0$, the entanglement entropy stays at $\\ln 2$, and $\\langle \\mathbf{S}_0 \\cdot \\mathbf{S}_1 \\rangle = -3/4$ for $S$ and $+1/4$ for $T_0$.\n", + "\n", + "Let's implement this!" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "7d4a98b8", + "metadata": {}, + "outputs": [], + "source": [ + "def singlet_triplet_circuit(tau, t_freeze=10):\n", + " \"\"\"Prepare the singlet (tau = π/4) or the triplet T0 (tau = 3π/4),\n", + " then evolve under the Heisenberg Hamiltonian to check it stays frozen.\n", + "\n", + " Returns the circuit and the total preparation time.\n", + " \"\"\"\n", + " t_flip = np.pi / 2 # I⊗X: |↑↑⟩ → |↑↓⟩\n", + " t_half_swap = np.pi / (2 * J) # Heisenberg until Jt = π/2\n", + "\n", + " circuit = AnalogCircuit()\n", + " circuit.evolve(duration=t_flip, gate=AnalogGate(hamiltonian=I @ X))\n", + " circuit.evolve(duration=t_half_swap, gate=AnalogGate(hamiltonian=H))\n", + " circuit.evolve(duration=tau, gate=AnalogGate(hamiltonian=Z @ I))\n", + " circuit.evolve(\n", + " duration=t_freeze, gate=AnalogGate(hamiltonian=H)\n", + " ) # should stay constant\n", + " circuit.measure()\n", + "\n", + " t_prep = t_flip + t_half_swap + tau\n", + " return circuit, t_prep\n", + "\n", + "\n", + "# Create the triplet and the singlet circuits\n", + "singlet_circuit, t_prep_S = singlet_triplet_circuit(tau=np.pi / 4)\n", + "triplet_circuit, t_prep_T = singlet_triplet_circuit(tau=3 * np.pi / 4)" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "6016936e", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Singlet state checks:\n", + " = -0.7499999999989727 (expected -0.75)\n", + " = -1.2648354450472965e-06 and = 1.2648366797263222e-06 (expected 0)\n", + "Entropy = 0.6931471805585281 (expected ln 2 = 0.6931471805599453 )\n", + "S0.S1 frozen? True\n", + "Counts: {'10': 468, '01': 532}\n" + ] + } + ], + "source": [ + "# Singlet state checks\n", + "\n", + "args = TaskArgsAnalog(n_shots=1000, metrics=metrics, dt=0.01)\n", + "results = QutipBackend().run(task=Task(program=singlet_circuit, args=args))\n", + "\n", + "t_all = np.array(results.times)\n", + "after_prep = t_all > t_prep_S\n", + "t = t_all[after_prep] - t_prep_S\n", + "\n", + "Z0 = np.array(results.metrics[\"Z0\"])[after_prep]\n", + "Z1 = np.array(results.metrics[\"Z1\"])[after_prep]\n", + "XX = np.array(results.metrics[\"XX\"])[after_prep]\n", + "YY = np.array(results.metrics[\"YY\"])[after_prep]\n", + "ZZ = np.array(results.metrics[\"ZZ\"])[after_prep]\n", + "S0 = np.array(results.metrics[\"EntropyVN0\"])[after_prep]\n", + "\n", + "S0S1 = (XX + YY + ZZ) / 4\n", + "\n", + "print(\"Singlet state checks:\")\n", + "print(\" =\", S0S1[0], \"(expected -0.75)\")\n", + "print(\" =\", Z0[0], \"and =\", Z1[0], \"(expected 0)\")\n", + "print(\"Entropy =\", S0[0], \"(expected ln 2 =\", np.log(2), \")\")\n", + "print(\"S0.S1 frozen?\", np.allclose(S0S1, S0S1[0]))\n", + "print(\"Counts:\", results.counts)" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "fa4be16f", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Triplet T0 state checks:\n", + " = 0.24999999999398945 (expected +0.25)\n", + " = -1.3101327853703992e-06 and = 1.310134020049425e-06 (expected 0)\n", + "Entropy = 0.6931471805584698 (expected ln 2 = 0.6931471805599453 )\n", + "S0.S1 frozen? True\n", + "Counts: {'01': 494, '10': 506}\n" + ] + } + ], + "source": [ + "# Triplet State checks:\n", + "\n", + "args = TaskArgsAnalog(n_shots=1000, metrics=metrics, dt=0.01)\n", + "results = QutipBackend().run(task=Task(program=triplet_circuit, args=args))\n", + "\n", + "t_all = np.array(results.times)\n", + "after_prep = t_all > t_prep_T\n", + "t = t_all[after_prep] - t_prep_T\n", + "\n", + "Z0 = np.array(results.metrics[\"Z0\"])[after_prep]\n", + "Z1 = np.array(results.metrics[\"Z1\"])[after_prep]\n", + "XX = np.array(results.metrics[\"XX\"])[after_prep]\n", + "YY = np.array(results.metrics[\"YY\"])[after_prep]\n", + "ZZ = np.array(results.metrics[\"ZZ\"])[after_prep]\n", + "S0 = np.array(results.metrics[\"EntropyVN0\"])[after_prep]\n", + "\n", + "S0S1 = (XX + YY + ZZ) / 4\n", + "\n", + "print(\"Triplet T0 state checks:\")\n", + "print(\" =\", S0S1[0], \"(expected +0.25)\")\n", + "print(\" =\", Z0[0], \"and =\", Z1[0], \"(expected 0)\")\n", + "print(\"Entropy =\", S0[0], \"(expected ln 2 =\", np.log(2), \")\")\n", + "print(\"S0.S1 frozen?\", np.allclose(S0S1, S0S1[0]))\n", + "print(\"Counts:\", results.counts)" + ] + }, + { + "cell_type": "markdown", + "id": "8badb27f", + "metadata": {}, + "source": [ + "All of our checks have passed: we successfully prepared the triplet and singlet states. It's interesting to note that their counts are roughly equal, showing that we can't tell these states apart with $Z$ measurements, because a $Z$ measurement is blind to the relative phase. We can, however, see the difference by measuring spin correlations: $\\langle \\mathbf{S}_0 \\cdot \\mathbf{S}_1 \\rangle = -3/4$ for the singlet and $+1/4$ for the triplet, since it includes the $XX$ and $YY$ terms, which are sensitive to the phase." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "oqd", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.12.14" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +}