{
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{
"cell_type": "code",
"execution_count": 1,
"id": "65235269",
"metadata": {
"execution": {
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"outputs": [],
"source": [
"# Copyright 2024 Keysight Technologies Inc."
]
},
{
"cell_type": "raw",
"id": "48a1fa4d",
"metadata": {
"raw_mimetype": "text/restructuredtext"
},
"source": [
"Example: Running Randomized Compiling\n",
"=====================================\n",
"\n",
"This example provides a short demonstration of |True-Q|'s\n",
":py:meth:`~trueq.randomly_compile` function and how it can be used to generate a set\n",
"of randomly compiled circuits from a single input circuit, while implementing the same\n",
"unitary as the original circuit. For more background information, check out our\n",
"Randomized Compiling (:tqdoc:`RC`\\) user guide page.\n",
"\n",
".. note::\n",
" Randomized compiling produces a new circuit collection after each call, so the\n",
" output of this example will be different if it's executed again.\n",
"\n",
"Generating randomly compiled circuits\n",
"-------------------------------------\n",
"\n",
"We begin by creating a simple two-qubit circuit with alternating cycles:"
]
},
{
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"id": "1cd8b4f2",
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"outputs": [
{
"data": {
"text/html": [
" 0 1 Key: Labels: (0,) Name: Gate.h Aliases: Gate.h Gate.f Gate.cliff12 Generators: Z: 127.28 X: 127.28 0.71 0.71 0.71 -0.71 H Labels: (0, 1) Name: Gate.cz Aliases: Gate.cz Locally Equivalent: CNOT Generators: ZZ: -90.00 ZI: 90.00 IZ: 90.00 1.00 1.00 1.00 -1.00 CZ CZ Labels: (1,) Name: Gate.h Aliases: Gate.h Gate.f Gate.cliff12 Generators: Z: 127.28 X: 127.28 0.71 0.71 0.71 -0.71 H Labels: (0,) Name: Gate.h Aliases: Gate.h Gate.f Gate.cliff12 Generators: Z: 127.28 X: 127.28 0.71 0.71 0.71 -0.71 H Labels: (0, 1) Name: Gate.cz Aliases: Gate.cz Locally Equivalent: CNOT Generators: ZZ: -90.00 ZI: 90.00 IZ: 90.00 1.00 1.00 1.00 -1.00 CZ CZ Labels: (1,) Name: Gate.h Aliases: Gate.h Gate.f Gate.cliff12 Generators: Z: 127.28 X: 127.28 0.71 0.71 0.71 -0.71 H Labels: (0,) Name: Gate.h Aliases: Gate.h Gate.f Gate.cliff12 Generators: Z: 127.28 X: 127.28 0.71 0.71 0.71 -0.71 H Labels: (0, 1) Name: Gate.cz Aliases: Gate.cz Locally Equivalent: CNOT Generators: ZZ: -90.00 ZI: 90.00 IZ: 90.00 1.00 1.00 1.00 -1.00 CZ CZ Labels: (1,) Name: Gate.h Aliases: Gate.h Gate.f Gate.cliff12 Generators: Z: 127.28 X: 127.28 0.71 0.71 0.71 -0.71 H 1 Labels: (0,) Name: Meas M Labels: (1,) Name: Meas M "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"sim = tq.Simulator()\n",
"ideal_result = sim.sample(circuit, n_shots=np.inf)\n",
"ideal_result.plot()"
]
},
{
"cell_type": "raw",
"id": "63866523",
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"raw_mimetype": "text/restructuredtext"
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"source": [
"We can also inspect the operator that this circuit is implementing:"
]
},
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{
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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"circuit_operator = sim.operator(circuit).mat()\n",
"tq.math.Superop(circuit_operator).plot_rowstack()"
]
},
{
"cell_type": "raw",
"id": "64d29c49",
"metadata": {
"raw_mimetype": "text/restructuredtext"
},
"source": [
"To generate a set of randomly compiled versions of this circuit, we call the\n",
":py:meth:`~trueq.randomly_compile` function and pass our circuit as argument,\n",
"together with the desired number of compilations:"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "29f2ec2f",
"metadata": {
"execution": {
"iopub.execute_input": "2024-04-26T18:19:46.354159Z",
"iopub.status.busy": "2024-04-26T18:19:46.353832Z",
"iopub.status.idle": "2024-04-26T18:19:46.361373Z",
"shell.execute_reply": "2024-04-26T18:19:46.360980Z"
}
},
"outputs": [],
"source": [
"n_compilations = 30\n",
"rc_circuits = tq.randomly_compile(circuit, n_compilations=n_compilations)"
]
},
{
"cell_type": "raw",
"id": "2269031b",
"metadata": {
"raw_mimetype": "text/restructuredtext"
},
"source": [
"This function returns a :py:class:`~trueq.CircuitCollection` of 30 randomized versions\n",
"of our original circuit. For example, the first circuit in this collection looks like\n",
"this:"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "6080b943",
"metadata": {
"execution": {
"iopub.execute_input": "2024-04-26T18:19:46.363511Z",
"iopub.status.busy": "2024-04-26T18:19:46.363198Z",
"iopub.status.idle": "2024-04-26T18:19:46.375756Z",
"shell.execute_reply": "2024-04-26T18:19:46.375397Z"
}
},
"outputs": [
{
"data": {
"text/html": [
" 0 1 Key: twirl: Paulis on [0, 1] protocol: RC Labels: (0,) Name: Gate.cliff13 Aliases: Gate.cliff13 Generators: Z: 127.28 X: -127.28 0.71 -0.71 -0.71 -0.71 13 Labels: (1,) Name: Gate.z Aliases: Gate.z Gate.cliff3 Generators: Z: 180.00 1.00 -1.00 Z 2 Labels: (0, 1) Name: Gate.cz Aliases: Gate.cz Locally Equivalent: CNOT Generators: ZZ: -90.00 ZI: 90.00 IZ: 90.00 1.00 1.00 1.00 -1.00 CZ CZ Labels: (0,) Name: Gate.sy Aliases: Gate.sy Gate.cliff7 Generators: Y: 90.00 0.71 -0.71 0.71 0.71 SY Labels: (1,) Name: Gate.cliff6 Aliases: Gate.cliff6 Generators: Y: -90.00 0.71 0.71 -0.71 0.71 6 3 Labels: (0, 1) Name: Gate.cz Aliases: Gate.cz Locally Equivalent: CNOT Generators: ZZ: -90.00 ZI: 90.00 IZ: 90.00 1.00 1.00 1.00 -1.00 CZ CZ Labels: (0,) Name: Gate.cliff13 Aliases: Gate.cliff13 Generators: Z: 127.28 X: -127.28 0.71 -0.71 -0.71 -0.71 13 Labels: (1,) Name: Gate.cliff13 Aliases: Gate.cliff13 Generators: Z: 127.28 X: -127.28 0.71 -0.71 -0.71 -0.71 13 4 Labels: (0, 1) Name: Gate.cz Aliases: Gate.cz Locally Equivalent: CNOT Generators: ZZ: -90.00 ZI: 90.00 IZ: 90.00 1.00 1.00 1.00 -1.00 CZ CZ Labels: (0,) Name: Gate.z Aliases: Gate.z Gate.cliff3 Generators: Z: 180.00 1.00 -1.00 Z Labels: (1,) Name: Gate.sy Aliases: Gate.sy Gate.cliff7 Generators: Y: 90.00 0.71 -0.71 0.71 0.71 SY 1 Labels: (0,) Name: Meas M Labels: (1,) Name: Meas M "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"rc_circuit_operator = sim.operator(rc_circuits[0]).mat()\n",
"tq.math.Superop(rc_circuit_operator).plot_rowstack()"
]
},
{
"cell_type": "raw",
"id": "ca8eefdd",
"metadata": {
"raw_mimetype": "text/restructuredtext"
},
"source": [
"For a phase-insensitive comparison, we can calculate the process infidelity between\n",
"these two operators. The process infidelity is a metric for how different two\n",
"operations are; an infidelity of zero means they are equivalent up to a phase. We can\n",
"use the built-in :py:meth:`~trueq.math.general.proc_infidelity` function for this:"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "a5e24ddd",
"metadata": {
"execution": {
"iopub.execute_input": "2024-04-26T18:19:46.476149Z",
"iopub.status.busy": "2024-04-26T18:19:46.475713Z",
"iopub.status.idle": "2024-04-26T18:19:46.478896Z",
"shell.execute_reply": "2024-04-26T18:19:46.478535Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
"-8.881784197001252e-16"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"tq.math.proc_infidelity(circuit_operator, rc_circuit_operator)"
]
},
{
"cell_type": "raw",
"id": "b1f4dcad",
"metadata": {
"raw_mimetype": "text/restructuredtext"
},
"source": [
"Finally, when we sample from the final state's probability distribution every\n",
"circuit yields the same result:"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "a084782b",
"metadata": {
"execution": {
"iopub.execute_input": "2024-04-26T18:19:46.480740Z",
"iopub.status.busy": "2024-04-26T18:19:46.480464Z",
"iopub.status.idle": "2024-04-26T18:19:46.501062Z",
"shell.execute_reply": "2024-04-26T18:19:46.500685Z"
}
},
"outputs": [],
"source": [
"for rc_circuit in rc_circuits:\n",
" assert tq.utils.dicts_close(sim.sample(rc_circuit, n_shots=np.inf), ideal_result)"
]
},
{
"cell_type": "raw",
"id": "f7f25a51",
"metadata": {
"raw_mimetype": "text/restructuredtext"
},
"source": [
"Measuring RC performance\n",
"------------------------\n",
"\n",
"To test how well Randomized Compiling works in practice, let's walk through a short\n",
"simulation of the circuit above with a noisy simulator and look at how the RC circuits\n",
"perform relative to the bare circuit.\n",
"\n",
"First, we create a simulator with an overrotation error as the noise source and\n",
"simulate the outcomes of the bare circuit under this noise model:"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "3d0f933c",
"metadata": {
"execution": {
"iopub.execute_input": "2024-04-26T18:19:46.502829Z",
"iopub.status.busy": "2024-04-26T18:19:46.502557Z",
"iopub.status.idle": "2024-04-26T18:19:46.599930Z",
"shell.execute_reply": "2024-04-26T18:19:46.599522Z"
}
},
"outputs": [
{
"data": {
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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"noisy_sim = tq.Simulator().add_overrotation(single_sys=0.1, multi_sys=0.1)\n",
"noisy_result = noisy_sim.sample(circuit, n_shots=np.inf)\n",
"noisy_result.plot()"
]
},
{
"cell_type": "raw",
"id": "cc046852",
"metadata": {
"raw_mimetype": "text/restructuredtext"
},
"source": [
"Note that we are no longer seeing the equal superposition that the noise-free\n",
"simulation produced.\n",
"\n",
"Next, we simulate the randomly compiled circuits under the same noise model, and\n",
"sum the outcomes over all circuits:"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "2ca9179e",
"metadata": {
"execution": {
"iopub.execute_input": "2024-04-26T18:19:46.601931Z",
"iopub.status.busy": "2024-04-26T18:19:46.601529Z",
"iopub.status.idle": "2024-04-26T18:19:46.711901Z",
"shell.execute_reply": "2024-04-26T18:19:46.711497Z"
}
},
"outputs": [
{
"data": {
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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# run all circuits on the simulator\n",
"noisy_sim.run(rc_circuits, n_shots=np.inf)\n",
"\n",
"# sum over the outcomes\n",
"rc_result = rc_circuits.sum_results()\n",
"\n",
"# for plotting, we normalize the summed results to be between 0 and 1\n",
"rc_result.normalized().plot()"
]
},
{
"cell_type": "raw",
"id": "834ee247",
"metadata": {
"raw_mimetype": "text/restructuredtext"
},
"source": [
"Under Randomized Compiling, the noisy simulation produces a result that is much\n",
"closer to the noise-free simulation. In fact, we can use the\n",
":py:meth:`trueq.Results.tvd` method of the :py:class:`~trueq.Results` class to\n",
"quantify this difference:"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "aad50130",
"metadata": {
"execution": {
"iopub.execute_input": "2024-04-26T18:19:46.714032Z",
"iopub.status.busy": "2024-04-26T18:19:46.713606Z",
"iopub.status.idle": "2024-04-26T18:19:46.718076Z",
"shell.execute_reply": "2024-04-26T18:19:46.717723Z"
},
"lines_to_next_cell": 2
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Noisy simulation without RC: 0.1686\n",
"Noisy simulation with RC: inf\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"Warning: divide by zero encountered in divide\n",
" (/home/jenkins/workspace/release trueq/trueq/results.py:489)\n"
]
}
],
"source": [
"bare_tvd = noisy_result.tvd(ideal_result)\n",
"rc_tvd = rc_result.normalized().tvd(ideal_result)\n",
"\n",
"print(\"Noisy simulation without RC: {:.4f}\".format(bare_tvd[0]))\n",
"print(\"Noisy simulation with RC: {:.4f}\".format(rc_tvd[0]))"
]
},
{
"cell_type": "raw",
"id": "6c1a4661",
"metadata": {
"raw_mimetype": "text/restructuredtext"
},
"source": [
"The TVD, or Total Variation Distance is a measure for how far two probability\n",
"distributions are apart. A value of zero means the distributions are equivalent.\n",
"\n",
"Finally, we can produce a visual summary of these results:"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "780f3731",
"metadata": {
"execution": {
"iopub.execute_input": "2024-04-26T18:19:46.720086Z",
"iopub.status.busy": "2024-04-26T18:19:46.719709Z",
"iopub.status.idle": "2024-04-26T18:19:46.858170Z",
"shell.execute_reply": "2024-04-26T18:19:46.857688Z"
},
"lines_to_next_cell": 0
},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"tq.visualization.plot_results(\n",
" ideal_result,\n",
" noisy_result,\n",
" rc_result,\n",
" labels=[\"Ideal Outcome\", \"Without RC\", \"With RC\"],\n",
")"
]
},
{
"cell_type": "raw",
"id": "593f4f54",
"metadata": {
"raw_mimetype": "text/restructuredtext"
},
"source": [
"Randomized Compiling with Qudits\n",
"--------------------------------\n",
"\n",
"Randomized compiling works for higher-dimensional qudits in the same way as for\n",
"qubits. The random gates which are added around hard cycles are drawn uniformly\n",
"from the :math:`d`\\-dimensional Weyl-Heisenberg group, and the original circuit must\n",
"be expressed in terms of gates belonging to the :math:`d`\\-dimensional Clifford group,\n",
"that is the group which preserves the :math:`d`\\-dimensional Weyl-Heisenberg group\n",
"(see :doc:`../../guides/fundamentals/qudit_math` for more information).\n",
"\n",
"Let's start by defining a simple circuit following the qubit example above but for\n",
"qutrits:"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "31baa808",
"metadata": {
"execution": {
"iopub.execute_input": "2024-04-26T18:19:46.860373Z",
"iopub.status.busy": "2024-04-26T18:19:46.860063Z",
"iopub.status.idle": "2024-04-26T18:19:46.887630Z",
"shell.execute_reply": "2024-04-26T18:19:46.887182Z"
}
},
"outputs": [
{
"data": {
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],
"text/plain": [
"DisplayWrapper("
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"tq.visualization.plot_results(\n",
" ideal_result,\n",
" noisy_result,\n",
" rc_result,\n",
" labels=[\"Ideal Outcome\", \"Without RC\", \"With RC\"],\n",
")"
]
}
],
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