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Add a solve_qubit function (#3)
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* Add a qubit solver and tutorial

Co-authored-by: Javier Robledo Moreno <j.robledomoreno@ibm.com>
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@caleb-johnson @jrm874
caleb-johnson and jrm874 authored Sep 10, 2024
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2 changes: 1 addition & 1 deletion README.md
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Expand Up @@ -47,7 +47,7 @@ For more installation information refer to these [installation instructions](doc

### Computational requirements

The computational cost of SQD is dominated by the eigenstate solver calls. At each step of the self-consistent configuration recovery iteration, `n_batches` of eigenstate solver calls are performed. The different calls are embarrassingly parallel. In this [tutorial](docs/tutorials/01_getting_started_fermionic.ipynb), those calls are inside a `for` loop. **It is highly recommended to perform these calls in parallel**.
The computational cost of SQD is dominated by the eigenstate solver calls. At each step of the self-consistent configuration recovery iteration, `n_batches` of eigenstate solver calls are performed. The different calls are embarrassingly parallel. In this [tutorial](docs/tutorials/01_chemistry_hamiltonian.ipynb), those calls are inside a `for` loop. **It is highly recommended to perform these calls in parallel**.

The [`qiskit_addon_sqd.fermion.solve_fermion()`](qiskit_addon_sqd/fermion.py) function is multithreaded and capable of handling systems with ~25 spacial orbitals and ~10 electrons with subspace dimensions of ~$10^7$, using ~10-30 cores.

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110 changes: 57 additions & 53 deletions docs/how_tos/benchmark_pauli_projection.ipynb
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255 changes: 196 additions & 59 deletions docs/how_tos/project_pauli_operators_onto_hilbert_subspaces.ipynb
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]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "74c16c91-cc5c-46ce-aff8-17d0e71ac50f",
"cell_type": "markdown",
"id": "c961d48a",
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"from qiskit_addon_sqd.qubit import matrix_elements_from_pauli_string, sort_and_remove_duplicates\n",
"\n",
"L = 22\n",
"\n",
"# Write all of the Pauli strings for the Heisenberg model\n",
"paulis = []\n",
"for i in range(L):\n",
" pstr = [\"I\" for i in range(L)]\n",
" # Sigma_x\n",
" pstr[i] = \"X\"\n",
" pstr[(i + 1) % L] = \"X\"\n",
" paulis.append(pstr)\n",
"\n",
" pstr = [\"I\" for i in range(L)]\n",
" # Sigma_y\n",
" pstr[i] = \"Y\"\n",
" pstr[(i + 1) % L] = \"Y\"\n",
" paulis.append(pstr)\n",
"\n",
" pstr = [\"I\" for i in range(L)]\n",
" # Sigma_z\n",
" pstr[i] = \"Z\"\n",
" pstr[(i + 1) % L] = \"Z\"\n",
" paulis.append(pstr)"
"We show different ways of projecting a weighted linear combination of pauli strings\n",
"into a subspace defined by a subset of size $d$ computational basis states. The \n",
"projected operator is stored as a $d \\times d$ ``scipy.sparse.coo_matrix``.\n",
"\n",
"As an example we consider the Hamiltonian of the 1D Heisenberg model with periodic\n",
"boundary conditions and $L = 22$ spins:\n",
"$$\n",
"H = \\sum_{\\langle i, j \\rangle}\\left( \\sigma^x_i\\sigma^x_j + \\sigma^y_i\\sigma^y_j + \\sigma^z_i\\sigma^z_j \\right).\n",
"$$\n",
"\n",
"This package provides two tools to perform this projection:\n",
"\n",
"- ``qiskit_addon_sqd.qubit.matrix_elements_from_pauli()``: is a lower-level function\n",
"that returns the non-zero matrix elements of a Pauli string and the corresponding addresses\n",
"of the non-zero elements.\n",
"\n",
"- ``qiskit_addon_sqd.qubit.project_operator_to_subspace()``: is a higher-level function that \n",
"directly returns a ``scipy.sparse`` matrix.\n",
"\n",
"This notebook shows how to use these two tools to produce the same sparse operator."
]
},
{
"cell_type": "markdown",
"id": "0540e60f",
"id": "6c87d5e5",
"metadata": {},
"source": [
"Let's make some random bitstrings"
"### Subspace definition\n",
"\n",
"For this example we just generate length-22 random bitstrings. For the projection\n",
"functions to work as expected, it is essential that the bitstrings that define\n",
"the subspace are unique and sorted according to their base-10 representation.\n",
"\n",
"This can be achieved with the ``qiskit_addon_sqd.qubit.sort_and_remove_duplicates()``\n",
"function."
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "56350454",
"execution_count": 1,
"id": "7b94f840",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Subspace dimension: 4194276\n",
"Subspace dimension: 49718\n",
"Full Hilbert space dimension: 4194304\n"
]
}
],
"source": [
"import numpy as np\n",
"from qiskit_addon_sqd.qubit import sort_and_remove_duplicates\n",
"\n",
"num_spins = 22\n",
"rand_seed = 22\n",
"np.random.seed(rand_seed)\n",
"\n",
Expand All @@ -74,62 +78,195 @@
" return np.round(np.random.rand(n_samples, n_qubits)).astype(\"int\").astype(\"bool\")\n",
"\n",
"\n",
"bts_matrix = random_bitstrings(50_000_000, L)\n",
"bitstring_matrix = random_bitstrings(50_000, num_spins)\n",
"\n",
"# NOTE: It is essential for the projection code to have the bitstrings sorted!\n",
"bts_matrix = sort_and_remove_duplicates(bts_matrix)\n",
"bitstring_matrix = sort_and_remove_duplicates(bitstring_matrix)\n",
"\n",
"print(\"Subspace dimension: \" + str(bts_matrix.shape[0]))\n",
"print(\"Full Hilbert space dimension: \" + str(2**L))"
"print(\"Subspace dimension: \" + str(bitstring_matrix.shape[0]))\n",
"print(\"Full Hilbert space dimension: \" + str(2**num_spins))"
]
},
{
"cell_type": "markdown",
"id": "5707b93c",
"metadata": {},
"source": [
"### First method: nonzero matrix elements and addresses."
]
},
{
"cell_type": "code",
"execution_count": 4,
"execution_count": 2,
"id": "74c16c91-cc5c-46ce-aff8-17d0e71ac50f",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"SparsePauliOp(['IIIIIIIIIIIIIIIIIIIIXX', 'IIIIIIIIIIIIIIIIIIIIYY', 'IIIIIIIIIIIIIIIIIIIIZZ', 'IIIIIIIIIIIIIIIIIIXXII', 'IIIIIIIIIIIIIIIIIIYYII', 'IIIIIIIIIIIIIIIIIIZZII', 'IIIIIIIIIIIIIIIIXXIIII', 'IIIIIIIIIIIIIIIIYYIIII', 'IIIIIIIIIIIIIIIIZZIIII', 'IIIIIIIIIIIIIIXXIIIIII', 'IIIIIIIIIIIIIIYYIIIIII', 'IIIIIIIIIIIIIIZZIIIIII', 'IIIIIIIIIIIIXXIIIIIIII', 'IIIIIIIIIIIIYYIIIIIIII', 'IIIIIIIIIIIIZZIIIIIIII', 'IIIIIIIIIIXXIIIIIIIIII', 'IIIIIIIIIIYYIIIIIIIIII', 'IIIIIIIIIIZZIIIIIIIIII', 'IIIIIIIIXXIIIIIIIIIIII', 'IIIIIIIIYYIIIIIIIIIIII', 'IIIIIIIIZZIIIIIIIIIIII', 'IIIIIIXXIIIIIIIIIIIIII', 'IIIIIIYYIIIIIIIIIIIIII', 'IIIIIIZZIIIIIIIIIIIIII', 'IIIIXXIIIIIIIIIIIIIIII', 'IIIIYYIIIIIIIIIIIIIIII', 'IIIIZZIIIIIIIIIIIIIIII', 'IIXXIIIIIIIIIIIIIIIIII', 'IIYYIIIIIIIIIIIIIIIIII', 'IIZZIIIIIIIIIIIIIIIIII', 'XXIIIIIIIIIIIIIIIIIIII', 'YYIIIIIIIIIIIIIIIIIIII', 'ZZIIIIIIIIIIIIIIIIIIII', 'XIIIIIIIIIIIIIIIIIIIIX', 'YIIIIIIIIIIIIIIIIIIIIY', 'ZIIIIIIIIIIIIIIIIIIIIZ', 'IIIIIIIIIIIIIIIIIIIXXI', 'IIIIIIIIIIIIIIIIIIIYYI', 'IIIIIIIIIIIIIIIIIIIZZI', 'IIIIIIIIIIIIIIIIIXXIII', 'IIIIIIIIIIIIIIIIIYYIII', 'IIIIIIIIIIIIIIIIIZZIII', 'IIIIIIIIIIIIIIIXXIIIII', 'IIIIIIIIIIIIIIIYYIIIII', 'IIIIIIIIIIIIIIIZZIIIII', 'IIIIIIIIIIIIIXXIIIIIII', 'IIIIIIIIIIIIIYYIIIIIII', 'IIIIIIIIIIIIIZZIIIIIII', 'IIIIIIIIIIIXXIIIIIIIII', 'IIIIIIIIIIIYYIIIIIIIII', 'IIIIIIIIIIIZZIIIIIIIII', 'IIIIIIIIIXXIIIIIIIIIII', 'IIIIIIIIIYYIIIIIIIIIII', 'IIIIIIIIIZZIIIIIIIIIII', 'IIIIIIIXXIIIIIIIIIIIII', 'IIIIIIIYYIIIIIIIIIIIII', 'IIIIIIIZZIIIIIIIIIIIII', 'IIIIIXXIIIIIIIIIIIIIII', 'IIIIIYYIIIIIIIIIIIIIII', 'IIIIIZZIIIIIIIIIIIIIII', 'IIIXXIIIIIIIIIIIIIIIII', 'IIIYYIIIIIIIIIIIIIIIII', 'IIIZZIIIIIIIIIIIIIIIII', 'IXXIIIIIIIIIIIIIIIIIII', 'IYYIIIIIIIIIIIIIIIIIII', 'IZZIIIIIIIIIIIIIIIIIII'],\n",
" coeffs=[1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n",
" 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n",
" 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n",
" 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n",
" 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n",
" 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n",
" 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n",
" 1.+0.j, 1.+0.j, 1.+0.j])\n"
]
}
],
"source": [
"from qiskit.transpiler import CouplingMap\n",
"from qiskit_addon_utils.problem_generators import generate_xyz_hamiltonian\n",
"\n",
"coupling_map = CouplingMap.from_ring(num_spins)\n",
"hamiltonian = generate_xyz_hamiltonian(coupling_map)\n",
"print(hamiltonian)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "f31f5e40",
"metadata": {},
"outputs": [],
"source": [
"from qiskit_addon_sqd.qubit import matrix_elements_from_pauli\n",
"from scipy.sparse import coo_matrix\n",
"from scipy.sparse.linalg import eigsh\n",
"\n",
"d = bts_matrix.shape[0]\n",
"d = bitstring_matrix.shape[0]\n",
"\n",
"# The first Pauli operator\n",
"matrix_elements, row_coords, col_coords = matrix_elements_from_pauli_string(bts_matrix, paulis[0])\n",
"# Initialize the coo_matrix object\n",
"operator_from_matrix_elements = coo_matrix((d, d), dtype=\"complex128\")\n",
"\n",
"# The complex double precision is required to match exactly Netket's results\n",
"# We can relax it to complex64 most likely\n",
"ham = coo_matrix((matrix_elements, (row_coords, col_coords)), (d, d), dtype=\"complex128\")\n",
"\n",
"# The remaining Pauli operators\n",
"# It will be a good idea to make this operation in parallel\n",
"for i in range(len(paulis) - 1):\n",
" matrix_elements, row_coords, col_coords = matrix_elements_from_pauli_string(\n",
" bts_matrix, paulis[i + 1]\n",
"for pauli in hamiltonian.paulis:\n",
" matrix_elements, row_addresses, col_addresses = matrix_elements_from_pauli(\n",
" bitstring_matrix, pauli\n",
" )\n",
" ham += coo_matrix((matrix_elements, (row_coords, col_coords)), (d, d))"
" operator_from_matrix_elements += coo_matrix(\n",
" (matrix_elements, (row_addresses, col_addresses)), (d, d)\n",
" )"
]
},
{
"cell_type": "markdown",
"id": "4479af24",
"metadata": {},
"source": [
"### Higher-level implementation"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "3ce6e519",
"execution_count": 4,
"id": "e58763df",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[-39.14735935]\n"
"Projecting term 1 out of 66: (1+0j) * IIIIIIIIIIIIIIIIIIIIXX ...\n",
"Projecting term 2 out of 66: (1+0j) * IIIIIIIIIIIIIIIIIIIIYY ...\n",
"Projecting term 3 out of 66: (1+0j) * IIIIIIIIIIIIIIIIIIIIZZ ...\n",
"Projecting term 4 out of 66: (1+0j) * IIIIIIIIIIIIIIIIIIXXII ...\n",
"Projecting term 5 out of 66: (1+0j) * IIIIIIIIIIIIIIIIIIYYII ...\n",
"Projecting term 6 out of 66: (1+0j) * IIIIIIIIIIIIIIIIIIZZII ...\n",
"Projecting term 7 out of 66: (1+0j) * IIIIIIIIIIIIIIIIXXIIII ...\n",
"Projecting term 8 out of 66: (1+0j) * IIIIIIIIIIIIIIIIYYIIII ...\n",
"Projecting term 9 out of 66: (1+0j) * IIIIIIIIIIIIIIIIZZIIII ...\n",
"Projecting term 10 out of 66: (1+0j) * IIIIIIIIIIIIIIXXIIIIII ...\n",
"Projecting term 11 out of 66: (1+0j) * IIIIIIIIIIIIIIYYIIIIII ...\n",
"Projecting term 12 out of 66: (1+0j) * IIIIIIIIIIIIIIZZIIIIII ...\n",
"Projecting term 13 out of 66: (1+0j) * IIIIIIIIIIIIXXIIIIIIII ...\n",
"Projecting term 14 out of 66: (1+0j) * IIIIIIIIIIIIYYIIIIIIII ...\n",
"Projecting term 15 out of 66: (1+0j) * IIIIIIIIIIIIZZIIIIIIII ...\n",
"Projecting term 16 out of 66: (1+0j) * IIIIIIIIIIXXIIIIIIIIII ...\n",
"Projecting term 17 out of 66: (1+0j) * IIIIIIIIIIYYIIIIIIIIII ...\n",
"Projecting term 18 out of 66: (1+0j) * IIIIIIIIIIZZIIIIIIIIII ...\n",
"Projecting term 19 out of 66: (1+0j) * IIIIIIIIXXIIIIIIIIIIII ...\n",
"Projecting term 20 out of 66: (1+0j) * IIIIIIIIYYIIIIIIIIIIII ...\n",
"Projecting term 21 out of 66: (1+0j) * IIIIIIIIZZIIIIIIIIIIII ...\n",
"Projecting term 22 out of 66: (1+0j) * IIIIIIXXIIIIIIIIIIIIII ...\n",
"Projecting term 23 out of 66: (1+0j) * IIIIIIYYIIIIIIIIIIIIII ...\n",
"Projecting term 24 out of 66: (1+0j) * IIIIIIZZIIIIIIIIIIIIII ...\n",
"Projecting term 25 out of 66: (1+0j) * IIIIXXIIIIIIIIIIIIIIII ...\n",
"Projecting term 26 out of 66: (1+0j) * IIIIYYIIIIIIIIIIIIIIII ...\n",
"Projecting term 27 out of 66: (1+0j) * IIIIZZIIIIIIIIIIIIIIII ...\n",
"Projecting term 28 out of 66: (1+0j) * IIXXIIIIIIIIIIIIIIIIII ...\n",
"Projecting term 29 out of 66: (1+0j) * IIYYIIIIIIIIIIIIIIIIII ...\n",
"Projecting term 30 out of 66: (1+0j) * IIZZIIIIIIIIIIIIIIIIII ...\n",
"Projecting term 31 out of 66: (1+0j) * XXIIIIIIIIIIIIIIIIIIII ...\n",
"Projecting term 32 out of 66: (1+0j) * YYIIIIIIIIIIIIIIIIIIII ...\n",
"Projecting term 33 out of 66: (1+0j) * ZZIIIIIIIIIIIIIIIIIIII ...\n",
"Projecting term 34 out of 66: (1+0j) * XIIIIIIIIIIIIIIIIIIIIX ...\n",
"Projecting term 35 out of 66: (1+0j) * YIIIIIIIIIIIIIIIIIIIIY ...\n",
"Projecting term 36 out of 66: (1+0j) * ZIIIIIIIIIIIIIIIIIIIIZ ...\n",
"Projecting term 37 out of 66: (1+0j) * IIIIIIIIIIIIIIIIIIIXXI ...\n",
"Projecting term 38 out of 66: (1+0j) * IIIIIIIIIIIIIIIIIIIYYI ...\n",
"Projecting term 39 out of 66: (1+0j) * IIIIIIIIIIIIIIIIIIIZZI ...\n",
"Projecting term 40 out of 66: (1+0j) * IIIIIIIIIIIIIIIIIXXIII ...\n",
"Projecting term 41 out of 66: (1+0j) * IIIIIIIIIIIIIIIIIYYIII ...\n",
"Projecting term 42 out of 66: (1+0j) * IIIIIIIIIIIIIIIIIZZIII ...\n",
"Projecting term 43 out of 66: (1+0j) * IIIIIIIIIIIIIIIXXIIIII ...\n",
"Projecting term 44 out of 66: (1+0j) * IIIIIIIIIIIIIIIYYIIIII ...\n",
"Projecting term 45 out of 66: (1+0j) * IIIIIIIIIIIIIIIZZIIIII ...\n",
"Projecting term 46 out of 66: (1+0j) * IIIIIIIIIIIIIXXIIIIIII ...\n",
"Projecting term 47 out of 66: (1+0j) * IIIIIIIIIIIIIYYIIIIIII ...\n",
"Projecting term 48 out of 66: (1+0j) * IIIIIIIIIIIIIZZIIIIIII ...\n",
"Projecting term 49 out of 66: (1+0j) * IIIIIIIIIIIXXIIIIIIIII ...\n",
"Projecting term 50 out of 66: (1+0j) * IIIIIIIIIIIYYIIIIIIIII ...\n",
"Projecting term 51 out of 66: (1+0j) * IIIIIIIIIIIZZIIIIIIIII ...\n",
"Projecting term 52 out of 66: (1+0j) * IIIIIIIIIXXIIIIIIIIIII ...\n",
"Projecting term 53 out of 66: (1+0j) * IIIIIIIIIYYIIIIIIIIIII ...\n",
"Projecting term 54 out of 66: (1+0j) * IIIIIIIIIZZIIIIIIIIIII ...\n",
"Projecting term 55 out of 66: (1+0j) * IIIIIIIXXIIIIIIIIIIIII ...\n",
"Projecting term 56 out of 66: (1+0j) * IIIIIIIYYIIIIIIIIIIIII ...\n",
"Projecting term 57 out of 66: (1+0j) * IIIIIIIZZIIIIIIIIIIIII ...\n",
"Projecting term 58 out of 66: (1+0j) * IIIIIXXIIIIIIIIIIIIIII ...\n",
"Projecting term 59 out of 66: (1+0j) * IIIIIYYIIIIIIIIIIIIIII ...\n",
"Projecting term 60 out of 66: (1+0j) * IIIIIZZIIIIIIIIIIIIIII ...\n",
"Projecting term 61 out of 66: (1+0j) * IIIXXIIIIIIIIIIIIIIIII ...\n",
"Projecting term 62 out of 66: (1+0j) * IIIYYIIIIIIIIIIIIIIIII ...\n",
"Projecting term 63 out of 66: (1+0j) * IIIZZIIIIIIIIIIIIIIIII ...\n",
"Projecting term 64 out of 66: (1+0j) * IXXIIIIIIIIIIIIIIIIIII ...\n",
"Projecting term 65 out of 66: (1+0j) * IYYIIIIIIIIIIIIIIIIIII ...\n",
"Projecting term 66 out of 66: (1+0j) * IZZIIIIIIIIIIIIIIIIIII ...\n"
]
}
],
"source": [
"# And we finally diagonalize\n",
"E, V = eigsh(ham, k=1, which=\"SA\")\n",
"from qiskit_addon_sqd.qubit import project_operator_to_subspace\n",
"\n",
"print(E)"
"operator = project_operator_to_subspace(bitstring_matrix, hamiltonian, verbose=True)"
]
},
{
"cell_type": "markdown",
"id": "1fce97a2",
"metadata": {},
"source": [
"### Check that both implementations yield the same coo_matrix"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "4bf56509",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0j\n"
]
}
],
"source": [
"print((operator.power(2) - operator_from_matrix_elements.power(2)).sum())"
]
}
],
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2 changes: 1 addition & 1 deletion docs/index.rst
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Expand Up @@ -32,7 +32,7 @@ For more installation information refer to the `installation instructions <insta
System sizes and computational requirements
-------------------------------------------

The computational cost of SQD is dominated by the eigenstate solver calls. At each step of the self-consistent configuration recovery iteration, `n_batches` of eigenstate solver calls are performed. The different calls are embarrassingly parallel. In this `tutorial <tutorials/01_getting_started_fermionic.ipynb>`_, those calls are inside a `for` loop. **It is highly recommended to perform these calls in parallel**.
The computational cost of SQD is dominated by the eigenstate solver calls. At each step of the self-consistent configuration recovery iteration, `n_batches` of eigenstate solver calls are performed. The different calls are embarrassingly parallel. In this `tutorial <tutorials/01_chemistry_hamiltonian.ipynb>`_, those calls are inside a `for` loop. **It is highly recommended to perform these calls in parallel**.

The :func:`qiskit_addon_sqd.fermion.solve_fermion` function is multithreaded and capable of handling systems with ~25 spacial orbitals and ~10 electrons with subspace dimensions of ~$10^7$, using ~10-30 cores.

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