microsoft/qdk
Publicmirrored fromhttps://github.com/microsoft/qdkAvailable
samples/estimation/df-chemistry/chemistry.py
501lines · modecode
| 1 | # Copyright (c) Microsoft Corporation. All rights reserved. |
| 2 | # Licensed under the MIT License. |
| 3 | import math |
| 4 | import numpy as np |
| 5 | import numpy.typing as npt |
| 6 | import qsharp |
| 7 | from argparse import ArgumentParser |
| 8 | from dataclasses import dataclass |
| 9 | from scipy import linalg as LA |
| 10 | from urllib.parse import urlparse |
| 11 | from urllib.request import urlretrieve |
| 12 | |
| 13 | |
| 14 | @dataclass |
| 15 | class FCIDumpFileContent: |
| 16 | num_orbitals: int |
| 17 | one_body_terms: list[tuple[list[int], float]] |
| 18 | two_body_terms: list[tuple[list[int], float]] |
| 19 | |
| 20 | @classmethod |
| 21 | def from_file(self, file_url): |
| 22 | """Read FCIDump file (given by either a local path or a URL) and parse |
| 23 | it to get the input data for double-factorized chemistry algorithm.""" |
| 24 | url = urlparse(file_url) |
| 25 | |
| 26 | file_name = "" |
| 27 | if url.scheme in ["http", "https"]: |
| 28 | # Download the file |
| 29 | file_name = url.path.rsplit("/", 1)[-1] |
| 30 | print(f"Downloading {file_url} to {file_name}...") |
| 31 | urlretrieve(file_url, file_name) |
| 32 | elif url.scheme in ["", "file"]: |
| 33 | # Use the whole URL as the file path |
| 34 | file_name = file_url |
| 35 | else: |
| 36 | raise f"Unsupported file location {file_url}" |
| 37 | |
| 38 | with open(file_name, "r") as f: |
| 39 | lines = [str.strip() for str in f.readlines()] |
| 40 | |
| 41 | assert lines[0].startswith("&FCI") |
| 42 | |
| 43 | parse_header = True |
| 44 | header = "" |
| 45 | header_values = {} |
| 46 | self.one_body_terms = [] |
| 47 | self.two_body_terms = [] |
| 48 | |
| 49 | for line in lines: |
| 50 | if parse_header: |
| 51 | # File header might not have key-value pairs in separate lines, |
| 52 | # so accumulate the whole header first and then parse. |
| 53 | header += line + " " |
| 54 | if line.endswith("&END"): |
| 55 | # Strip "&FCI" and "&END" |
| 56 | rest_header = header[4:-4] |
| 57 | |
| 58 | # Find each key-value pair based on the "=" sign |
| 59 | while (ind := rest_header.find("=")) > -1: |
| 60 | key = rest_header[0:ind].strip() |
| 61 | rest_header = rest_header[ind + 1 :] |
| 62 | # Figure out which part of the rest is value: until |
| 63 | # either whitespace or (if key is not ORBSYM) comma |
| 64 | ind = rest_header.find("," if key != "ORBSYM" else " ") |
| 65 | value = rest_header[0:ind].strip() |
| 66 | rest_header = rest_header[ind + 1 :] |
| 67 | if key == "ORBSYM": |
| 68 | value = value[:-1] |
| 69 | header_values[key] = value |
| 70 | parse_header = False |
| 71 | else: |
| 72 | tokens = line.split() |
| 73 | coefficient = float(tokens[0]) |
| 74 | indices = [int(str) - 1 for str in tokens[1:] if str != "0"] |
| 75 | |
| 76 | if len(indices) == 2: |
| 77 | indices.sort() |
| 78 | self.one_body_terms.append((indices, coefficient)) |
| 79 | elif len(indices) == 4: |
| 80 | # conversion from Mulliken to Dirac |
| 81 | i = indices[0] |
| 82 | j = indices[2] |
| 83 | k = indices[3] |
| 84 | l = indices[1] |
| 85 | |
| 86 | symmetries = [ |
| 87 | [i, j, k, l], |
| 88 | [j, i, l, k], |
| 89 | [k, l, i, j], |
| 90 | [l, k, j, i], |
| 91 | [i, k, j, l], |
| 92 | [k, i, l, j], |
| 93 | [j, l, i, k], |
| 94 | [l, j, k, i], |
| 95 | ] |
| 96 | symmetries.sort() |
| 97 | self.two_body_terms.append((symmetries[0], coefficient)) |
| 98 | |
| 99 | self.num_orbitals = int(header_values["NORB"]) |
| 100 | |
| 101 | return self |
| 102 | |
| 103 | |
| 104 | @dataclass |
| 105 | class TwoBodyResult: |
| 106 | eigenvalues: list[npt.NDArray[np.float64]] |
| 107 | eigenvectors: list[npt.NDArray[np.float64]] |
| 108 | one_norms: list[float] |
| 109 | two_norms: list[float] |
| 110 | |
| 111 | |
| 112 | @dataclass |
| 113 | class DoubleFactorization: |
| 114 | num_orbitals: int |
| 115 | rank: int |
| 116 | one_body_norm: float |
| 117 | two_body_norm: float |
| 118 | one_body_eigenvalues: list[float] |
| 119 | one_body_eigenvectors: npt.NDArray[npt.NDArray[np.float64]] |
| 120 | two_body_eigenvalues: npt.NDArray[npt.NDArray[np.float64]] |
| 121 | two_body_eigenvectors: list[npt.NDArray[npt.NDArray[np.float64]]] |
| 122 | |
| 123 | @classmethod |
| 124 | def process_fcidump(self, structure: FCIDumpFileContent, error: float): |
| 125 | |
| 126 | # The `structure` provides us with one- and two electron integrals |
| 127 | # h_{ij} and h_{ijkl} as described in Eq. (2). These coefficients are |
| 128 | # real and satisfy some symmetries which are outlined in Eq. (6). |
| 129 | |
| 130 | # In this step we compute R (`rank`) as in Eq. (7), h_{ij} |
| 131 | # (`one_electron_vector`), and L_{ij}^{(r)} (`two_electron_vectors`). |
| 132 | (rank, eigenvalue_signs, one_electron_vector, two_electron_vectors) = ( |
| 133 | self.perform_svd(structure) |
| 134 | ) |
| 135 | |
| 136 | # This computes Eq. (15). It stores L^{-1}_{ij} into |
| 137 | # `one_body_eigenvectors`, which is repurposed from |
| 138 | # `one_electron_vector` and uses the same indices. It also returns the |
| 139 | # Schatten norm, which is the first summand in Eq. (16). |
| 140 | (one_body_eigenvalues, one_body_eigenvectors, one_body_norm, norm2) = ( |
| 141 | self.process_one_body_term( |
| 142 | structure.num_orbitals, |
| 143 | rank, |
| 144 | one_electron_vector, |
| 145 | eigenvalue_signs, |
| 146 | two_electron_vectors, |
| 147 | ) |
| 148 | ) |
| 149 | |
| 150 | assert len(one_body_eigenvectors) == structure.num_orbitals**2 |
| 151 | |
| 152 | # This computes the second sum of Eq. (9), it computes the eigenvalues |
| 153 | # \lambda_m^{(r)} and eigenvectors $\vec R_{m,i}^{(r)}$. It does not |
| 154 | # normalize the vectors, but returns the one- and two-norms of the |
| 155 | # eigenvalues. |
| 156 | two_body_result = self.process_two_body_terms( |
| 157 | structure.num_orbitals, rank, two_electron_vectors |
| 158 | ) |
| 159 | |
| 160 | # Discard terms that will make the description exceed the error budget |
| 161 | self.truncate_terms(structure.num_orbitals, error, two_body_result) |
| 162 | |
| 163 | # This computes the second summand in Eq. (16). |
| 164 | two_body_norm = 0.0 |
| 165 | two_body_norm += sum(0.25 * norm * norm for norm in two_body_result.one_norms) |
| 166 | |
| 167 | # Reshape the one body eigenvectors so that they are represented |
| 168 | # row-wise in a 2D array |
| 169 | one_body_eigenvectors = np.reshape( |
| 170 | one_body_eigenvectors, (structure.num_orbitals, structure.num_orbitals) |
| 171 | ) |
| 172 | |
| 173 | for i in range(len(two_body_result.eigenvectors)): |
| 174 | cols = structure.num_orbitals |
| 175 | rows = int(len(two_body_result.eigenvectors[i]) / cols) |
| 176 | assert rows * cols == len(two_body_result.eigenvectors[i]) |
| 177 | |
| 178 | # Reshape the two body eigenvectors so that they represented |
| 179 | # row-wise in a 2D array |
| 180 | two_body_result.eigenvectors[i] = np.reshape( |
| 181 | two_body_result.eigenvectors[i], (rows, cols) |
| 182 | ) |
| 183 | |
| 184 | self.num_orbitals = structure.num_orbitals |
| 185 | # Use the post-truncation rank |
| 186 | self.rank = len(two_body_result.eigenvectors) |
| 187 | self.one_body_norm = one_body_norm |
| 188 | self.two_body_norm = two_body_norm |
| 189 | self.one_body_eigenvalues = one_body_eigenvalues |
| 190 | self.one_body_eigenvectors = one_body_eigenvectors |
| 191 | self.two_body_eigenvalues = two_body_result.eigenvalues |
| 192 | self.two_body_eigenvectors = two_body_result.eigenvectors |
| 193 | |
| 194 | return self |
| 195 | |
| 196 | def combined_index(i: int, j: int) -> int: |
| 197 | return int(max(i, j) * (max(i, j) + 1) / 2 + min(i, j)) |
| 198 | |
| 199 | def vectors_to_sym_mat( |
| 200 | vector: npt.NDArray[float], dimension: int |
| 201 | ) -> npt.NDArray[npt.NDArray[float]]: |
| 202 | matrix = np.zeros((dimension, dimension), dtype=float) |
| 203 | |
| 204 | # Create lower triangular matrix |
| 205 | matrix[np.tril_indices(dimension, 0)] = vector |
| 206 | |
| 207 | # Convert lower triangular matrix to symmetrix matrix |
| 208 | matrix = matrix + matrix.T |
| 209 | |
| 210 | # Halve elements of diagonal to avoid doubling |
| 211 | matrix = matrix - 0.5 * np.diag(np.diagonal(matrix, 0)) |
| 212 | |
| 213 | return matrix |
| 214 | |
| 215 | @classmethod |
| 216 | def populate_two_body_terms( |
| 217 | self, two_body_terms: list[tuple[list[int], float]] |
| 218 | ) -> list[tuple[list[int], float]]: |
| 219 | complete_two_body_terms = [] |
| 220 | |
| 221 | for [i, j, k, l], val in two_body_terms: |
| 222 | ii = self.combined_index(i, l) |
| 223 | jj = self.combined_index(j, k) |
| 224 | |
| 225 | complete_two_body_terms.append(([ii, jj], val)) |
| 226 | if ii != jj: |
| 227 | complete_two_body_terms.append(([jj, ii], val)) |
| 228 | |
| 229 | return complete_two_body_terms |
| 230 | |
| 231 | @classmethod |
| 232 | def eigen_svd( |
| 233 | self, orbitals: int, two_body_terms: list[tuple[list[int], float]] |
| 234 | ) -> (int, list[int], list[float]): |
| 235 | # combined = nC2 for n = orbitals |
| 236 | combined = int(orbitals * (orbitals + 1) / 2) |
| 237 | |
| 238 | coeff_matrix = np.zeros((combined, combined), dtype=float) |
| 239 | for [i, j], v in two_body_terms: |
| 240 | coeff_matrix[int(i)][int(j)] = v |
| 241 | |
| 242 | # Compute the eigen decomposition of the symmetric coefficient matrix |
| 243 | # with two body terms |
| 244 | evals, evecs = LA.eigh(coeff_matrix) |
| 245 | rows, cols = np.shape(evecs) |
| 246 | |
| 247 | evals_signs = np.zeros(cols, dtype=int) |
| 248 | |
| 249 | # let eigenvectors be represented as row vectors |
| 250 | evecs = np.transpose(evecs) |
| 251 | |
| 252 | # Scale eigenvector by square root of corresponding eigenvalue |
| 253 | for i in range(len(evals)): |
| 254 | evecs[i] = math.sqrt(abs(evals[i])) * evecs[i] |
| 255 | evals_signs[i] = np.sign(evals[i]) |
| 256 | |
| 257 | # Collect eigenvectors as 1D array |
| 258 | scaled_evecs_1D = np.reshape(evecs, cols * rows) |
| 259 | |
| 260 | return (cols, evals_signs.tolist(), scaled_evecs_1D) |
| 261 | |
| 262 | @classmethod |
| 263 | def perform_svd( |
| 264 | self, structure: FCIDumpFileContent |
| 265 | ) -> (int, npt.NDArray[int], npt.NDArray[float], npt.NDArray[float]): |
| 266 | |
| 267 | full_two_body_terms = self.populate_two_body_terms(structure.two_body_terms) |
| 268 | |
| 269 | # Compute the eigen decomposition of two-electron terms |
| 270 | (rank, eigenvalue_signs, two_electron_vectors) = self.eigen_svd( |
| 271 | structure.num_orbitals, full_two_body_terms |
| 272 | ) |
| 273 | |
| 274 | length = ( |
| 275 | self.combined_index(structure.num_orbitals - 1, structure.num_orbitals - 1) |
| 276 | + 1 |
| 277 | ) |
| 278 | one_electron_vector = np.zeros((length), dtype=float) |
| 279 | |
| 280 | # Collect one-electron terms into a single 2D array |
| 281 | for [i, j], v in structure.one_body_terms: |
| 282 | one_electron_vector[self.combined_index(i, j)] = v |
| 283 | |
| 284 | return (rank, eigenvalue_signs, one_electron_vector, two_electron_vectors) |
| 285 | |
| 286 | @classmethod |
| 287 | def eigen_decomp( |
| 288 | self, dimension: int, vector: npt.NDArray[float] |
| 289 | ) -> (npt.NDArray[float], npt.NDArray[float], float, float): |
| 290 | matrix = np.zeros((dimension, dimension), dtype=float) |
| 291 | |
| 292 | # Create lower triangular matrix |
| 293 | matrix[np.tril_indices(dimension, 0)] = vector |
| 294 | |
| 295 | # Compute the eigen decomposition of the lower triangular matrix |
| 296 | evals, evecs = LA.eigh(matrix, lower=True) |
| 297 | norm1 = np.linalg.norm(evals, 1) |
| 298 | norm2 = np.linalg.norm(evals) |
| 299 | |
| 300 | (rows, cols) = np.shape(evecs) |
| 301 | evecs_1D = np.reshape(np.transpose(evecs), cols * rows) |
| 302 | |
| 303 | return (evals, evecs_1D, norm1, norm2) |
| 304 | |
| 305 | @classmethod |
| 306 | def process_one_body_term( |
| 307 | self, |
| 308 | orbitals: int, |
| 309 | rank: int, |
| 310 | one_electron_vector: npt.NDArray[float], |
| 311 | eigenvalue_signs: npt.NDArray[bool], |
| 312 | two_electron_vectors: npt.NDArray[float], |
| 313 | ) -> (list[float], npt.NDArray[float], float, float): |
| 314 | # combined = nC2 for n = orbitals |
| 315 | combined = int(orbitals * (orbitals + 1) / 2) |
| 316 | |
| 317 | vector = np.zeros(combined, dtype=float) |
| 318 | |
| 319 | for l in range(rank): |
| 320 | matrix = np.zeros((orbitals, orbitals), dtype=float) |
| 321 | H_l = self.vectors_to_sym_mat( |
| 322 | two_electron_vectors[range(combined * l, combined * (l + 1))], orbitals |
| 323 | ) |
| 324 | |
| 325 | H_issj = eigenvalue_signs[l] * np.matmul(H_l, H_l) |
| 326 | |
| 327 | H_ssij = eigenvalue_signs[l] * np.trace(H_l) * H_l |
| 328 | |
| 329 | matrix = -0.5 * H_issj + H_ssij |
| 330 | |
| 331 | # Convert symmetric matrix to lower triangular matrix |
| 332 | vector += matrix[np.tril_indices(orbitals, 0)] |
| 333 | |
| 334 | one_electron_vector += vector |
| 335 | |
| 336 | (one_body_eigenvalues, one_body_eigenvectors, one_body_norm, norm2) = ( |
| 337 | self.eigen_decomp(orbitals, one_electron_vector) |
| 338 | ) |
| 339 | |
| 340 | return (one_body_eigenvalues, one_body_eigenvectors, one_body_norm, norm2) |
| 341 | |
| 342 | @classmethod |
| 343 | def process_two_body_terms( |
| 344 | self, orbitals: int, rank: int, two_electron_vectors: npt.NDArray[float] |
| 345 | ) -> TwoBodyResult: |
| 346 | |
| 347 | two_body_eigenvectors = [] |
| 348 | two_body_eigenvalues = [] |
| 349 | one_norms = [] |
| 350 | two_norms = [] |
| 351 | combined = int(orbitals * (orbitals + 1) / 2) |
| 352 | |
| 353 | for i in range(rank): |
| 354 | matrix = two_electron_vectors[range(combined * i, combined * (i + 1))] |
| 355 | (evals, evecs, norm1, norm2) = self.eigen_decomp(orbitals, matrix) |
| 356 | |
| 357 | two_body_eigenvalues.append(evals) |
| 358 | two_body_eigenvectors.append(evecs) |
| 359 | one_norms.append(norm1) |
| 360 | two_norms.append(norm2) |
| 361 | |
| 362 | two_body_result = TwoBodyResult( |
| 363 | two_body_eigenvalues, two_body_eigenvectors, one_norms, two_norms |
| 364 | ) |
| 365 | |
| 366 | return two_body_result |
| 367 | |
| 368 | @classmethod |
| 369 | def truncate_terms( |
| 370 | self, orbitals: int, error_eigenvalues: float, two_body_result: TwoBodyResult |
| 371 | ): |
| 372 | values_with_error = [] |
| 373 | for r, values in enumerate(two_body_result.eigenvalues): |
| 374 | for i, v in enumerate(values): |
| 375 | error = abs(v) * two_body_result.two_norms[r] |
| 376 | values_with_error.append((error, r, i)) |
| 377 | |
| 378 | # Sort in ascending order by error values |
| 379 | values_with_error = sorted(values_with_error, key=lambda tup: tup[0]) |
| 380 | |
| 381 | # Truncate the list so that the sum of squares of errors left is less |
| 382 | # than the square of the input error |
| 383 | total_error = 0 |
| 384 | truncate = len(values_with_error) |
| 385 | for i, (error, _, _) in enumerate(values_with_error): |
| 386 | error_compare = error**2 |
| 387 | if total_error + error_compare < error_eigenvalues**2: |
| 388 | total_error += error_compare |
| 389 | else: |
| 390 | truncate = i |
| 391 | break |
| 392 | |
| 393 | # Keep the first `truncate` values |
| 394 | values_with_error = values_with_error[:truncate] |
| 395 | |
| 396 | indices_by_rank = [] |
| 397 | for _, r, i in values_with_error: |
| 398 | while r >= len(indices_by_rank): |
| 399 | indices_by_rank.append([]) |
| 400 | indices_by_rank[r].append(i) |
| 401 | |
| 402 | for r, indices in reversed(list(enumerate(indices_by_rank))): |
| 403 | if len(indices) == orbitals: |
| 404 | # All indices are to be removed: fully remove the r^th entry |
| 405 | # for the norms, eigenvalues and eigenvectors. |
| 406 | del two_body_result.eigenvalues[r] |
| 407 | del two_body_result.eigenvectors[r] |
| 408 | del two_body_result.one_norms[r] |
| 409 | del two_body_result.two_norms[r] |
| 410 | else: |
| 411 | indices.sort() |
| 412 | # Remove only eigenvalues/vectors corresponding to `indices` |
| 413 | two_body_result.eigenvalues[r] = np.delete( |
| 414 | arr=two_body_result.eigenvalues[r], obj=indices |
| 415 | ) |
| 416 | arr = np.reshape(two_body_result.eigenvectors[r], (orbitals, orbitals)) |
| 417 | arr = np.delete(arr=arr, obj=indices, axis=0) |
| 418 | (rows, cols) = np.shape(arr) |
| 419 | two_body_result.eigenvectors[r] = np.reshape(arr, rows * cols) |
| 420 | |
| 421 | # Check that same number of terms are removed for norms, |
| 422 | # eigenvalues and eigenvectors |
| 423 | assert ( |
| 424 | len(two_body_result.one_norms) == len(two_body_result.two_norms) |
| 425 | and len(two_body_result.one_norms) == len(two_body_result.eigenvalues) |
| 426 | and len(two_body_result.one_norms) == len(two_body_result.eigenvectors) |
| 427 | ) |
| 428 | |
| 429 | |
| 430 | # Convert 2D array into string representation |
| 431 | def ndarray2d_to_string(arr): |
| 432 | str_arr = [] |
| 433 | for elem in arr: |
| 434 | str_arr.append(np.array2string(elem, separator=",")) |
| 435 | return f"[{','.join(str_arr)}]" |
| 436 | |
| 437 | |
| 438 | # The script takes one required positional argument, URI of the FCIDUMP file |
| 439 | parser = ArgumentParser(description="Double-factorized chemistry sample") |
| 440 | # Use n2-10e-8o as the default sample. |
| 441 | # Pass a different filename to get estimates for different compounds |
| 442 | parser.add_argument( |
| 443 | "-f", |
| 444 | "--fcidumpfile", |
| 445 | default="https://aka.ms/fcidump/n2-10e-8o", |
| 446 | help="Path to the FCIDUMP file describing the Hamiltonian", |
| 447 | ) |
| 448 | args = parser.parse_args() |
| 449 | |
| 450 | # ----- Read the FCIDUMP file and get resource estimates from Q# algorithm ----- |
| 451 | structure = FCIDumpFileContent.from_file(args.fcidumpfile) |
| 452 | df = DoubleFactorization.process_fcidump(structure, 0.001) |
| 453 | |
| 454 | # Load Q# project |
| 455 | qsharp.init(project_root=".") |
| 456 | |
| 457 | # Construct the Q# operation call for which we need to perform resource estimate |
| 458 | str_one_body_eigenvalues = np.array2string(df.one_body_eigenvalues, separator=",") |
| 459 | |
| 460 | str_one_body_eigenvectors = ndarray2d_to_string(df.one_body_eigenvectors) |
| 461 | |
| 462 | str_two_body_eigenvalues = ndarray2d_to_string(df.two_body_eigenvalues) |
| 463 | |
| 464 | str_two_body_eigenvectors = ( |
| 465 | "[" |
| 466 | + ",".join( |
| 467 | [ndarray2d_to_string(eigenvectors) for eigenvectors in df.two_body_eigenvectors] |
| 468 | ) |
| 469 | + "]" |
| 470 | ) |
| 471 | |
| 472 | qsharp_string = ( |
| 473 | "Microsoft.Quantum.Applications.Chemistry.DoubleFactorizedChemistry(" |
| 474 | "Microsoft.Quantum.Applications.Chemistry.DoubleFactorizedChemistryProblem(" |
| 475 | f"{df.num_orbitals}, {df.one_body_norm}, {df.two_body_norm}, " |
| 476 | f"{str_one_body_eigenvalues}, {str_one_body_eigenvectors}, " |
| 477 | f"[1.0, size = {df.rank}], {str_two_body_eigenvalues}, " |
| 478 | f"{str_two_body_eigenvectors})," |
| 479 | "Microsoft.Quantum.Applications.Chemistry.DoubleFactorizedChemistryParameters(0.001,))" |
| 480 | ) |
| 481 | |
| 482 | # Get resource estimates |
| 483 | res = qsharp.estimate( |
| 484 | qsharp_string, |
| 485 | params={ |
| 486 | "errorBudget": 0.01, |
| 487 | "qubitParams": {"name": "qubit_maj_ns_e6"}, |
| 488 | "qecScheme": {"name": "floquet_code"}, |
| 489 | }, |
| 490 | ) |
| 491 | |
| 492 | # Store estimates in json file |
| 493 | with open("resource_estimate.json", "w") as f: |
| 494 | f.write(res.json) |
| 495 | |
| 496 | # Print high-level resource estimation results |
| 497 | print(f"Algorithm runtime: {res['physicalCountsFormatted']['runtime']}") |
| 498 | print( |
| 499 | f"Number of physical qubits required: {res['physicalCountsFormatted']['physicalQubits']}" |
| 500 | ) |
| 501 | print("For more detailed resource counts, see file resource_estimate.json") |
| 502 | |