├── .gitignore ├── LICENSE ├── README.md ├── dist ├── pygridsynth-1.1.0-py3-none-any.whl └── pygridsynth-1.1.0.tar.gz ├── pygridsynth ├── __init__.py ├── __main__.py ├── diophantine.py ├── grid_op.py ├── gridsynth.py ├── mymath.py ├── myplot.py ├── normal_form.py ├── odgp.py ├── region.py ├── ring.py ├── synthesis_of_cliffordT.py ├── tdgp.py ├── to_upright.py └── unitary.py ├── pyproject.toml └── requirements.txt /.gitignore: -------------------------------------------------------------------------------- 1 | **/__pycache__/** 2 | build/ 3 | .venv/ 4 | pygridsynth.egg-info/ -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | Version 3, 29 June 2007 3 | 4 | Copyright (C) 2007 Free Software Foundation, Inc. 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU General Public License is a free, copyleft license for 11 | software and other kinds of works. 12 | 13 | The licenses for most software and other practical works are designed 14 | to take away your freedom to share and change the works. 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If not, see . 649 | 650 | Also add information on how to contact you by electronic and paper mail. 651 | 652 | If the program does terminal interaction, make it output a short 653 | notice like this when it starts in an interactive mode: 654 | 655 | Copyright (C) 656 | This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. 657 | This is free software, and you are welcome to redistribute it 658 | under certain conditions; type `show c' for details. 659 | 660 | The hypothetical commands `show w' and `show c' should show the appropriate 661 | parts of the General Public License. Of course, your program's commands 662 | might be different; for a GUI interface, you would use an "about box". 663 | 664 | You should also get your employer (if you work as a programmer) or school, 665 | if any, to sign a "copyright disclaimer" for the program, if necessary. 666 | For more information on this, and how to apply and follow the GNU GPL, see 667 | . 668 | 669 | The GNU General Public License does not permit incorporating your program 670 | into proprietary programs. If your program is a subroutine library, you 671 | may consider it more useful to permit linking proprietary applications with 672 | the library. If this is what you want to do, use the GNU Lesser General 673 | Public License instead of this License. But first, please read 674 | . 675 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # pygridsynth 2 | 3 | `pygridsynth` is a Python library for approximating arbitrary Z-rotations using the Clifford+T gate set, based on a given angle `θ` and tolerance `ε`. It is particularly useful for addressing approximate gate synthesis problems in quantum computing and algorithm research. 4 | 5 | ## Features 6 | 7 | - **Inspired by Established Work:** This library is based on P. Selinger's gridsynth program ([newsynth](https://www.mathstat.dal.ca/~selinger/newsynth/)), adapted for Python with additional functionality. 8 | - **High Precision:** Utilizes the `mpmath` library to support high-precision calculations. 9 | - **Customizable:** Allows adjustment of calculation precision (`dps`) and verbosity of output. 10 | - **Graph Visualization:** Provides an option to visualize decomposition results as a graph. 11 | 12 | ## Installation 13 | 14 | You can install `pygridsynth` via pip: 15 | 16 | ```bash 17 | pip install pygridsynth 18 | ``` 19 | 20 | Or, to install from source: 21 | 22 | ```bash 23 | pip install git+https://github.com/quantum-programming/pygridsynth.git 24 | ``` 25 | 26 | ## Usage 27 | 28 | `pygridsynth` can be used as a command-line tool. 29 | 30 | ### Command-Line Example 31 | 32 | ```bash 33 | python -m pygridsynth [options] 34 | ``` 35 | 36 | ### Arguments 37 | 38 | - `theta` (required): The rotation angle to decompose, specified in radians (e.g., `0.5`). 39 | - `epsilon` (required): The allowable error tolerance (e.g., `1e-10`). 40 | 41 | ### Options 42 | 43 | - `--dps`: Sets the calculation precision (default: `128`). 44 | - `--dtimeout`, `-dt`: Sets the timeout for solving diophantine equations in milliseconds (default: `200`). 45 | - `--ftimeout`, `-ft`: Sets the timeout for factorization in milliseconds (default: `50`). 46 | - `--verbose`, `-v`: Enables detailed output. 47 | - `--time`, `-t`: Measures the execution time. 48 | - `--showgraph`, `-g`: Displays the decomposition result as a graph. 49 | 50 | ### Example Execution 51 | 52 | ```bash 53 | python -m pygridsynth 0.5 1e-50 --dps 256 --verbose --time 54 | ``` 55 | 56 | This command will: 57 | 1. Compute the Clifford+T gate decomposition of a Z-rotation gate with $\theta = 0.5$ and $\epsilon = 0.01$. 58 | 2. Set the calculation precision to 256 decimal places. 59 | 3. Display detailed output and measure the execution time. 60 | 61 | ## Using as a Library 62 | 63 | You can also use `pygridsynth` directly in your scripts: 64 | 65 | ```python 66 | from pygridsynth.gridsynth import gridsynth_gates 67 | import mpmath 68 | 69 | mpmath.mp.dps = 128 70 | theta = mpmath.mpmathify("0.5") 71 | epsilon = mpmath.mpmathify("1e-10") 72 | 73 | gates = gridsynth_gates(theta=theta, epsilon=epsilon) 74 | print(gates) 75 | ``` 76 | 77 | ## Contributing 78 | 79 | Bug reports and feature requests are welcome. Please submit them via the [GitHub repository](https://github.com/quantum-programming/pygridsynth) Issues section. Contributions must comply with the GNU General Public License v3 or later. 80 | 81 | ## License 82 | 83 | This project is licensed under the GNU General Public License v3 or later. 84 | 85 | ## References 86 | 87 | - Brett Giles and Peter Selinger. Remarks on Matsumoto and Amano's normal form for single-qubit Clifford+T operators, 2019. 88 | - Ken Matsumoto and Kazuyuki Amano. Representation of Quantum Circuits with Clifford and π/8 Gates, 2008. 89 | - Neil J. Ross and Peter Selinger. Optimal ancilla-free Clifford+T approximation of z-rotations, 2016. 90 | - Peter Selinger. Efficient Clifford+T approximation of single-qubit operators, 2014. 91 | - Peter Selinger and Neil J. Ross. Exact and approximate synthesis of quantum circuits. https://www.mathstat.dal.ca/~selinger/newsynth/, 2018. 92 | - Vadym Kliuchnikov, Dmitri Maslov, and Michele Mosca. Fast and efficient exact synthesis of single qubit unitaries generated by Clifford and T gates, 2013. -------------------------------------------------------------------------------- /dist/pygridsynth-1.1.0-py3-none-any.whl: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/quantum-programming/pygridsynth/5868c650ce819227adcd80eaa8d8e065f4001022/dist/pygridsynth-1.1.0-py3-none-any.whl -------------------------------------------------------------------------------- /dist/pygridsynth-1.1.0.tar.gz: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/quantum-programming/pygridsynth/5868c650ce819227adcd80eaa8d8e065f4001022/dist/pygridsynth-1.1.0.tar.gz -------------------------------------------------------------------------------- /pygridsynth/__init__.py: -------------------------------------------------------------------------------- 1 | from .gridsynth import * 2 | -------------------------------------------------------------------------------- /pygridsynth/__main__.py: -------------------------------------------------------------------------------- 1 | import argparse 2 | import mpmath 3 | 4 | from .gridsynth import gridsynth_gates 5 | 6 | 7 | def main(): 8 | parser = argparse.ArgumentParser() 9 | 10 | parser.add_argument('theta', type=str) 11 | parser.add_argument('epsilon', type=str) 12 | parser.add_argument('--dps', type=int, default=128) 13 | parser.add_argument('--dtimeout', '-dt', type=int, default=200) 14 | parser.add_argument('--ftimeout', '-ft', type=int, default=50) 15 | parser.add_argument('--verbose', '-v', action='store_true') 16 | parser.add_argument('--time', '-t', action='store_true') 17 | parser.add_argument('--showgraph', '-g', action='store_true') 18 | 19 | args = parser.parse_args() 20 | mpmath.mp.dps = args.dps 21 | mpmath.mp.pretty = True 22 | theta = mpmath.mpmathify(args.theta) 23 | epsilon = mpmath.mpmathify(args.epsilon) 24 | 25 | gates = gridsynth_gates(theta=theta, epsilon=epsilon, 26 | verbose=args.verbose, measure_time=args.time, 27 | show_graph=args.showgraph) 28 | print(gates) 29 | return gates 30 | 31 | 32 | if __name__ == "__main__": 33 | main() 34 | -------------------------------------------------------------------------------- /pygridsynth/diophantine.py: -------------------------------------------------------------------------------- 1 | import warnings 2 | import numbers 3 | import math 4 | import random 5 | import time 6 | 7 | from .ring import ZRootTwo, ZOmega, DOmega 8 | 9 | NO_SOLUTION = "no solution" 10 | 11 | 12 | def _find_factor(n, factoring_timeout, M=128): 13 | if not (n & 1) and n > 2: 14 | return 2 15 | 16 | a = random.randint(1, n) 17 | y, r, k = a, 1, 0 18 | L = int(10 ** (len(str(n)) / 4) * 1.1774 + 10) 19 | 20 | start_factoring = time.time() 21 | while True: 22 | x = y + n 23 | while k < r: 24 | q = 1 25 | y0 = y 26 | for _ in range(M): 27 | y = (y * y + a) % n 28 | q = q * (x - y) % n 29 | k += 1 30 | if k == r: 31 | break 32 | g = math.gcd(q, n) 33 | if g != 1: 34 | if g == n: 35 | y = y0 36 | for _ in range(M): 37 | y = (y * y + a) % n 38 | g = math.gcd(x - y, n) 39 | if g != 1: 40 | break 41 | return None if g == n else g 42 | if k >= L or (time.time() - start_factoring) * 1000 >= factoring_timeout: 43 | return None 44 | r <<= 1 45 | 46 | 47 | def _sqrt_negative_one(p, L=100): 48 | for _ in range(L): 49 | b = random.randint(1, p - 1) 50 | h = pow(b, (p - 1) >> 2, p) 51 | r = h * h % p 52 | if r == p - 1: 53 | return h 54 | elif r != 1: 55 | return None 56 | 57 | 58 | class F_p2(): 59 | base = 0 60 | p = 0 61 | 62 | def __init__(self, a, b): 63 | if a < 0 or a >= self.__class__.p: 64 | a %= self.__class__.p 65 | if b < 0 or b >= self.__class__.p: 66 | b %= self.__class__.p 67 | self._a = a 68 | self._b = b 69 | 70 | @property 71 | def a(self): 72 | return self._a 73 | 74 | @property 75 | def b(self): 76 | return self._b 77 | 78 | def __mul__(self, other): 79 | if isinstance(other, self.__class__): 80 | new_a = self._a * other.a + self._b * other.b % self.__class__.p * self.__class__.base 81 | new_b = self._a * other.b + self._b * other.a 82 | return self.__class__(new_a, new_b) 83 | else: 84 | return NotImplemented 85 | 86 | def __pow__(self, other): 87 | if isinstance(other, numbers.Integral): 88 | if other < 0: 89 | return NotImplemented 90 | else: 91 | new = self.__class__(1, 0) 92 | tmp = self 93 | while other > 0: 94 | if other & 1: 95 | new *= tmp 96 | tmp *= tmp 97 | other >>= 1 98 | return new 99 | else: 100 | return NotImplemented 101 | 102 | 103 | def _root_mod(x, p, L=100): 104 | x = x % p 105 | if p == 2: 106 | return x 107 | if x == 0: 108 | return 0 109 | if not (p & 1) and p > 2: 110 | return None 111 | if pow(x, (p - 1) // 2, p) != 1: 112 | return None 113 | 114 | for _ in range(L): 115 | b = random.randint(1, p - 1) 116 | r = pow(b, p - 1, p) 117 | if r != 1: 118 | return None 119 | 120 | base = (b * b + p - x) % p 121 | if pow(base, (p - 1) // 2, p) != 1: 122 | F_p2.p = p 123 | F_p2.base = base 124 | return (F_p2(b, 1) ** ((p + 1) // 2)).a 125 | 126 | 127 | def _is_prime(n, L=4): 128 | if n < 0: 129 | n = -n 130 | if n == 0 or n == 1: 131 | return False 132 | if not (n & 1): 133 | return True if n == 2 else False 134 | 135 | r, d = 0, n - 1 136 | while not (d & 1): 137 | r += 1 138 | d >>= 1 139 | for _ in range(L): 140 | a = random.randint(1, n - 1) 141 | a = pow(a, d, n) 142 | if a == 1: 143 | return True 144 | 145 | for _ in range(r): 146 | if a == n - 1: 147 | return True 148 | a = a * a % n 149 | return False 150 | 151 | 152 | def _decompose_relatively_int_prime(partial_facs): 153 | u = 1 154 | stack = list(reversed(partial_facs)) 155 | facs = [] 156 | while len(stack): 157 | b, k_b = stack.pop() 158 | i = 0 159 | while True: 160 | if i >= len(facs): 161 | if b == 1 or b == -1: 162 | if b == -1 and (k_b & 1): 163 | u = -u 164 | else: 165 | facs.append((b, k_b)) 166 | break 167 | a, k_a = facs[i] 168 | if a == b or a == -b: 169 | if a == -b and (k_b & 1): 170 | u = -u 171 | facs[i] = (a, k_a + k_b) 172 | break 173 | else: 174 | g = math.gcd(a, b) 175 | if g == 1 or g == -1: 176 | i += 1 177 | continue 178 | else: 179 | partial_facs = [(a // g, k_a), (g, k_a + k_b)] 180 | u_a, facs_a = _decompose_relatively_int_prime(partial_facs) 181 | u *= u_a 182 | facs[i] = facs_a[0] 183 | facs = facs + facs_a[1:] 184 | stack.append((b // g, k_b)) 185 | break 186 | 187 | return u, facs 188 | 189 | 190 | def _adj_decompose_int_prime(p): 191 | if p < 0: 192 | p = -p 193 | if p == 0 or p == 1: 194 | return ZOmega.from_int(p) 195 | if p == 2: 196 | return ZOmega(-1, 0, 1, 0) 197 | 198 | if _is_prime(p): 199 | if p & 0b11 == 1: 200 | h = _sqrt_negative_one(p) 201 | if h is None: 202 | return None 203 | else: 204 | t = ZOmega.gcd(h + ZOmega(0, 1, 0, 0), p) 205 | return t if t.conj * t == p or t.conj * t == -p else None 206 | elif p & 0b111 == 3: 207 | h = _root_mod(-2, p) 208 | if h is None: 209 | return None 210 | else: 211 | t = ZOmega.gcd(h + ZOmega(1, 0, 1, 0), p) 212 | return t if t.conj * t == p or t.conj * t == -p else None 213 | elif p & 0b111 == 7: 214 | h = _root_mod(2, p) 215 | if h is not None: 216 | return NO_SOLUTION 217 | else: 218 | return None 219 | else: 220 | return None 221 | else: 222 | if p & 0b111 == 7: 223 | h = _root_mod(2, p) 224 | if h is not None: 225 | return NO_SOLUTION 226 | else: 227 | return None 228 | else: 229 | return None 230 | 231 | 232 | def _adj_decompose_int_prime_power(p, k): 233 | if not (k & 1): 234 | return p ** (k // 2) 235 | else: 236 | t = _adj_decompose_int_prime(p) 237 | if t is None or t == NO_SOLUTION: 238 | return t 239 | else: 240 | return t ** k 241 | 242 | 243 | def _adj_decompose_int(n, diophantine_timeout, factoring_timeout, start_time): 244 | if n < 0: 245 | n = -n 246 | facs = [(n, 1)] 247 | t = ZOmega.from_int(1) 248 | while len(facs): 249 | p, k = facs.pop() 250 | t_p = _adj_decompose_int_prime_power(p, k) 251 | if t_p == NO_SOLUTION: 252 | return NO_SOLUTION 253 | elif t_p is None: 254 | fac = _find_factor(p, factoring_timeout) 255 | if fac is None: 256 | facs.append((p, k)) 257 | if (time.time() - start_time) * 1000 >= diophantine_timeout: 258 | return NO_SOLUTION 259 | else: 260 | facs.append((p // fac, k)) 261 | facs.append((fac, k)) 262 | _, facs = _decompose_relatively_int_prime(facs) 263 | else: 264 | t *= t_p 265 | return t 266 | 267 | 268 | def _adj_decompose_selfassociate(xi, diophantine_timeout, factoring_timeout, start_time): 269 | # xi \sim xi.conj_sq2 270 | if xi == 0: 271 | return ZOmega.from_int(0) 272 | 273 | n = math.gcd(xi.a, xi.b) 274 | r = xi // n 275 | t1 = _adj_decompose_int(n, diophantine_timeout, factoring_timeout, start_time) 276 | t2 = ZOmega(0, 0, 1, 1) if r % ZRootTwo(0, 1) == 0 else 1 277 | if t1 is None: 278 | return None 279 | elif t1 == NO_SOLUTION: 280 | return NO_SOLUTION 281 | else: 282 | return t1 * t2 283 | 284 | 285 | def _decompose_relatively_zomega_prime(partial_facs): 286 | u = 1 287 | stack = list(reversed(partial_facs)) 288 | facs = [] 289 | while len(stack): 290 | b, k_b = stack.pop() 291 | i = 0 292 | while True: 293 | if i >= len(facs): 294 | if ZRootTwo.sim(b, 1): 295 | u *= b ** k_b 296 | else: 297 | facs.append((b, k_b)) 298 | break 299 | a, k_a = facs[i] 300 | if ZRootTwo.sim(a, b): 301 | u *= (b // a) ** k_b 302 | facs[i] = (a, k_a + k_b) 303 | break 304 | else: 305 | g = ZRootTwo.gcd(a, b) 306 | if ZRootTwo.sim(g, 1): 307 | i += 1 308 | continue 309 | else: 310 | partial_facs = [(a // g, k_a), (g, k_a + k_b)] 311 | u_a, facs_a = _decompose_relatively_zomega_prime(partial_facs) 312 | u *= u_a 313 | facs[i] = facs_a[0] 314 | facs = facs + facs_a[1:] 315 | stack.append((b // g, k_b)) 316 | break 317 | 318 | return u, facs 319 | 320 | 321 | def _adj_decompose_zomega_prime(eta): 322 | p = eta.norm 323 | 324 | if p < 0: 325 | p = -p 326 | if p == 0 or p == 1: 327 | return ZOmega.from_int(p) 328 | elif p == 2: 329 | return ZOmega(-1, 0, 1, 0) 330 | 331 | if _is_prime(p): 332 | if p & 0b11 == 1: 333 | h = _sqrt_negative_one(p) 334 | if h is None: 335 | return None 336 | else: 337 | t = ZOmega.gcd(h + ZOmega(0, 1, 0, 0), eta) 338 | return t if ZRootTwo.sim(t.conj * t, eta) else None 339 | elif p & 0b111 == 3: 340 | h = _root_mod(-2, p) 341 | if h is None: 342 | return None 343 | else: 344 | t = ZOmega.gcd(h + ZOmega(1, 0, 1, 0), eta) 345 | return t if ZRootTwo.sim(t.conj * t, eta) else None 346 | elif p & 0b111 == 7: 347 | h = _root_mod(2, p) 348 | if h is not None: 349 | return NO_SOLUTION 350 | else: 351 | return None 352 | else: 353 | return None 354 | else: 355 | if p & 0b111 == 7: 356 | h = _root_mod(2, p) 357 | if h is not None: 358 | return NO_SOLUTION 359 | else: 360 | return None 361 | else: 362 | return None 363 | 364 | 365 | def _adj_decompose_zomega_prime_power(eta, k): 366 | if not (k & 1): 367 | return eta ** (k // 2) 368 | else: 369 | t = _adj_decompose_zomega_prime(eta) 370 | if t is None or t == NO_SOLUTION: 371 | return t 372 | else: 373 | return t ** k 374 | 375 | 376 | def _adj_decompose_selfcoprime(xi, diophantine_timeout, factoring_timeout, start_time): 377 | # gcd(xi, xi.conj_sq2) = 1 378 | facs = [(xi, 1)] 379 | t = ZOmega.from_int(1) 380 | while len(facs): 381 | eta, k = facs.pop() 382 | t_eta = _adj_decompose_zomega_prime_power(eta, k) 383 | if t_eta == NO_SOLUTION: 384 | return NO_SOLUTION 385 | elif t_eta is None: 386 | n = eta.norm 387 | if n < 0: 388 | n = -n 389 | fac_n = _find_factor(n, factoring_timeout) 390 | if fac_n is None: 391 | facs.append((eta, k)) 392 | if (time.time() - start_time) * 1000 >= diophantine_timeout: 393 | return NO_SOLUTION 394 | else: 395 | fac = ZRootTwo.gcd(xi, fac_n) 396 | facs.append((eta // fac, k)) 397 | facs.append((fac, k)) 398 | _, facs = _decompose_relatively_zomega_prime(facs) 399 | else: 400 | t *= t_eta 401 | return t 402 | 403 | 404 | def _adj_decompose(xi, diophantine_timeout, factoring_timeout, start_time): 405 | if xi == 0: 406 | return ZOmega.from_int(0) 407 | 408 | d = ZRootTwo.gcd(xi, xi.conj_sq2) 409 | eta = xi // d 410 | t1 = _adj_decompose_selfassociate(d, diophantine_timeout, factoring_timeout, start_time) 411 | if t1 == NO_SOLUTION: 412 | return NO_SOLUTION 413 | else: 414 | t2 = _adj_decompose_selfcoprime(eta, diophantine_timeout, factoring_timeout, start_time) 415 | if t2 == NO_SOLUTION: 416 | return NO_SOLUTION 417 | else: 418 | return t1 * t2 419 | 420 | 421 | def _diophantine(xi, diophantine_timeout, factoring_timeout, start_time): 422 | if xi == 0: 423 | return ZOmega.from_int(0) 424 | elif xi < 0 or xi.conj_sq2 < 0: 425 | return NO_SOLUTION 426 | 427 | t = _adj_decompose(xi, diophantine_timeout, factoring_timeout, start_time) 428 | if t == NO_SOLUTION: 429 | return NO_SOLUTION 430 | else: 431 | xi_associate = ZRootTwo.from_zomega(t.conj * t) 432 | u = xi // xi_associate 433 | v = u.sqrt() 434 | if v is None: 435 | warnings.warn("cannot find square root of u") 436 | return NO_SOLUTION 437 | else: 438 | return v * t 439 | 440 | 441 | def diophantine_dyadic(xi, diophantine_timeout=200, factoring_timeout=50): 442 | k_div_2, k_mod_2 = xi.k >> 1, xi.k & 1 443 | 444 | t = _diophantine(xi.alpha * ZRootTwo(1, 1) if k_mod_2 else xi.alpha, 445 | diophantine_timeout=diophantine_timeout, factoring_timeout=factoring_timeout, 446 | start_time=time.time()) 447 | if t == NO_SOLUTION: 448 | return NO_SOLUTION 449 | else: 450 | if k_mod_2: 451 | t *= ZOmega(0, -1, 1, 0) 452 | return DOmega(t, k_div_2 + k_mod_2) 453 | -------------------------------------------------------------------------------- /pygridsynth/grid_op.py: -------------------------------------------------------------------------------- 1 | from functools import cached_property 2 | import mpmath 3 | 4 | from .ring import ZOmega, DOmega 5 | 6 | 7 | class EllipsePair(): 8 | def __init__(self, A, B): 9 | self.A = A 10 | self.B = B 11 | 12 | @property 13 | def skew(self): 14 | return self.A.skew + self.B.skew 15 | 16 | @property 17 | def bias(self): 18 | return self.B.bias / self.A.bias 19 | 20 | def __rmul__(self, other): 21 | if isinstance(other, GridOp): 22 | return self.__class__(other * self.A, other.conj_sq2 * self.B) 23 | else: 24 | return NotImplemented 25 | 26 | 27 | class GridOp(): 28 | def __init__(self, u0, u1): 29 | self._u0 = u0 30 | self._u1 = u1 31 | # d0 + b0 + d1 + b1 : even 32 | # a0 + c0 + a1 + c1 : even 33 | 34 | @property 35 | def u0(self): 36 | return self._u0 37 | 38 | @property 39 | def u1(self): 40 | return self._u1 41 | 42 | @property 43 | def a0(self): 44 | return self._u0.a 45 | 46 | @property 47 | def b0(self): 48 | return self._u0.b 49 | 50 | @property 51 | def c0(self): 52 | return self._u0.c 53 | 54 | @property 55 | def d0(self): 56 | return self._u0.d 57 | 58 | @property 59 | def a1(self): 60 | return self._u1.a 61 | 62 | @property 63 | def b1(self): 64 | return self._u1.b 65 | 66 | @property 67 | def c1(self): 68 | return self._u1.c 69 | 70 | @property 71 | def d1(self): 72 | return self._u1.d 73 | 74 | def __str__(self): 75 | return (f"[[{self.d0}{self.c0 - self.a0:+}/√2, {self.d1}{self.c1 - self.a1:+}/√2],\n" 76 | f" [{self.b0}{self.c0 + self.a0:+}/√2, {self.b1}{self.c1 + self.a1:+}/√2]]") 77 | 78 | @cached_property 79 | def _det_vec(self): 80 | return self._u0.conj * self._u1 81 | 82 | @cached_property 83 | def is_special(self): 84 | v = self._det_vec 85 | return v.a + v.c == 0 and (v.b == 1 or v.b == -1) 86 | 87 | @cached_property 88 | def toMat(self): 89 | return mpmath.matrix([[self._u0.real, self._u1.real], [self._u0.imag, self._u1.imag]]) 90 | 91 | def __mul__(self, other): 92 | if isinstance(other, self.__class__): 93 | return GridOp(self * other.u0, self * other.u1) 94 | elif isinstance(other, ZOmega): 95 | new_d = (self.d0 * other.d + self.d1 * other.b 96 | + (self.c1 - self.a1 + self.c0 - self.a0) // 2 * other.c 97 | + (self.c1 - self.a1 - self.c0 + self.a0) // 2 * other.a) 98 | new_c = (self.c0 * other.d + self.c1 * other.b 99 | + (self.b1 + self.d1 + self.b0 + self.d0) // 2 * other.c 100 | + (self.b1 + self.d1 - self.b0 - self.d0) // 2 * other.a) 101 | new_b = (self.b0 * other.d + self.b1 * other.b 102 | + (self.c1 + self.a1 + self.c0 + self.a0) // 2 * other.c 103 | + (self.c1 + self.a1 - self.c0 - self.a0) // 2 * other.a) 104 | new_a = (self.a0 * other.d + self.a1 * other.b 105 | + (self.b1 - self.d1 + self.b0 - self.d0) // 2 * other.c 106 | + (self.b1 - self.d1 - self.b0 + self.d0) // 2 * other.a) 107 | return ZOmega(new_a, new_b, new_c, new_d) 108 | elif isinstance(other, DOmega): 109 | return DOmega(self * other.u, other.k) 110 | else: 111 | return NotImplemented 112 | 113 | @cached_property 114 | def inv(self): 115 | if not self.is_special: 116 | return None 117 | 118 | new_c0 = (self.c1 + self.a1 - self.c0 - self.a0) // 2 119 | new_a0 = (- self.c1 - self.a1 - self.c0 - self.a0) // 2 120 | new_u0 = ZOmega(new_a0, -self.b0, new_c0, self.b1) 121 | new_c1 = (- self.c1 + self.a1 + self.c0 - self.a0) // 2 122 | new_a1 = (self.c1 - self.a1 + self.c0 - self.a0) // 2 123 | new_u1 = ZOmega(new_a1, self.d0, new_c1, -self.d1) 124 | if self._det_vec.b == -1: 125 | new_u0 = -new_u0 126 | new_u1 = -new_u1 127 | return GridOp(new_u0, new_u1) 128 | 129 | def __pow__(self, other): 130 | if isinstance(other, int): 131 | if other < 0: 132 | return self.inv ** (-other) 133 | 134 | new = self.__class__(ZOmega(0, 0, 0, 1), ZOmega(0, 1, 0, 0)) 135 | tmp = self 136 | while other > 0: 137 | if other & 1: 138 | new *= tmp 139 | tmp *= tmp 140 | other >>= 1 141 | return new 142 | else: 143 | return NotImplemented 144 | 145 | @cached_property 146 | def adj(self): 147 | new_c0 = (self.c1 - self.a1 + self.c0 - self.a0) // 2 148 | new_a0 = (self.c1 - self.a1 - self.c0 + self.a0) // 2 149 | new_u0 = ZOmega(new_a0, self.d1, new_c0, self.d0) 150 | new_c1 = (self.c1 + self.a1 + self.c0 + self.a0) // 2 151 | new_a1 = (self.c1 + self.a1 - self.c0 - self.a0) // 2 152 | new_u1 = ZOmega(new_a1, self.b1, new_c1, self.b0) 153 | return self.__class__(new_u0, new_u1) 154 | 155 | @cached_property 156 | def conj_sq2(self): 157 | return self.__class__(self._u0.conj_sq2, self._u1.conj_sq2) 158 | -------------------------------------------------------------------------------- /pygridsynth/gridsynth.py: -------------------------------------------------------------------------------- 1 | import mpmath 2 | import time 3 | 4 | from .mymath import sqrt, solve_quadratic 5 | from .ring import DRootTwo 6 | from .region import Ellipse, ConvexSet 7 | from .to_upright import to_upright_set_pair 8 | from .tdgp import solve_TDGP 9 | from .diophantine import NO_SOLUTION, diophantine_dyadic 10 | from .unitary import DOmegaUnitary 11 | from .synthesis_of_cliffordT import decompose_domega_unitary 12 | 13 | 14 | class EpsilonRegion(ConvexSet): 15 | def __init__(self, theta, epsilon): 16 | self._theta = theta 17 | self._epsilon = epsilon 18 | self._d = 1 - epsilon ** 2 / 2 19 | self._z_x = mpmath.cos(-theta / 2) 20 | self._z_y = mpmath.sin(-theta / 2) 21 | D_1 = mpmath.matrix([[self._z_x, -self._z_y], [self._z_y, self._z_x]]) 22 | D_2 = mpmath.matrix([[4 * (1 / epsilon) ** 4, 0], [0, (1 / epsilon) ** 2]]) 23 | D_3 = mpmath.matrix([[self._z_x, self._z_y], [-self._z_y, self._z_x]]) 24 | p = mpmath.matrix([self._d * self._z_x, self._d * self._z_y]) 25 | ellipse = Ellipse(D_1 * D_2 * D_3, p) 26 | super().__init__(ellipse) 27 | 28 | @property 29 | def theta(self): 30 | return self._theta 31 | 32 | @property 33 | def epsilon(self): 34 | return self._epsilon 35 | 36 | def inside(self, u): 37 | cos_similarity = (self._z_x * u.real + self._z_y * u.imag) 38 | return DRootTwo.fromDOmega(u.conj * u) <= 1 and cos_similarity >= self._d 39 | 40 | def intersect(self, u0, v): 41 | a = v.conj * v 42 | b = 2 * v.conj * u0 43 | c = u0.conj * u0 - 1 44 | 45 | vz = self._z_x * v.real + self._z_y * v.imag 46 | rhs = self._d - self._z_x * u0.real - self._z_y * u0.imag 47 | t = solve_quadratic(a.real, b.real, c.real) 48 | if t is None: 49 | return None 50 | t0, t1 = t 51 | if vz > 0: 52 | t2 = rhs / vz 53 | return (t0, t1) if t0 > t2 else (t2, t1) 54 | elif vz < 0: 55 | t2 = rhs / vz 56 | return (t0, t1) if t1 < t2 else (t0, t2) 57 | else: 58 | return (t0, t1) if rhs <= 0 else None 59 | 60 | 61 | class UnitDisk(ConvexSet): 62 | def __init__(self): 63 | ellipse = Ellipse(mpmath.matrix([[1, 0], [0, 1]]), mpmath.matrix([0, 0])) 64 | super().__init__(ellipse) 65 | 66 | def inside(self, u): 67 | return DRootTwo.fromDOmega(u.conj * u) <= 1 68 | 69 | def intersect(self, u0, v): 70 | a = v.conj * v 71 | b = 2 * v.conj * u0 72 | c = u0.conj * u0 - 1 73 | return solve_quadratic(a.real, b.real, c.real) 74 | 75 | 76 | def generate_complex_unitary(sol): 77 | u, t = sol 78 | return mpmath.matrix([[u.to_complex, -t.conj.to_complex], 79 | [t.to_complex, u.conj.to_complex]]) 80 | 81 | 82 | def generate_target_Rz(theta): 83 | return mpmath.matrix([[mpmath.exp(- 1.j * theta / 2), 0], 84 | [0, mpmath.exp(1.j * theta / 2)]]) 85 | 86 | 87 | def error(theta, gates): 88 | Rz = generate_target_Rz(theta) 89 | U = DOmegaUnitary.from_gates(gates).to_complex_matrix 90 | E = U - Rz 91 | return sqrt(mpmath.fabs(E[0, 0] * E[1, 1] - E[0, 1] * E[1, 0])) 92 | 93 | 94 | def check(theta, gates): 95 | t_count = gates.count("T") 96 | h_count = gates.count("H") 97 | U_decomp = DOmegaUnitary.from_gates(gates) 98 | # Rz = generate_target_Rz(theta) 99 | # U = U_decomp.to_complex_matrix 100 | e = error(theta, gates) 101 | print(f"{gates=}") 102 | print(f"{t_count=}, {h_count=}") 103 | # print(f"{Rz=}") 104 | print(f"U_decomp={U_decomp.to_matrix}") 105 | # print(f"{U=}") 106 | print(f"{e=}") 107 | 108 | 109 | def gridsynth(theta, epsilon, 110 | diophantine_timeout=200, factoring_timeout=50, 111 | verbose=False, measure_time=False, show_graph=False): 112 | epsilon_region = EpsilonRegion(theta, epsilon) 113 | unit_disk = UnitDisk() 114 | k = 0 115 | 116 | if measure_time: 117 | start = time.time() 118 | transformed = to_upright_set_pair(epsilon_region, unit_disk, 119 | verbose=verbose, show_graph=show_graph) 120 | if measure_time: 121 | print(f"to_upright_set_pair: {time.time() - start} s") 122 | if verbose: 123 | print("------------------") 124 | 125 | time_of_solve_TDGP = 0 126 | time_of_diophantine_dyadic = 0 127 | while True: 128 | if measure_time: 129 | start = time.time() 130 | sol = solve_TDGP(epsilon_region, unit_disk, *transformed, k, 131 | verbose=verbose, show_graph=show_graph) 132 | if measure_time: 133 | time_of_solve_TDGP += time.time() - start 134 | start = time.time() 135 | 136 | for z in sol: 137 | if (z * z.conj).residue == 0: 138 | continue 139 | xi = 1 - DRootTwo.fromDOmega(z.conj * z) 140 | w = diophantine_dyadic(xi, 141 | diophantine_timeout=diophantine_timeout, 142 | factoring_timeout=factoring_timeout) 143 | if w != NO_SOLUTION: 144 | z = z.reduce_denomexp() 145 | w = w.reduce_denomexp() 146 | if z.k > w.k: 147 | w = w.renew_denomexp(z.k) 148 | elif z.k < w.k: 149 | z = z.renew_denomexp(w.k) 150 | if (z + w).reduce_denomexp().k < z.k: 151 | u_approx = DOmegaUnitary(z, w, 0) 152 | else: 153 | u_approx = DOmegaUnitary(z, w.mul_by_omega(), 0) 154 | if measure_time: 155 | time_of_diophantine_dyadic += time.time() - start 156 | print(f"time of solve_TDGP: {time_of_solve_TDGP * 1000} ms") 157 | print(f"time of diophantine_dyadic: {time_of_diophantine_dyadic * 1000} ms") 158 | if verbose: 159 | print(f"{z=}, {w=}") 160 | print("------------------") 161 | return u_approx 162 | if measure_time: 163 | time_of_diophantine_dyadic += time.time() - start 164 | k += 1 165 | 166 | 167 | def gridsynth_gates(theta, epsilon, 168 | diophantine_timeout=200, factoring_timeout=50, 169 | verbose=False, measure_time=False, show_graph=False): 170 | if measure_time: 171 | start_total = time.time() 172 | u_approx = gridsynth(theta=theta, epsilon=epsilon, 173 | diophantine_timeout=diophantine_timeout, 174 | factoring_timeout=factoring_timeout, 175 | verbose=verbose, measure_time=measure_time, show_graph=show_graph) 176 | if measure_time: 177 | start = time.time() 178 | gates = decompose_domega_unitary(u_approx) 179 | if measure_time: 180 | print(f"time of decompose_domega_unitary: {(time.time() - start) * 1000} ms") 181 | print(f"total time: {(time.time() - start_total) * 1000} ms") 182 | return gates 183 | -------------------------------------------------------------------------------- /pygridsynth/mymath.py: -------------------------------------------------------------------------------- 1 | import mpmath 2 | from itertools import accumulate 3 | 4 | 5 | def SQRT2(): 6 | return mpmath.sqrt(2) 7 | 8 | 9 | def ntz(n): 10 | return 0 if n == 0 else ((n & -n) - 1).bit_count() 11 | 12 | 13 | def floor(x): 14 | return int(mpmath.floor(x, prec=0)) 15 | 16 | 17 | def ceil(x): 18 | return int(mpmath.ceil(x, prec=0)) 19 | 20 | 21 | def sqrt(x): 22 | return mpmath.sqrt(x) 23 | 24 | 25 | def log(x): 26 | return mpmath.log(x) 27 | 28 | 29 | def sign(x): 30 | return 1 if x > 0 else -1 if x < 0 else 0 31 | 32 | 33 | def floorsqrt(x): 34 | if x < 0: 35 | raise ValueError 36 | ok = 0 37 | ng = ceil(x) + 1 38 | while ng - ok > 1: 39 | mid = ok + (ng - ok) // 2 40 | if mid * mid <= x: 41 | ok = mid 42 | else: 43 | ng = mid 44 | return ok 45 | 46 | 47 | def rounddiv(x, y): 48 | return (x + y // 2) // y if y > 0 else (x - (- y) // 2) // y 49 | 50 | 51 | def pow_sqrt2(k): 52 | k_div_2, k_mod_2 = k >> 1, k & 1 53 | return (1 << k_div_2) * SQRT2() if k_mod_2 else 1 << k_div_2 54 | 55 | 56 | def floorlog(x, y): 57 | if x <= 0: 58 | raise ValueError("math domain error") 59 | 60 | tmp = y 61 | m = 0 62 | while x >= tmp or x * tmp < 1: 63 | tmp *= tmp 64 | m += 1 65 | 66 | pow_y = reversed(list(accumulate([0] * (m - 1), lambda x0, x1: x0 * x0, initial=y))) 67 | n, r = (0, x) if x >= 1 else (-1, x * tmp) 68 | for p in pow_y: 69 | n <<= 1 70 | if r > p: 71 | r /= p 72 | n += 1 73 | return (n, r) 74 | 75 | 76 | def solve_quadratic(a, b, c): 77 | if a < 0: 78 | a, b, c = -a, -b, -c 79 | discriminant = b ** 2 - 4 * a * c 80 | if discriminant < 0: 81 | return None 82 | s1 = - b - sqrt(discriminant) 83 | s2 = - b + sqrt(discriminant) 84 | if b >= 0: 85 | return (s1 / (2 * a), s2 / (2 * a)) 86 | else: 87 | return ((2 * c) / s2, (2 * c) / s1) 88 | -------------------------------------------------------------------------------- /pygridsynth/myplot.py: -------------------------------------------------------------------------------- 1 | 2 | def plot_sol(sol_list, ellipseA, ellipseB, bboxA=None, bboxB=None, 3 | color_list=None, size_list=None): 4 | import matplotlib.pyplot as plt 5 | 6 | if color_list is None: 7 | color_list = plt.rcParams['axes.prop_cycle'].by_key()['color'] 8 | if size_list is None: 9 | size_list = [5] * len(sol_list) 10 | 11 | fig = plt.figure(figsize=(12, 6)) 12 | ax1 = fig.add_subplot(1, 2, 1) 13 | ax1.set_aspect('equal') 14 | ax1.set_xlabel(r"$\mathrm{Re}[u]$") 15 | ax1.set_ylabel(r"$\mathrm{Im}[u]$") 16 | ax2 = fig.add_subplot(1, 2, 2) 17 | ax2.set_aspect('equal') 18 | ax2.set_xlabel(r"$\mathrm{Re}[u^\bullet]$") 19 | ax2.set_ylabel(r"$\mathrm{Im}[u^\bullet]$") 20 | 21 | for sol, color, size in zip(sol_list, color_list, size_list): 22 | x = [u.real for u in sol] 23 | y = [u.imag for u in sol] 24 | ax1.scatter(x, y, c=color, s=size) 25 | x = [u.conj_sq2.real for u in sol] 26 | y = [u.conj_sq2.imag for u in sol] 27 | ax2.scatter(x, y, c=color, s=size) 28 | 29 | ellipseA.plot(ax1) 30 | ellipseB.plot(ax2) 31 | 32 | if bboxA is not None: 33 | bboxA.plot(ax1) 34 | if bboxB is not None: 35 | bboxB.plot(ax2) 36 | 37 | plt.show() 38 | -------------------------------------------------------------------------------- /pygridsynth/normal_form.py: -------------------------------------------------------------------------------- 1 | from enum import Enum 2 | 3 | 4 | class Axis(Enum): 5 | I = 0 6 | H = 1 7 | SH = 2 8 | 9 | 10 | class Syllable(Enum): 11 | I = 0 12 | T = 1 13 | HT = 2 14 | SHT = 3 15 | 16 | 17 | CONJ2_TABLE = [(0, 0), (0, 0), (1, 0), (3, 2), (2, 0), (2, 4), (3, 0), (1, 6)] 18 | CONJ3_TABLE = [(0, 0, 0, 0), (0, 0, 1, 0), (0, 0, 2, 0), (0, 0, 3, 0), 19 | (0, 1, 0, 0), (0, 1, 1, 0), (0, 1, 2, 0), (0, 1, 3, 0), 20 | (1, 0, 0, 0), (2, 0, 3, 6), (1, 1, 2, 2), (2, 1, 3, 6), 21 | (1, 0, 2, 0), (2, 1, 1, 0), (1, 1, 0, 6), (2, 0, 1, 4), 22 | (2, 0, 0, 0), (1, 1, 3, 4), (2, 1, 0, 0), (1, 0, 1, 2), 23 | (2, 1, 2, 2), (1, 1, 1, 0), (2, 0, 2, 6), (1, 0, 3, 2)] 24 | CINV_TABLE = [(0, 0, 0, 0), (0, 0, 3, 0), (0, 0, 2, 0), (0, 0, 1, 0), 25 | (0, 1, 0, 0), (0, 1, 1, 6), (0, 1, 2, 4), (0, 1, 3, 2), 26 | (2, 0, 0, 0), (1, 0, 1, 2), (2, 1, 0, 0), (1, 1, 3, 4), 27 | (2, 1, 1, 2), (1, 1, 1, 6), (2, 0, 2, 2), (1, 0, 3, 4), 28 | (1, 0, 0, 0), (2, 1, 3, 6), (1, 1, 2, 2), (2, 0, 3, 6), 29 | (1, 0, 2, 0), (2, 1, 1, 6), (1, 1, 0, 2), (2, 0, 1, 6)] 30 | TCONJ_TABLE = [(Axis.I, 0, 0), (Axis.I, 1, 7), 31 | (Axis.H, 3, 3), (Axis.H, 2, 0), 32 | (Axis.SH, 0, 5), (Axis.SH, 1, 4)] 33 | 34 | 35 | class Clifford(): 36 | def __init__(self, a, b, c, d): 37 | if a >= 3 or a < 0: 38 | a %= 3 39 | if b >= 2 or b < 0: 40 | b &= 1 41 | if c >= 4 or c < 0: 42 | c &= 0b11 43 | if d >= 8 or d < 0: 44 | d &= 0b111 45 | self._a = a 46 | self._b = b 47 | self._c = c 48 | self._d = d 49 | 50 | @property 51 | def a(self): 52 | return self._a 53 | 54 | @property 55 | def b(self): 56 | return self._b 57 | 58 | @property 59 | def c(self): 60 | return self._c 61 | 62 | @property 63 | def d(self): 64 | return self._d 65 | 66 | def __repr__(self): 67 | return f"Clifford({self._a}, {self._b}, {self._c}, {self._d})" 68 | 69 | def __str__(self): 70 | return f"E^{self._a} X^{self._b} S^{self._c} ω^{self._d}" 71 | 72 | @classmethod 73 | def from_str(cls, g): 74 | if g == "H": 75 | return CLIFFORD_H 76 | elif g == "S": 77 | return CLIFFORD_S 78 | elif g == "X": 79 | return CLIFFORD_X 80 | elif g == "W": 81 | return CLIFFORD_W 82 | else: 83 | raise ValueError 84 | 85 | def __eq__(self, other): 86 | if isinstance(other, self.__class__): 87 | return (self._a == other.a and self._b == other.b 88 | and self._c == other.c and self._d == other.d) 89 | else: 90 | return False 91 | 92 | @classmethod 93 | def _conj2(cls, c, b): 94 | return CONJ2_TABLE[c << 1 | b] 95 | 96 | @classmethod 97 | def _conj3(cls, b, c, a): 98 | return CONJ3_TABLE[a << 3 | b << 2 | c] 99 | 100 | @classmethod 101 | def _cinv(cls, a, b, c): 102 | return CINV_TABLE[a << 3 | b << 2 | c] 103 | 104 | @classmethod 105 | def _tconj(cls, a, b): 106 | return TCONJ_TABLE[a << 1 | b] 107 | 108 | def __mul__(self, other): 109 | if isinstance(other, self.__class__): 110 | a1, b1, c1, d1 = self.__class__._conj3(self._b, self._c, other.a) 111 | c2, d2 = self.__class__._conj2(c1, other.b) 112 | new_a = self._a + a1 113 | new_b = b1 + other.b 114 | new_c = c2 + other.c 115 | new_d = d2 + d1 + self._d + other.d 116 | return self.__class__(new_a, new_b, new_c, new_d) 117 | else: 118 | return NotImplemented 119 | 120 | def inv(self): 121 | a1, b1, c1, d1 = self.__class__._cinv(self._a, self._b, self._c) 122 | return self.__class__(a1, b1, c1, d1 - self._d) 123 | 124 | def decompose_coset(self): 125 | if self._a == 0: 126 | return Axis.I, self 127 | elif self._a == 1: 128 | return Axis.H, CLIFFORD_H.inv() * self 129 | elif self._a == 2: 130 | return Axis.SH, CLIFFORD_SH.inv() * self 131 | 132 | def decompose_tconj(self): 133 | axis, c1, d1 = self.__class__._tconj(self._a, self._b) 134 | return axis, self.__class__(0, self._b, c1 + self._c, d1 + self._d) 135 | 136 | def to_gates(self): 137 | axis, c = self.decompose_coset() 138 | return ("" if axis == Axis.I else axis.name) + "X" * c.b + "S" * c.c + "W" * c.d 139 | 140 | 141 | class NormalForm(): 142 | def __init__(self, syllables, c): 143 | self._syllables = syllables 144 | self._c = c 145 | 146 | @property 147 | def syllables(self): 148 | return self._syllables 149 | 150 | @property 151 | def c(self): 152 | return self._c 153 | 154 | @c.setter 155 | def c(self, c): 156 | self._c = c 157 | 158 | def __repr__(self): 159 | return f"NormalForm({repr(self._syllables)}, {repr(self._c)})" 160 | 161 | def _append_gate(self, g): 162 | if g in ["H", "S", "X", "W"]: 163 | self.c *= Clifford.from_str(g) 164 | elif g == "T": 165 | axis, new_c = self.c.decompose_tconj() 166 | if axis == Axis.I: 167 | if len(self._syllables) == 0: 168 | self._syllables.append(Syllable.T) 169 | elif self._syllables[-1] == Syllable.T: 170 | self._syllables[-1].pop() 171 | self.c = CLIFFORD_S * new_c 172 | elif self._syllables[-1] == Syllable.HT: 173 | self._syllables.pop() 174 | self.c = CLIFFORD_HS * new_c 175 | elif self._syllables[-1] == Syllable.SHT: 176 | self._syllables.pop() 177 | self.c = CLIFFORD_SHS * new_c 178 | elif axis == Axis.H: 179 | self._syllables.append(Syllable.HT) 180 | self.c = new_c 181 | elif axis == Axis.SH: 182 | self._syllables.append(Syllable.SHT) 183 | self.c = new_c 184 | 185 | @classmethod 186 | def from_gates(cls, gates): 187 | normal_form = NormalForm([], CLIFFORD_I) 188 | for g in gates: 189 | normal_form._append_gate(g) 190 | return normal_form 191 | 192 | def to_gates(self): 193 | gates = "" 194 | for syllable in self._syllables: 195 | if syllable != Syllable.I: 196 | gates += syllable.name 197 | gates += self._c.to_gates() 198 | return "I" if gates == "" else gates 199 | 200 | 201 | CLIFFORD_I = Clifford(0, 0, 0, 0) 202 | CLIFFORD_X = Clifford(0, 1, 0, 0) 203 | CLIFFORD_H = Clifford(1, 0, 1, 5) 204 | CLIFFORD_S = Clifford(0, 0, 1, 0) 205 | CLIFFORD_W = Clifford(0, 0, 0, 1) 206 | CLIFFORD_SH = CLIFFORD_S * CLIFFORD_H 207 | CLIFFORD_HS = CLIFFORD_H * CLIFFORD_S 208 | CLIFFORD_SHS = CLIFFORD_S * CLIFFORD_H * CLIFFORD_S 209 | -------------------------------------------------------------------------------- /pygridsynth/odgp.py: -------------------------------------------------------------------------------- 1 | from .mymath import SQRT2, floor, ceil, pow_sqrt2, floorlog 2 | from .ring import ZRootTwo, DRootTwo, LAMBDA 3 | 4 | 5 | def _solve_ODGP_internal(I, J): 6 | if I.width < 0 or J.width < 0: 7 | return [] 8 | elif I.width > 0 and J.width <= 0: 9 | sol = _solve_ODGP_internal(J, I) 10 | return [beta.conj_sq2 for beta in sol] 11 | else: 12 | (n, _) = (0, 0) if J.width <= 0 else floorlog(J.width, LAMBDA.to_real) 13 | if n == 0: 14 | sol = [] 15 | a_min = ceil((I.l + J.l) / 2) 16 | a_max = floor((I.r + J.r) / 2) 17 | for a in range(a_min, a_max + 1): 18 | b_min = ceil(SQRT2() * (a - J.r) / 2) 19 | b_max = floor(SQRT2() * (a - J.l) / 2) 20 | for b in range(b_min, b_max + 1): 21 | sol.append(ZRootTwo(a, b)) 22 | return sol 23 | else: 24 | lambda_n = LAMBDA ** n 25 | lambda_inv_n = LAMBDA ** -n 26 | lambda_conj_sq2_n = LAMBDA.conj_sq2 ** n 27 | sol = _solve_ODGP_internal(I * lambda_n.to_real, J * lambda_conj_sq2_n.to_real) 28 | sol = [beta * lambda_inv_n for beta in sol] 29 | return sol 30 | 31 | 32 | def solve_ODGP(I, J): 33 | if I.width < 0 or J.width < 0: 34 | return [] 35 | 36 | a = floor((I.l + J.l) / 2) 37 | b = floor(SQRT2() * (I.l - J.l) / 4) 38 | alpha = ZRootTwo(a, b) 39 | sol = _solve_ODGP_internal(I - alpha.to_real, J - alpha.conj_sq2.to_real) 40 | sol = [beta + alpha for beta in sol] 41 | sol = [beta for beta in sol if I.within(beta.to_real) and J.within(beta.conj_sq2.to_real)] 42 | return sol 43 | 44 | 45 | def solve_ODGP_with_parity(I, J, beta): 46 | p = beta.parity 47 | sol = solve_ODGP((I - p) * SQRT2() / 2, (J - p) * (- SQRT2()) / 2) 48 | sol = [alpha * ZRootTwo(0, 1) + p for alpha in sol] 49 | return sol 50 | 51 | 52 | def solve_scaled_ODGP(I, J, k): 53 | scale = pow_sqrt2(k) 54 | sol = solve_ODGP(I * scale, -J * scale if k & 1 else J * scale) 55 | return [DRootTwo(alpha, k) for alpha in sol] 56 | 57 | 58 | def solve_scaled_ODGP_with_parity(I, J, k, beta): 59 | if k == 0: 60 | sol = solve_ODGP_with_parity(I, J, beta.renew_denomexp(0)) 61 | return [DRootTwo.from_zroottwo(alpha) for alpha in sol] 62 | else: 63 | p = beta.renew_denomexp(k).parity 64 | offset = DRootTwo.from_int(0) if p == 0 else DRootTwo.power_of_inv_sqrt2(k) 65 | sol = solve_scaled_ODGP(I - offset.to_real, J - offset.conj_sq2.to_real, k - 1) 66 | return [alpha + offset for alpha in sol] 67 | -------------------------------------------------------------------------------- /pygridsynth/region.py: -------------------------------------------------------------------------------- 1 | from abc import ABC, abstractmethod 2 | from functools import cached_property 3 | import numbers 4 | import mpmath 5 | 6 | from .mymath import sqrt 7 | from .grid_op import GridOp 8 | 9 | 10 | class Interval(): 11 | def __init__(self, l, r): 12 | self.l = l 13 | self.r = r 14 | 15 | def __str__(self): 16 | return f"[{self.l}, {self.r}]" 17 | 18 | def __add__(self, other): 19 | if isinstance(other, numbers.Real): 20 | return self.__class__(self.l + other, self.r + other) 21 | elif isinstance(other, self.__class__): 22 | return self.__class__(self.l + other.l, self.r + other.r) 23 | else: 24 | return NotImplemented 25 | 26 | def __radd__(self, other): 27 | if isinstance(other, numbers.Real): 28 | return self + other 29 | elif isinstance(other, self.__class__): 30 | return self + other 31 | else: 32 | return NotImplemented 33 | 34 | def __sub__(self, other): 35 | return self + (-other) 36 | 37 | def __rsub__(self, other): 38 | return (-self) + other 39 | 40 | def __neg__(self): 41 | return self.__class__(- self.r, - self.l) 42 | 43 | def __mul__(self, other): 44 | if isinstance(other, numbers.Real): 45 | if other >= 0: 46 | return self.__class__(self.l * other, self.r * other) 47 | else: 48 | return self.__class__(self.r * other, self.l * other) 49 | else: 50 | return NotImplemented 51 | 52 | def __rmul__(self, other): 53 | return self * other 54 | 55 | def __truediv__(self, other): 56 | if isinstance(other, numbers.Real): 57 | if other > 0: 58 | return self.__class__(self.l / other, self.r / other) 59 | else: 60 | return self.__class__(self.r / other, self.l / other) 61 | else: 62 | return NotImplemented 63 | 64 | @cached_property 65 | def width(self): 66 | return self.r - self.l 67 | 68 | def fatten(self, eps): 69 | return Interval(self.l - eps, self.r + eps) 70 | 71 | def within(self, x): 72 | return self.l <= x <= self.r 73 | 74 | 75 | class Rectangle(): 76 | def __init__(self, x_l, x_r, y_l, y_r): 77 | self.I_x = Interval(x_l, x_r) 78 | self.I_y = Interval(y_l, y_r) 79 | 80 | def __str__(self): 81 | return f"{self.I_x}×{self.I_y}" 82 | 83 | def __mul__(self, other): 84 | if isinstance(other, numbers.Real): 85 | if other >= 0: 86 | new_I_x = self.I_x * other 87 | new_I_y = self.I_y * other 88 | return self.__class__(new_I_x.l, new_I_x.r, new_I_y.l, new_I_y.r) 89 | else: 90 | new_I_x = self.I_x * other 91 | new_I_y = self.I_y * other 92 | return self.__class__(new_I_x.r, new_I_x.l, new_I_y.r, new_I_y.l) 93 | else: 94 | return NotImplemented 95 | 96 | def __rmul__(self, other): 97 | if isinstance(other, numbers.Real): 98 | return self * other 99 | else: 100 | return NotImplemented 101 | 102 | @cached_property 103 | def area(self): 104 | return self.I_x.width * self.I_y.width 105 | 106 | def plot(self, ax, color='black'): 107 | x = [self.I_x.l, self.I_x.l, self.I_x.r, self.I_x.r, self.I_x.l] 108 | y = [self.I_y.l, self.I_y.r, self.I_y.r, self.I_y.l, self.I_y.l] 109 | ax.plot(x, y, c=color) 110 | 111 | 112 | class Ellipse(): 113 | def __init__(self, D, p): 114 | self.D = D 115 | self.p = p 116 | 117 | @property 118 | def px(self): 119 | return self.p[0] 120 | 121 | @px.setter 122 | def px(self, px): 123 | self.p[0] = px 124 | 125 | @property 126 | def py(self): 127 | return self.p[1] 128 | 129 | @py.setter 130 | def py(self, py): 131 | self.p[1] = py 132 | 133 | @property 134 | def a(self): 135 | return self.D[0, 0] 136 | 137 | @a.setter 138 | def a(self, a): 139 | self.D[0, 0] = a 140 | 141 | @property 142 | def b(self): 143 | return self.D[0, 1] 144 | 145 | @b.setter 146 | def b(self, b): 147 | self.D[0, 1] = b 148 | self.D[1, 0] = b 149 | 150 | @property 151 | def d(self): 152 | return self.D[1, 1] 153 | 154 | @d.setter 155 | def d(self, d): 156 | self.D[1, 1] = d 157 | 158 | def inside(self, v): 159 | x = v[0] - self.px 160 | y = v[1] - self.py 161 | tmp = self.a * x * x + 2 * self.b * x * y + self.d * y * y 162 | return tmp <= 1 163 | 164 | def bbox(self): 165 | sqrt_det = self.sqrt_det 166 | w = sqrt(self.d) / sqrt_det 167 | h = sqrt(self.a) / sqrt_det 168 | return Rectangle(self.px - w, self.px + w, self.py - h, self.py + h) 169 | 170 | def __mul__(self, other): 171 | if isinstance(other, numbers.Real): 172 | return self.__class__(self.D * (1 / other) ** 2, self.p * other) 173 | else: 174 | return NotImplemented 175 | 176 | def __rmul__(self, other): 177 | if isinstance(other, GridOp): 178 | M00 = other.inv.toMat[0, 0] 179 | M01 = other.inv.toMat[0, 1] 180 | M10 = other.inv.toMat[1, 0] 181 | M11 = other.inv.toMat[1, 1] 182 | a = self.a * M00 * M00 + 2 * self.b * M00 * M10 + self.d * M10 * M10 183 | b = self.a * M00 * M01 + self.b * (M00 * M11 + M01 * M10) + self.d * M10 * M11 184 | d = self.a * M01 * M01 + 2 * self.b * M11 * M01 + self.d * M11 * M11 185 | new_D = mpmath.matrix([[a, b], [b, d]]) 186 | 187 | M00 = other.toMat[0, 0] 188 | M01 = other.toMat[0, 1] 189 | M10 = other.toMat[1, 0] 190 | M11 = other.toMat[1, 1] 191 | px = M00 * self.px + M01 * self.py 192 | py = M10 * self.px + M11 * self.py 193 | new_p = mpmath.matrix([px, py]) 194 | 195 | return self.__class__(new_D, new_p) 196 | elif isinstance(other, numbers.Real): 197 | return self * other 198 | else: 199 | return NotImplemented 200 | 201 | def __truediv__(self, other): 202 | if isinstance(other, numbers.Real): 203 | return self.__class__(self.D * other ** 2, self.p / other) 204 | else: 205 | return NotImplemented 206 | 207 | @property 208 | def area(self): 209 | return mpmath.mp.pi / self.sqrt_det 210 | 211 | @property 212 | def sqrt_det(self): 213 | det = self.d * self.a - self.b ** 2 214 | return sqrt(det) 215 | 216 | def normalize(self): 217 | return self.__class__(self.D / self.sqrt_det, self.p * sqrt(self.sqrt_det)) 218 | 219 | @property 220 | def skew(self): 221 | return self.b ** 2 222 | 223 | @property 224 | def bias(self): 225 | return self.d / self.a 226 | 227 | def plot(self, ax, n=5000): 228 | eig_val, eig_vec = mpmath.eigsy(self.D) 229 | vx = [self.px] * n 230 | vy = [self.py] * n 231 | for i in range(n): 232 | t = mpmath.mp.pi * 2 * i / n 233 | vx[i] += eig_vec[0, 0] * mpmath.cos(t) / sqrt(eig_val[0]) 234 | vx[i] += eig_vec[0, 1] * mpmath.sin(t) / sqrt(eig_val[1]) 235 | vy[i] += eig_vec[1, 0] * mpmath.cos(t) / sqrt(eig_val[0]) 236 | vy[i] += eig_vec[1, 1] * mpmath.sin(t) / sqrt(eig_val[1]) 237 | ax.plot(vx, vy, c='orangered') 238 | 239 | 240 | class ConvexSet(ABC): 241 | def __init__(self, ellipse): 242 | self._ellipse = ellipse 243 | 244 | @abstractmethod 245 | def inside(self, u): 246 | pass 247 | 248 | @property 249 | def ellipse(self): 250 | return self._ellipse 251 | 252 | @abstractmethod 253 | def intersect(self, u, v): 254 | pass 255 | -------------------------------------------------------------------------------- /pygridsynth/ring.py: -------------------------------------------------------------------------------- 1 | import numbers 2 | from functools import cached_property, total_ordering 3 | import mpmath 4 | 5 | from .mymath import SQRT2, ntz, sign, floorsqrt, rounddiv, pow_sqrt2 6 | 7 | 8 | @total_ordering 9 | class ZRootTwo(): 10 | def __init__(self, a, b): 11 | self._a = a 12 | self._b = b 13 | 14 | @property 15 | def a(self): 16 | return self._a 17 | 18 | @property 19 | def b(self): 20 | return self._b 21 | 22 | @cached_property 23 | def coef(self): 24 | return [self._a, self._b] 25 | 26 | def __repr__(self): 27 | return f"ZRootTwo({self._a}, {self._b})" 28 | 29 | def __str__(self): 30 | return f"{self._a}{self._b:+}√2" 31 | 32 | @classmethod 33 | def from_int(cls, x): 34 | return cls(x, 0) 35 | 36 | @classmethod 37 | def from_zomega(cls, x): 38 | if x.b == 0 and x.a == -x.c: 39 | return cls(x.d, x.c) 40 | else: 41 | raise ValueError 42 | 43 | def __eq__(self, other): 44 | if isinstance(other, numbers.Integral): 45 | return self == self.from_int(other) 46 | elif isinstance(other, self.__class__): 47 | return self._a == other.a and self._b == other.b 48 | else: 49 | return False 50 | 51 | def __lt__(self, other): 52 | if isinstance(other, numbers.Integral): 53 | return self < self.from_int(other) 54 | elif isinstance(other, self.__class__): 55 | if self._b < other.b: 56 | return self._a < other.a or (self._a - other.a) ** 2 < 2 * (self._b - other.b) ** 2 57 | else: 58 | return self._a < other.a and (self._a - other.a) ** 2 > 2 * (self._b - other.b) ** 2 59 | else: 60 | return False 61 | 62 | def __add__(self, other): 63 | if isinstance(other, numbers.Integral): 64 | return self + self.from_int(other) 65 | elif isinstance(other, self.__class__): 66 | return self.__class__(self._a + other.a, self._b + other.b) 67 | else: 68 | return NotImplemented 69 | 70 | def __radd__(self, other): 71 | if isinstance(other, numbers.Integral): 72 | return self + other 73 | elif isinstance(other, self.__class__): 74 | return self + other 75 | else: 76 | return NotImplemented 77 | 78 | def __sub__(self, other): 79 | return self + (- other) 80 | 81 | def __rsub__(self, other): 82 | return (-self) + other 83 | 84 | def __neg__(self): 85 | return self.__class__(-self._a, -self._b) 86 | 87 | def __mul__(self, other): 88 | if isinstance(other, numbers.Integral): 89 | return self * self.from_int(other) 90 | elif isinstance(other, self.__class__): 91 | new_a = self._a * other.a + 2 * self._b * other.b 92 | new_b = self._a * other.b + self._b * other.a 93 | return self.__class__(new_a, new_b) 94 | else: 95 | return NotImplemented 96 | 97 | def __rmul__(self, other): 98 | if isinstance(other, numbers.Integral): 99 | return self * other 100 | elif isinstance(other, self.__class__): 101 | return self * other 102 | else: 103 | return NotImplemented 104 | 105 | @cached_property 106 | def inv(self): 107 | if self.norm == 1: 108 | return self.conj_sq2 109 | elif self.norm == -1: 110 | return -self.conj_sq2 111 | else: 112 | raise ZeroDivisionError 113 | 114 | def __pow__(self, other): 115 | if isinstance(other, numbers.Integral): 116 | if other < 0: 117 | return self.inv ** -other 118 | else: 119 | new = self.__class__(1, 0) 120 | tmp = self 121 | while other > 0: 122 | if other & 1: 123 | new *= tmp 124 | tmp *= tmp 125 | other >>= 1 126 | return new 127 | else: 128 | return NotImplemented 129 | 130 | def sqrt(self): 131 | norm = self.norm 132 | if norm < 0 or self._a < 0: 133 | return None 134 | r = floorsqrt(norm) 135 | a1 = floorsqrt((self._a + r) // 2) 136 | b1 = floorsqrt((self._a - r) // 4) 137 | a2 = floorsqrt((self._a - r) // 2) 138 | b2 = floorsqrt((self._a + r) // 4) 139 | if sign(self._a) * sign(self._b) >= 0: 140 | w1 = ZRootTwo(a1, b1) 141 | w2 = ZRootTwo(a2, b2) 142 | else: 143 | w1 = ZRootTwo(a1, -b1) 144 | w2 = ZRootTwo(a2, -b2) 145 | if self == w1 * w1: 146 | return w1 147 | elif self == w2 * w2: 148 | return w2 149 | else: 150 | return None 151 | 152 | def __divmod__(self, other): 153 | if isinstance(other, numbers.Integral): 154 | return divmod(self, self.from_int(other)) 155 | elif isinstance(other, self.__class__): 156 | p = self * other.conj_sq2 157 | k = other.norm 158 | q = self.__class__(rounddiv(p.a, k), rounddiv(p.b, k)) 159 | r = self - other * q 160 | return q, r 161 | else: 162 | return NotImplemented 163 | 164 | def __rdivmod__(self, other): 165 | if isinstance(other, numbers.Integral): 166 | return divmod(self.from_int(other), self) 167 | elif isinstance(other, self.__class__): 168 | return divmod(other, self) 169 | else: 170 | return NotImplemented 171 | 172 | def __floordiv__(self, other): 173 | q, _ = divmod(self, other) 174 | return q 175 | 176 | def __rfloordiv__(self, other): 177 | q, _ = divmod(other, self) 178 | return q 179 | 180 | def __mod__(self, other): 181 | _, r = divmod(self, other) 182 | return r 183 | 184 | def __rmod__(self, other): 185 | _, r = divmod(other, self) 186 | return r 187 | 188 | @classmethod 189 | def sim(cls, a, b): 190 | return a % b == 0 and b % a == 0 191 | 192 | @classmethod 193 | def ext_gcd(cls, a, b): 194 | if isinstance(a, numbers.Integral): 195 | a = cls.from_int(a) 196 | if isinstance(b, numbers.Integral): 197 | b = cls.from_int(b) 198 | x = cls.from_int(1) 199 | y = cls.from_int(0) 200 | z = cls.from_int(0) 201 | w = cls.from_int(1) 202 | while b != 0: 203 | q, r = divmod(a, b) 204 | x, y = y, x - y * q 205 | z, w = w, z - w * q 206 | a, b = b, r 207 | return x, z, a 208 | 209 | @classmethod 210 | def gcd(cls, a, b): 211 | _, _, g = cls.ext_gcd(a, b) 212 | return g 213 | 214 | @cached_property 215 | def parity(self): 216 | return self._a & 1 217 | 218 | @cached_property 219 | def norm(self): 220 | return self._a ** 2 - 2 * self._b ** 2 221 | 222 | @cached_property 223 | def to_real(self): 224 | return self._a + SQRT2() * self._b 225 | 226 | @cached_property 227 | def conj_sq2(self): 228 | return self.__class__(self._a, -self._b) 229 | 230 | 231 | @total_ordering 232 | class DRootTwo(): 233 | def __init__(self, alpha, k): 234 | self._alpha = alpha 235 | self._k = k 236 | 237 | @property 238 | def alpha(self): 239 | return self._alpha 240 | 241 | @property 242 | def k(self): 243 | return self._k 244 | 245 | def __repr__(self): 246 | return f"DRootTwo({self._alpha}, {self._k})" 247 | 248 | def __str__(self): 249 | return f"{self._alpha} / √2^{self._k}" 250 | 251 | @classmethod 252 | def from_int(cls, x): 253 | return cls(ZRootTwo.from_int(x), 0) 254 | 255 | @classmethod 256 | def from_zroottwo(cls, x): 257 | return cls(x, 0) 258 | 259 | @classmethod 260 | def from_zomega(cls, x): 261 | return cls(ZRootTwo.from_zomega(x), 0) 262 | 263 | @classmethod 264 | def fromDOmega(cls, x): 265 | return cls(ZRootTwo.from_zomega(x.u), x.k) 266 | 267 | def __eq__(self, other): 268 | if isinstance(other, numbers.Integral): 269 | return self == self.from_int(other) 270 | elif isinstance(other, ZRootTwo): 271 | return self == self.from_zroottwo(other) 272 | elif isinstance(other, self.__class__): 273 | if self._k < other.k: 274 | return self.renew_denomexp(other.k) == other 275 | elif self._k > other.k: 276 | return self == other.renew_denomexp(self._k) 277 | else: 278 | return self._alpha == other.alpha and self._k == other.k 279 | else: 280 | return False 281 | 282 | def __lt__(self, other): 283 | if isinstance(other, numbers.Integral): 284 | return self < self.from_int(other) 285 | elif isinstance(other, ZRootTwo): 286 | return self < self.from_zroottwo(other) 287 | elif isinstance(other, self.__class__): 288 | if self._k < other.k: 289 | return self.renew_denomexp(other.k) < other 290 | elif self._k > other.k: 291 | return self < other.renew_denomexp(self._k) 292 | else: 293 | return self._alpha < other.alpha 294 | else: 295 | return False 296 | 297 | def __add__(self, other): 298 | if isinstance(other, numbers.Integral): 299 | return self + self.from_int(other) 300 | elif isinstance(other, ZRootTwo): 301 | return self + self.from_zroottwo(other) 302 | elif isinstance(other, self.__class__): 303 | if self._k < other.k: 304 | return self.renew_denomexp(other.k) + other 305 | elif self._k > other.k: 306 | return self + other.renew_denomexp(self._k) 307 | else: 308 | return self.__class__(self._alpha + other.alpha, self._k) 309 | else: 310 | return NotImplemented 311 | 312 | def __radd__(self, other): 313 | if isinstance(other, numbers.Integral): 314 | return self + other 315 | elif isinstance(other, ZRootTwo): 316 | return self + other 317 | elif isinstance(other, self.__class__): 318 | return self + other 319 | else: 320 | return NotImplemented 321 | 322 | def __sub__(self, other): 323 | return self + (- other) 324 | 325 | def __rsub__(self, other): 326 | return (-self) + other 327 | 328 | def __neg__(self): 329 | return self.__class__(-self._alpha, self._k) 330 | 331 | def __mul__(self, other): 332 | if isinstance(other, numbers.Integral): 333 | return self * self.from_int(other) 334 | elif isinstance(other, ZRootTwo): 335 | return self * self.from_zroottwo(other) 336 | elif isinstance(other, self.__class__): 337 | return self.__class__(self._alpha * other.alpha, self._k + other.k) 338 | else: 339 | return NotImplemented 340 | 341 | def __rmul__(self, other): 342 | if isinstance(other, numbers.Integral): 343 | return self * other 344 | elif isinstance(other, ZRootTwo): 345 | return self * other 346 | elif isinstance(other, self.__class__): 347 | return self * other 348 | else: 349 | return NotImplemented 350 | 351 | def renew_denomexp(self, new_k): 352 | new_alpha = self.mul_by_sqrt2_power(new_k - self._k).alpha 353 | return self.__class__(new_alpha, new_k) 354 | 355 | def reduce_denomexp(self): 356 | k_a = self._k if self._alpha.a == 0 else ntz(self._alpha.a) 357 | k_b = self._k if self._alpha.b == 0 else ntz(self._alpha.b) 358 | new_k = self._k - k_a * 2 if k_a <= k_b else self._k - k_b * 2 - 1 359 | return self.renew_denomexp(0 if new_k < 0 else new_k) 360 | 361 | def mul_by_inv_sqrt2(self): 362 | if not (self._alpha.a & 1): 363 | new_alpha = ZRootTwo(self._alpha.b, self._alpha.a >> 1) 364 | else: 365 | raise ValueError 366 | return self.__class__(new_alpha, self._k) 367 | 368 | def mul_by_sqrt2_power(self, d): 369 | if d < 0: 370 | if d == -1: 371 | return self.mul_by_inv_sqrt2() 372 | d_div_2, d_mod_2 = (-d) >> 1, (-d) & 1 373 | if d_mod_2 == 0: 374 | bit = (1 << d_div_2) - 1 375 | if self._alpha.a & bit == 0 and self._alpha.b & bit == 0: 376 | new_alpha = ZRootTwo(self._alpha.a >> d_div_2, self._alpha.b >> d_div_2) 377 | else: 378 | raise ValueError 379 | else: 380 | bit = (1 << d_div_2) - 1 381 | bit2 = (1 << (d_div_2 + 1)) - 1 382 | if self._alpha.a & bit2 == 0 and self._alpha.b & bit == 0: 383 | new_alpha = ZRootTwo(self._alpha.b >> d_div_2, self._alpha.a >> (d_div_2 + 1)) 384 | else: 385 | raise ValueError 386 | return self.__class__(new_alpha, self._k) 387 | else: 388 | d_div_2, d_mod_2 = d >> 1, d & 1 389 | new_alpha = self._alpha * (1 << d_div_2) 390 | if d_mod_2: 391 | new_alpha *= ZRootTwo(0, 1) 392 | return self.__class__(new_alpha, self._k) 393 | 394 | def mul_by_sqrt2_power_renewing_denomexp(self, d): 395 | if d > self._k: 396 | raise ValueError 397 | return self.__class__(self._alpha, self._k - d) 398 | 399 | @cached_property 400 | def parity(self): 401 | return self._alpha.parity 402 | 403 | @cached_property 404 | def scale(self): 405 | return pow_sqrt2(self._k) 406 | 407 | @cached_property 408 | def squared_scale(self): 409 | return 1 << self._k 410 | 411 | @cached_property 412 | def to_real(self): 413 | return self.alpha.to_real / self.scale 414 | 415 | @cached_property 416 | def conj_sq2(self): 417 | return (self.__class__(- self._alpha.conj_sq2, self._k) if self._k & 1 418 | else self.__class__(self._alpha.conj_sq2, self._k)) 419 | 420 | @classmethod 421 | def power_of_inv_sqrt2(cls, k): 422 | return cls(ZRootTwo(1, 0), k) 423 | 424 | 425 | class ZOmega(): 426 | def __init__(self, a, b, c, d): 427 | self._a = a 428 | self._b = b 429 | self._c = c 430 | self._d = d 431 | 432 | @property 433 | def a(self): 434 | return self._a 435 | 436 | @property 437 | def b(self): 438 | return self._b 439 | 440 | @property 441 | def c(self): 442 | return self._c 443 | 444 | @property 445 | def d(self): 446 | return self._d 447 | 448 | @cached_property 449 | def coef(self): 450 | return [self._d, self._c, self._b, self._a] 451 | 452 | def __repr__(self): 453 | return f"ZOmega({self._a}, {self._b}, {self._c}, {self._d})" 454 | 455 | def __str__(self): 456 | return f"{self._a}ω^3{self._b:+}ω^2{self._c:+}ω{self._d:+}" 457 | 458 | @classmethod 459 | def from_int(cls, x): 460 | return cls(0, 0, 0, x) 461 | 462 | @classmethod 463 | def from_zroottwo(cls, x): 464 | return cls(-x.b, 0, x.b, x.a) 465 | 466 | def __eq__(self, other): 467 | if isinstance(other, numbers.Integral): 468 | return self == self.from_int(other) 469 | elif isinstance(other, ZRootTwo): 470 | return self == self.from_zroottwo(other) 471 | elif isinstance(other, self.__class__): 472 | return (self._a == other.a and self._b == other.b 473 | and self._c == other.c and self._d == other.d) 474 | else: 475 | return False 476 | 477 | def __add__(self, other): 478 | if isinstance(other, numbers.Integral): 479 | return self + self.from_int(other) 480 | elif isinstance(other, ZRootTwo): 481 | return self + self.from_zroottwo(other) 482 | elif isinstance(other, self.__class__): 483 | return self.__class__(self._a + other.a, self._b + other.b, 484 | self._c + other.c, self._d + other.d) 485 | else: 486 | return NotImplemented 487 | 488 | def __radd__(self, other): 489 | if isinstance(other, numbers.Integral): 490 | return self + other 491 | elif isinstance(other, ZRootTwo): 492 | return self + other 493 | elif isinstance(other, self.__class__): 494 | return self + other 495 | else: 496 | return NotImplemented 497 | 498 | def __sub__(self, other): 499 | return self + (- other) 500 | 501 | def __rsub__(self, other): 502 | return (-self) + other 503 | 504 | def __neg__(self): 505 | return self.__class__(-self._a, -self._b, -self._c, -self._d) 506 | 507 | def __mul__(self, other): 508 | if isinstance(other, numbers.Integral): 509 | return self * self.from_int(other) 510 | elif isinstance(other, ZRootTwo): 511 | return self * self.from_zroottwo(other) 512 | elif isinstance(other, self.__class__): 513 | new_coef = [0] * 4 514 | for i in range(4): 515 | for j in range(4): 516 | if i + j < 4: 517 | new_coef[i + j] += self.coef[i] * other.coef[j] 518 | else: 519 | new_coef[i + j - 4] -= self.coef[i] * other.coef[j] 520 | return self.__class__(*reversed(new_coef)) 521 | else: 522 | return NotImplemented 523 | 524 | def __rmul__(self, other): 525 | if isinstance(other, numbers.Integral): 526 | return self * other 527 | elif isinstance(other, ZRootTwo): 528 | return self * other 529 | elif isinstance(other, self.__class__): 530 | return self * other 531 | else: 532 | return NotImplemented 533 | 534 | @cached_property 535 | def inv(self): 536 | if self.norm == 1: 537 | return self.conj_sq2 * self.conj * self.conj.conj_sq2 538 | else: 539 | raise ZeroDivisionError 540 | 541 | def __pow__(self, other): 542 | if isinstance(other, int): 543 | if other < 0: 544 | return NotImplemented 545 | else: 546 | new = self.from_int(1) 547 | tmp = self 548 | while other > 0: 549 | if other & 1: 550 | new *= tmp 551 | tmp *= tmp 552 | other >>= 1 553 | return new 554 | else: 555 | return NotImplemented 556 | 557 | def __divmod__(self, other): 558 | if isinstance(other, numbers.Integral): 559 | return divmod(self, self.from_int(other)) 560 | elif isinstance(other, ZRootTwo): 561 | return divmod(self, self.from_zroottwo(other)) 562 | elif isinstance(other, self.__class__): 563 | p = self * other.conj * other.conj.conj_sq2 * other.conj_sq2 564 | k = other.norm 565 | q = self.__class__(rounddiv(p.a, k), rounddiv(p.b, k), 566 | rounddiv(p.c, k), rounddiv(p.d, k)) 567 | r = self - other * q 568 | return q, r 569 | else: 570 | return NotImplemented 571 | 572 | def __rdivmod__(self, other): 573 | if isinstance(other, numbers.Integral): 574 | return divmod(self.from_int(other), self) 575 | elif isinstance(other, ZRootTwo): 576 | return divmod(self.from_zroottwo(other), self) 577 | elif isinstance(other, self.__class__): 578 | return divmod(other, self) 579 | else: 580 | return NotImplemented 581 | 582 | def __floordiv__(self, other): 583 | q, _ = divmod(self, other) 584 | return q 585 | 586 | def __rfloordiv__(self, other): 587 | q, _ = divmod(other, self) 588 | return q 589 | 590 | def __mod__(self, other): 591 | _, r = divmod(self, other) 592 | return r 593 | 594 | def __rmod__(self, other): 595 | _, r = divmod(other, self) 596 | return r 597 | 598 | @classmethod 599 | def sim(cls, a, b): 600 | return a % b == 0 and b % a == 0 601 | 602 | @classmethod 603 | def ext_gcd(cls, a, b): 604 | if isinstance(a, numbers.Integral): 605 | a = cls.from_int(a) 606 | elif isinstance(a, ZRootTwo): 607 | a = cls.from_zroottwo(a) 608 | if isinstance(b, numbers.Integral): 609 | b = cls.from_int(b) 610 | elif isinstance(b, ZRootTwo): 611 | b = cls.from_zroottwo(b) 612 | x = cls.from_int(1) 613 | y = cls.from_int(0) 614 | z = cls.from_int(0) 615 | w = cls.from_int(1) 616 | while b != 0: 617 | q, r = divmod(a, b) 618 | x, y = y, x - y * q 619 | z, w = w, z - w * q 620 | a, b = b, r 621 | return x, z, a 622 | 623 | @classmethod 624 | def gcd(cls, a, b): 625 | _, _, g = cls.ext_gcd(a, b) 626 | return g 627 | 628 | def mul_by_omega(self): 629 | return self.__class__(self._b, self._c, self._d, -self._a) 630 | 631 | def mul_by_omega_inv(self): 632 | return self.__class__(-self._d, self._a, self._b, self._c) 633 | 634 | def mul_by_omega_power(self, n): 635 | if n >= 8 or n < 0: 636 | n &= 0b111 637 | if n & 0b100: 638 | return (-self).mul_by_omega_power(n & 0b11) 639 | else: 640 | coef = self.coef 641 | new_coef = [0] * 4 642 | for i in range(n): 643 | new_coef[i] = -coef[i - n] 644 | for i in range(n, 4): 645 | new_coef[i] = coef[i - n] 646 | return self.__class__(*reversed(new_coef)) 647 | 648 | @cached_property 649 | def residue(self): 650 | return (self._a & 1) << 3 | (self._b & 1) << 2 | (self._c & 1) << 1 | (self._d & 1) 651 | 652 | @cached_property 653 | def norm(self): 654 | return ((self._a ** 2 + self._b ** 2 + self._c ** 2 + self._d ** 2) ** 2 655 | - 2 * (self._a * self._b + self._b * self._c 656 | + self._c * self._d - self._d * self._a) ** 2) 657 | 658 | @cached_property 659 | def real(self): 660 | return self._d + SQRT2() * (self._c - self._a) / 2 661 | 662 | @cached_property 663 | def imag(self): 664 | return self._b + SQRT2() * (self._c + self._a) / 2 665 | 666 | @cached_property 667 | def to_complex(self): 668 | return self.real + 1.j * self.imag 669 | 670 | @cached_property 671 | def to_vector(self): 672 | return mpmath.matrix([self.real, self.imag]) 673 | 674 | @cached_property 675 | def conj(self): 676 | return self.__class__(-self._c, -self._b, -self._a, self._d) 677 | 678 | @cached_property 679 | def conj_sq2(self): 680 | return self.__class__(-self._a, self._b, -self._c, self._d) 681 | 682 | 683 | class DOmega(): 684 | def __init__(self, u, k): 685 | self._u = u 686 | self._k = k 687 | 688 | @property 689 | def u(self): 690 | return self._u 691 | 692 | @property 693 | def k(self): 694 | return self._k 695 | 696 | def __repr__(self): 697 | return f"DOmega({repr(self._u)}, {self._k})" 698 | 699 | def __str__(self): 700 | return f"{self._u} / √2^{self._k}" 701 | 702 | @classmethod 703 | def from_int(cls, x): 704 | return cls(ZOmega.from_int(x), 0) 705 | 706 | @classmethod 707 | def from_zroottwo(cls, x): 708 | return cls(ZOmega.from_zroottwo(x), 0) 709 | 710 | @classmethod 711 | def from_droottwo(cls, x): 712 | return cls(ZOmega.from_zroottwo(x.alpha), x.k) 713 | 714 | @classmethod 715 | def from_droottwo_vector(cls, x, y, k): 716 | return (cls.from_droottwo(x) + cls.from_droottwo(y) * ZOmega(0, 1, 0, 0)).renew_denomexp(k) 717 | 718 | @classmethod 719 | def from_zomega(cls, x): 720 | return cls(x, 0) 721 | 722 | def __eq__(self, other): 723 | if isinstance(other, numbers.Integral): 724 | return self == self.from_int(other) 725 | elif isinstance(other, ZRootTwo): 726 | return self == self.from_zroottwo(other) 727 | elif isinstance(other, ZOmega): 728 | return self == self.from_zomega(other) 729 | elif isinstance(other, self.__class__): 730 | if self._k < other.k: 731 | return self.renew_denomexp(other.k) == other 732 | elif self._k > other.k: 733 | return self == other.renew_denomexp(self._k) 734 | else: 735 | return self._u == other.u and self._k == other.k 736 | else: 737 | return False 738 | 739 | def __add__(self, other): 740 | if isinstance(other, numbers.Integral): 741 | return self + self.from_int(other) 742 | elif isinstance(other, ZRootTwo): 743 | return self + self.from_zroottwo(other) 744 | elif isinstance(other, ZOmega): 745 | return self + self.from_zomega(other) 746 | elif isinstance(other, self.__class__): 747 | if self._k < other.k: 748 | return self.renew_denomexp(other.k) + other 749 | elif self._k > other.k: 750 | return self + other.renew_denomexp(self._k) 751 | else: 752 | return self.__class__(self._u + other.u, self._k) 753 | else: 754 | return NotImplemented 755 | 756 | def __radd__(self, other): 757 | if isinstance(other, numbers.Integral): 758 | return self + other 759 | elif isinstance(other, ZRootTwo): 760 | return self + other 761 | elif isinstance(other, ZOmega): 762 | return self + other 763 | elif isinstance(other, self.__class__): 764 | return self + other 765 | else: 766 | return NotImplemented 767 | 768 | def __sub__(self, other): 769 | return self + (- other) 770 | 771 | def __rsub__(self, other): 772 | return (-self) + other 773 | 774 | def __neg__(self): 775 | return self.__class__(-self._u, self._k) 776 | 777 | def __mul__(self, other): 778 | if isinstance(other, numbers.Integral): 779 | return self * self.from_int(other) 780 | elif isinstance(other, ZRootTwo): 781 | return self * self.from_zroottwo(other) 782 | elif isinstance(other, ZOmega): 783 | return self * self.from_zomega(other) 784 | elif isinstance(other, self.__class__): 785 | return self.__class__(self._u * other.u, self._k + other.k) 786 | else: 787 | return NotImplemented 788 | 789 | def __rmul__(self, other): 790 | if isinstance(other, numbers.Integral): 791 | return self * other 792 | elif isinstance(other, ZRootTwo): 793 | return self * other 794 | elif isinstance(other, ZOmega): 795 | return self * other 796 | elif isinstance(other, self.__class__): 797 | return self * other 798 | else: 799 | return NotImplemented 800 | 801 | def renew_denomexp(self, new_k): 802 | new_u = self.mul_by_sqrt2_power(new_k - self._k).u 803 | return self.__class__(new_u, new_k) 804 | 805 | def reduce_denomexp(self): 806 | k_a = self._k if self._u.a == 0 else ntz(self._u.a) 807 | k_b = self._k if self._u.b == 0 else ntz(self._u.b) 808 | k_c = self._k if self._u.c == 0 else ntz(self._u.c) 809 | k_d = self._k if self._u.d == 0 else ntz(self._u.d) 810 | reduce_k = min(k_a, k_b, k_c, k_d) 811 | new_k = self._k - reduce_k * 2 812 | bit = (1 << (reduce_k + 1)) - 1 813 | if (self._u.c + self._u.a) & bit == 0 and (self._u.b + self._u.d) & bit == 0: 814 | new_k -= 1 815 | return self.renew_denomexp(0 if new_k < 0 else new_k) 816 | 817 | def mul_by_inv_sqrt2(self): 818 | if not ((self._u.b + self._u.d) & 1) and not ((self._u.c + self._u.a) & 1): 819 | new_u = ZOmega((self._u.b - self._u.d) >> 1, 820 | (self._u.c + self._u.a) >> 1, 821 | (self._u.b + self._u.d) >> 1, 822 | (self._u.c - self._u.a) >> 1) 823 | else: 824 | raise ValueError 825 | return self.__class__(new_u, self._k) 826 | 827 | def mul_by_sqrt2_power(self, d): 828 | if d < 0: 829 | if d == -1: 830 | return self.mul_by_inv_sqrt2() 831 | d_div_2, d_mod_2 = (-d) >> 1, (-d) & 1 832 | if d_mod_2 == 0: 833 | bit = (1 << d_div_2) - 1 834 | if (self._u.a & bit == 0 and self._u.b & bit == 0 835 | and self._u.c & bit == 0 and self._u.c & bit == 0): 836 | new_u = ZOmega(self._u.a >> d_div_2, self._u.b >> d_div_2, 837 | self._u.c >> d_div_2, self._u.d >> d_div_2) 838 | else: 839 | raise ValueError 840 | else: 841 | bit = (1 << (d_div_2 + 1)) - 1 842 | if ((self._u.b - self._u.d) & bit == 0 843 | and (self._u.c + self._u.a) & bit == 0 844 | and (self._u.b + self._u.d) & bit == 0 845 | and (self._u.c - self._u.a) & bit == 0): 846 | new_u = ZOmega((self._u.b - self._u.d) >> (d_div_2 + 1), 847 | (self._u.c + self._u.a) >> (d_div_2 + 1), 848 | (self._u.b + self._u.d) >> (d_div_2 + 1), 849 | (self._u.c - self._u.a) >> (d_div_2 + 1)) 850 | else: 851 | raise ValueError 852 | return self.__class__(new_u, self._k) 853 | else: 854 | d_div_2, d_mod_2 = d >> 1, d & 1 855 | new_u = self._u * (1 << d_div_2) 856 | if d_mod_2: 857 | new_u *= ZOmega(-1, 0, 1, 0) 858 | return self.__class__(new_u, self._k) 859 | 860 | def mul_by_omega(self): 861 | return self.__class__(self._u.mul_by_omega(), self._k) 862 | 863 | def mul_by_omega_inv(self): 864 | return self.__class__(self._u.mul_by_omega_inv(), self._k) 865 | 866 | def mul_by_omega_power(self, n): 867 | return self.__class__(self._u.mul_by_omega_power(n), self._k) 868 | 869 | @cached_property 870 | def scale(self): 871 | return pow_sqrt2(self._k) 872 | 873 | @cached_property 874 | def squared_scale(self): 875 | return 1 << self._k 876 | 877 | @property 878 | def residue(self): 879 | return self._u.residue 880 | 881 | @cached_property 882 | def real(self): 883 | return self._u.real / self.scale 884 | 885 | @cached_property 886 | def imag(self): 887 | return self._u.imag / self.scale 888 | 889 | @cached_property 890 | def to_complex(self): 891 | return self.real + 1.j * self.imag 892 | 893 | @cached_property 894 | def to_vector(self): 895 | return mpmath.matrix([self.real, self.imag]) 896 | 897 | @cached_property 898 | def conj(self): 899 | return self.__class__(self._u.conj, self._k) 900 | 901 | @cached_property 902 | def conj_sq2(self): 903 | return (self.__class__(- self._u.conj_sq2, self._k) if self._k & 1 904 | else self.__class__(self._u.conj_sq2, self._k)) 905 | 906 | 907 | LAMBDA = ZRootTwo(1, 1) 908 | OMEGA = ZOmega(0, 0, 1, 0) 909 | OMEGA_POWER = [ZOmega(0, 0, 0, 1), ZOmega(0, 0, 1, 0), ZOmega(0, 1, 0, 0), ZOmega(1, 0, 0, 0), 910 | ZOmega(0, 0, 0, -1), ZOmega(0, 0, -1, 0), ZOmega(0, -1, 0, 0), ZOmega(-1, 0, 0, 0)] 911 | -------------------------------------------------------------------------------- /pygridsynth/synthesis_of_cliffordT.py: -------------------------------------------------------------------------------- 1 | from .ring import OMEGA_POWER 2 | from .unitary import DOmegaUnitary 3 | from .normal_form import NormalForm 4 | 5 | BIT_SHIFT = [0, 0, 1, 0, 2, 0, 1, 3, 3, 3, 0, 2, 2, 1, 0, 0] 6 | BIT_COUNT = [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4] 7 | 8 | 9 | def _reduce_denomexp(unitary): 10 | T_POWER_and_H = ["H", "TH", "SH", "TSH"] 11 | residue_z = unitary.z.residue 12 | residue_w = unitary.w.residue 13 | residue_squared_z = (unitary.z.u * unitary.z.conj.u).residue 14 | 15 | m = BIT_SHIFT[residue_w] - BIT_SHIFT[residue_z] 16 | if m < 0: 17 | m += 4 18 | if residue_squared_z == 0b0000: 19 | unitary = unitary.mul_by_H_and_T_power_from_left(0).renew_denomexp(unitary.k - 1) 20 | return T_POWER_and_H[0], unitary 21 | elif residue_squared_z == 0b1010: 22 | unitary = unitary.mul_by_H_and_T_power_from_left(-m).renew_denomexp(unitary.k - 1) 23 | return T_POWER_and_H[m], unitary 24 | elif residue_squared_z == 0b0001: 25 | if BIT_COUNT[residue_z] == BIT_COUNT[residue_w]: 26 | unitary = unitary.mul_by_H_and_T_power_from_left(-m).renew_denomexp(unitary.k - 1) 27 | return T_POWER_and_H[m], unitary 28 | else: 29 | unitary = unitary.mul_by_H_and_T_power_from_left(-m) 30 | return T_POWER_and_H[m], unitary 31 | 32 | 33 | def decompose_domega_unitary(unitary): 34 | gates = "" 35 | while unitary.k > 0: 36 | g, unitary = _reduce_denomexp(unitary) 37 | gates += g 38 | 39 | if unitary.n & 1: 40 | gates += "T" 41 | unitary = unitary.mul_by_T_inv_from_left() 42 | if unitary.z == 0: 43 | gates += "X" 44 | unitary = unitary.mul_by_X_from_left() 45 | for m in range(8): 46 | if unitary.z == OMEGA_POWER[m]: 47 | m_W = m 48 | unitary = unitary.mul_by_W_power_from_left(-m_W) 49 | break 50 | m_S = unitary.n >> 1 51 | gates += "S" * m_S 52 | unitary = unitary.mul_by_S_power_from_left(-m_S) 53 | gates += "W" * m_W 54 | 55 | assert unitary == DOmegaUnitary.identity(), "decomposition failed..." 56 | gates = NormalForm.from_gates(gates).to_gates() 57 | return gates 58 | -------------------------------------------------------------------------------- /pygridsynth/tdgp.py: -------------------------------------------------------------------------------- 1 | from .ring import DRootTwo, DOmega 2 | from .region import Interval 3 | from .odgp import solve_scaled_ODGP, solve_scaled_ODGP_with_parity 4 | from .myplot import plot_sol 5 | 6 | 7 | def solve_TDGP(setA, setB, opG, ellipseA_upright, ellipseB_upright, bboxA, bboxB, k, 8 | verbose=False, show_graph=False): 9 | sol_sufficient = [] 10 | sol_x = solve_scaled_ODGP(bboxA.I_x, bboxB.I_x, k + 1) 11 | sol_y = solve_scaled_ODGP(bboxA.I_y.fatten(bboxA.I_y.width * 1e-4), 12 | bboxB.I_y.fatten(bboxB.I_y.width * 1e-4), 13 | k + 1) 14 | if len(sol_x) <= 0 or len(sol_y) <= 0: 15 | sol_sufficient = [] 16 | else: 17 | alpha0 = sol_x[0] 18 | for beta in sol_y: 19 | dx = DRootTwo.power_of_inv_sqrt2(k) 20 | z0 = opG.inv * DOmega.from_droottwo_vector(alpha0, beta, k + 1) 21 | v = opG.inv * DOmega.from_droottwo_vector(dx, DRootTwo.from_int(0), k) 22 | t_A = setA.intersect(z0, v) 23 | t_B = setB.intersect(z0.conj_sq2, v.conj_sq2) 24 | if t_A is None or t_B is None: 25 | continue 26 | 27 | parity = (beta - alpha0).mul_by_sqrt2_power_renewing_denomexp(k) 28 | intA, intB = Interval(*t_A), Interval(*t_B) 29 | dtA = 10 / max(10, (1 << k) * intB.width) 30 | dtB = 10 / max(10, (1 << k) * intA.width) 31 | intA, intB = intA.fatten(dtA), intB.fatten(dtB) 32 | sol_t = solve_scaled_ODGP_with_parity(intA, intB, 1, parity) 33 | sol_x = [alpha * dx + alpha0 for alpha in sol_t] 34 | for alpha in sol_x: 35 | sol_sufficient.append(DOmega.from_droottwo_vector(alpha, beta, k)) 36 | sol_transformed = [opG.inv * z for z in sol_sufficient] 37 | sol = [z for z in sol_transformed if setA.inside(z) and setB.inside(z.conj_sq2)] 38 | 39 | if verbose and len(sol_sufficient) > 0: 40 | print(f"{k=}") 41 | print(f"size of sol_sufficient: {len(sol_sufficient)}, size of sol: {len(sol)}") 42 | if show_graph and len(sol_sufficient) > 0: 43 | plot_sol([sol_transformed, sol], setA.ellipse, setB.ellipse, None, None, 44 | color_list=['limegreen', 'blue'], size_list=[5, 10]) 45 | 46 | return sol 47 | -------------------------------------------------------------------------------- /pygridsynth/to_upright.py: -------------------------------------------------------------------------------- 1 | from .mymath import log, floorsqrt 2 | from .ring import ZOmega, LAMBDA 3 | from .grid_op import EllipsePair, GridOp 4 | from .myplot import plot_sol 5 | 6 | 7 | def _reduction(ellipse_pair, opG_l, opG_r, new_opG): 8 | return new_opG * ellipse_pair, opG_l, new_opG * opG_r, False 9 | 10 | 11 | def _shift_ellipse_pair(ellipse_pair, n): 12 | lambda_n = LAMBDA ** n 13 | lambda_inv_n = LAMBDA ** -n 14 | ellipse_pair.A.a *= lambda_inv_n.to_real 15 | ellipse_pair.A.d *= lambda_n.to_real 16 | ellipse_pair.B.a *= lambda_n.to_real 17 | ellipse_pair.B.d *= lambda_inv_n.to_real 18 | if n & 1: 19 | ellipse_pair.B.b = -ellipse_pair.B.b 20 | return ellipse_pair 21 | 22 | 23 | def _step_lemma(ellipse_pair, opG_l, opG_r, verbose=False): 24 | A = ellipse_pair.A 25 | B = ellipse_pair.B 26 | if verbose: 27 | print("-----") 28 | print(f"skew: {ellipse_pair.skew}, bias: {ellipse_pair.bias}") 29 | print(f"bias(A): {A.bias}, bias(B): {B.bias}, " 30 | + "sign(A.b):" + ("+" if A.b >= 0 else "-") 31 | + ", sign(B.b):" + ("+" if B.b >= 0 else "-")) 32 | print("-----") 33 | if B.b < 0: 34 | if verbose: 35 | print("Z") 36 | OP_Z = GridOp(ZOmega(0, 0, 0, 1), ZOmega(0, -1, 0, 0)) 37 | return _reduction(ellipse_pair, opG_l, opG_r, OP_Z) 38 | elif A.bias * B.bias < 1: 39 | if verbose: 40 | print("X") 41 | OP_X = GridOp(ZOmega(0, 1, 0, 0), ZOmega(0, 0, 0, 1)) 42 | return _reduction(ellipse_pair, opG_l, opG_r, OP_X) 43 | elif ellipse_pair.bias > 33.971 or ellipse_pair.bias < 0.029437: 44 | n = round(log(ellipse_pair.bias) / log(LAMBDA.to_real) / 8) 45 | OP_S = GridOp(ZOmega(-1, 0, 1, 1), ZOmega(1, -1, 1, 0)) 46 | if verbose: 47 | print(f"S ({n=})") 48 | return _reduction(ellipse_pair, opG_l, opG_r, OP_S ** n) 49 | elif ellipse_pair.skew <= 15: 50 | return ellipse_pair, opG_l, opG_r, True 51 | elif ellipse_pair.bias > 5.8285 or ellipse_pair.bias < 0.17157: 52 | n = round(log(ellipse_pair.bias) / log(LAMBDA.to_real) / 4) 53 | ellipse_pair = _shift_ellipse_pair(ellipse_pair, n) 54 | if verbose: 55 | print(f"sigma ({n=})") 56 | if n >= 0: 57 | OP_SIGMA_L = GridOp(ZOmega(-1, 0, 1, 1), ZOmega(0, 1, 0, 0)) ** n 58 | OP_SIGMA_R = GridOp(ZOmega(0, 0, 0, 1), ZOmega(1, -1, 1, 0)) ** n 59 | else: 60 | OP_SIGMA_L = GridOp(ZOmega(-1, 0, 1, -1), ZOmega(0, 1, 0, 0)) ** (-n) 61 | OP_SIGMA_R = GridOp(ZOmega(0, 0, 0, 1), ZOmega(1, 1, 1, 0)) ** (-n) 62 | return ellipse_pair, opG_l * OP_SIGMA_L, OP_SIGMA_R * opG_r, False 63 | elif 0.24410 <= A.bias <= 4.0968 and 0.24410 <= B.bias <= 4.0968: 64 | if verbose: 65 | print("R") 66 | OP_R = GridOp(ZOmega(0, 0, 1, 0), ZOmega(1, 0, 0, 0)) 67 | return _reduction(ellipse_pair, opG_l, opG_r, OP_R) 68 | elif A.b >= 0 and A.bias <= 1.6969: 69 | if verbose: 70 | print("K") 71 | OP_K = GridOp(ZOmega(-1, -1, 0, 0), ZOmega(0, -1, 1, 0)) 72 | return _reduction(ellipse_pair, opG_l, opG_r, OP_K) 73 | elif A.b >= 0 and B.bias <= 1.6969: 74 | if verbose: 75 | print("K_conj_sq2") 76 | OP_K_conj_sq2 = GridOp(ZOmega(1, -1, 0, 0), ZOmega(0, -1, -1, 0)) 77 | return _reduction(ellipse_pair, opG_l, opG_r, OP_K_conj_sq2) 78 | elif A.b >= 0: 79 | n = max(1, floorsqrt(min(A.bias, B.bias) / 4)) 80 | if verbose: 81 | print(f"A ({n=})") 82 | OP_A_n = GridOp(ZOmega(0, 0, 0, 1), ZOmega(0, 1, 0, 2 * n)) 83 | return _reduction(ellipse_pair, opG_l, opG_r, OP_A_n) 84 | else: 85 | n = max(1, floorsqrt(min(A.bias, B.bias) / 2)) 86 | if verbose: 87 | print(f"B ({n=})") 88 | OP_B_n = GridOp(ZOmega(0, 0, 0, 1), ZOmega(n, 1, -n, 0)) 89 | return _reduction(ellipse_pair, opG_l, opG_r, OP_B_n) 90 | 91 | 92 | def _to_upright_ellipse_pair(ellipseA, ellipseB, verbose=False): 93 | ellipseA_normalized = ellipseA.normalize() 94 | ellipseB_normalized = ellipseB.normalize() 95 | ellipse_pair = EllipsePair(ellipseA_normalized, ellipseB_normalized) 96 | OP_I = GridOp(ZOmega(0, 0, 0, 1), ZOmega(0, 1, 0, 0)) 97 | opG_l, opG_r = OP_I, OP_I 98 | while True: 99 | ellipse_pair, opG_l, opG_r, end = _step_lemma(ellipse_pair, opG_l, opG_r, verbose=verbose) 100 | if end: 101 | break 102 | return opG_l * opG_r 103 | 104 | 105 | def to_upright_set_pair(setA, setB, show_graph, verbose=False): 106 | opG = _to_upright_ellipse_pair(setA.ellipse, setB.ellipse, verbose=verbose) 107 | ellipse_pair = opG * EllipsePair(setA.ellipse, setB.ellipse) 108 | ellipseA_upright = ellipse_pair.A 109 | ellipseB_upright = ellipse_pair.B 110 | bboxA = ellipseA_upright.bbox() 111 | bboxB = ellipseB_upright.bbox() 112 | upA = ellipseA_upright.area / bboxA.area 113 | upB = ellipseB_upright.area / bboxB.area 114 | if verbose: 115 | print(f"{upA=}, {upB=}") 116 | if show_graph: 117 | plot_sol([], ellipseA_upright, ellipseB_upright, bboxA, bboxB) 118 | return opG, ellipseA_upright, ellipseB_upright, bboxA, bboxB 119 | -------------------------------------------------------------------------------- /pygridsynth/unitary.py: -------------------------------------------------------------------------------- 1 | from functools import cached_property 2 | import mpmath 3 | 4 | from .ring import DOmega 5 | 6 | 7 | class DOmegaUnitary(): 8 | def __init__(self, z, w, n, k=None): 9 | if n >= 8 or n < 0: 10 | n &= 0b111 11 | self._n = n 12 | if k is None: 13 | if z.k > w.k: 14 | w = w.renew_denomexp(z.k) 15 | elif z.k < w.k: 16 | z = z.renew_denomexp(w.k) 17 | else: 18 | z = z.renew_denomexp(k) 19 | w = w.renew_denomexp(k) 20 | self._z = z 21 | self._w = w 22 | 23 | @property 24 | def z(self): 25 | return self._z 26 | 27 | @property 28 | def w(self): 29 | return self._w 30 | 31 | @property 32 | def n(self): 33 | return self._n 34 | 35 | @property 36 | def k(self): 37 | return self._w.k 38 | 39 | @cached_property 40 | def to_matrix(self): 41 | return [[self._z, -self._w.conj.mul_by_omega_power(self._n)], 42 | [self._w, self._z.conj.mul_by_omega_power(self._n)]] 43 | 44 | @cached_property 45 | def to_complex_matrix(self): 46 | return mpmath.matrix([[self._z.to_complex, -self._w.conj.mul_by_omega_power(self._n).to_complex], 47 | [self._w.to_complex, self._z.conj.mul_by_omega_power(self._n).to_complex]]) 48 | 49 | def __repr__(self): 50 | return f"DOmegaUnitary({repr(self._z)}, {repr(self._w)}, {self._n})" 51 | 52 | def __str__(self): 53 | return str(self.to_matrix) 54 | 55 | def __eq__(self, other): 56 | if isinstance(other, self.__class__): 57 | return self._z == other.z and self._w == other.w and self._n == other.n 58 | else: 59 | return False 60 | 61 | def mul_by_T_from_left(self): 62 | return self.__class__(self._z, self._w.mul_by_omega(), self._n + 1) 63 | 64 | def mul_by_T_inv_from_left(self): 65 | return self.__class__(self._z, self._w.mul_by_omega_inv(), self._n - 1) 66 | 67 | def mul_by_T_power_from_left(self, m): 68 | if m >= 8 or m < 0: 69 | m &= 0b111 70 | return self.__class__(self._z, self._w.mul_by_omega_power(m), self._n + m) 71 | 72 | def mul_by_S_from_left(self): 73 | return self.__class__(self._z, self._w.mul_by_omega_power(2), self._n + 2) 74 | 75 | def mul_by_S_power_from_left(self, m): 76 | if m >= 4 or m < 0: 77 | m &= 0b11 78 | return self.__class__(self._z, self._w.mul_by_omega_power(m << 1), self._n + (m << 1)) 79 | 80 | def mul_by_H_from_left(self): 81 | new_z = (self._z + self._w).mul_by_inv_sqrt2() 82 | new_w = (self._z - self._w).mul_by_inv_sqrt2() 83 | return self.__class__(new_z, new_w, self._n + 4) 84 | 85 | def mul_by_H_and_T_power_from_left(self, m): 86 | return self.mul_by_T_power_from_left(m).mul_by_H_from_left() 87 | 88 | def mul_by_X_from_left(self): 89 | return self.__class__(self._w, self._z, self._n + 4) 90 | 91 | def mul_by_W_from_left(self): 92 | return self.__class__(self._z.mul_by_omega(), self._w.mul_by_omega(), self._n + 2) 93 | 94 | def mul_by_W_power_from_left(self, m): 95 | if m >= 8 or m < 0: 96 | m &= 0b111 97 | return self.__class__(self._z.mul_by_omega_power(m), self._w.mul_by_omega_power(m), 98 | self._n + (m << 1)) 99 | 100 | def renew_denomexp(self, new_k): 101 | return self.__class__(self._z, self._w, self._n, new_k) 102 | 103 | def reduce_denomexp(self): 104 | new_z = self._z.reduce_denomexp() 105 | new_w = self._w.reduce_denomexp() 106 | return self.__class__(new_z, new_w, self._n) 107 | 108 | @classmethod 109 | def identity(cls): 110 | return cls(DOmega.from_int(1), DOmega.from_int(0), 0) 111 | 112 | @classmethod 113 | def from_gates(cls, gates): 114 | unitary = cls.identity() 115 | for g in reversed(gates): 116 | if g == "H": 117 | unitary = unitary.renew_denomexp(unitary.k + 1).mul_by_H_from_left() 118 | elif g == "T": 119 | unitary = unitary.mul_by_T_from_left() 120 | elif g == "S": 121 | unitary = unitary.mul_by_S_from_left() 122 | elif g == "X": 123 | unitary = unitary.mul_by_X_from_left() 124 | elif g == "W": 125 | unitary = unitary.mul_by_W_from_left() 126 | return unitary.reduce_denomexp() 127 | -------------------------------------------------------------------------------- /pyproject.toml: -------------------------------------------------------------------------------- 1 | [project] 2 | name = "pygridsynth" 3 | version = "1.1.0" 4 | authors = [{ name="Shuntaro Yamamoto", email="shun0923@g.ecc.u-tokyo.ac.jp" }, { name="Nobuyuki Yoshioka", email="nyoshioka@g.ecc.u-tokyo.ac.jp" }] 5 | description = "Python version of the gridsynth program that computes approximations of z-rotations over the Clifford+T gate set." 6 | readme = "README.md" 7 | license = {file = "LICENSE"} 8 | requires-python = ">=3.8" 9 | classifiers = [ 10 | "Development Status :: 4 - Beta", 11 | "Programming Language :: Python :: 3", 12 | "License :: OSI Approved :: GNU General Public License v3 or later (GPLv3+)", 13 | ] 14 | 15 | dependencies = [ 16 | "mpmath", 17 | ] 18 | 19 | [tool.setuptools] 20 | packages = ["pygridsynth"] 21 | 22 | [project.scripts] 23 | pygridsynth = "pygridsynth:main" 24 | 25 | [project.urls] 26 | "Homepage" = "https://github.com/quantum-programming/clifford-T-decomp" 27 | "Bug Tracker" = "https://github.com/quantum-programming/clifford-T-decomp/issues" 28 | -------------------------------------------------------------------------------- /requirements.txt: -------------------------------------------------------------------------------- 1 | mpmath --------------------------------------------------------------------------------