microsoft/qdk
Publicmirrored from https://github.com/microsoft/qdkAvailable
source/paulimer/tests/clifford_test.rs
1274lines · modecode
| 1 | // Copyright (c) Microsoft Corporation. |
| 2 | // Licensed under the MIT License. |
| 3 | |
| 4 | use paulimer::bits::{BitMatrix, BitVec, Bitwise, IndexSet}; |
| 5 | use paulimer::clifford::generic_algos::{clifford_from_images, clifford_to_prepare_bell_states}; |
| 6 | use paulimer::clifford::{ |
| 7 | apply_qubit_clifford_by_axis, group_encoding_clifford_of, prepare_all_plus, prepare_all_zero, |
| 8 | random_clifford_via_operations_sampling, split_clifford_encoder_mod_pauli, split_phased_css, |
| 9 | split_qubit_cliffords_and_css, split_qubit_tensor_product_encoder, Clifford, CliffordMutable, |
| 10 | CliffordStringParsingError, MutablePreImages, PreimageViews, Swap, XOrZ, |
| 11 | }; |
| 12 | type CliffordUnitary = paulimer::clifford::CliffordUnitary; |
| 13 | type CliffordUnitaryModPauli = paulimer::clifford::CliffordUnitaryModPauli; |
| 14 | |
| 15 | use paulimer::pauli::{ |
| 16 | anti_commutes_with, apply_pauli_exponent, apply_root_x, apply_root_y, apply_root_z, |
| 17 | pauli_random, pauli_random_order_two, DensePauli, DensePauliProjective, PauliMutable, |
| 18 | SparsePauliProjective, |
| 19 | }; |
| 20 | use paulimer::pauli::{commutes_with, Pauli, PauliBinaryOps, PauliUnitary, Phase, SparsePauli}; |
| 21 | |
| 22 | use paulimer::operations::{css_operations, diagonal_operations}; |
| 23 | use paulimer::quantum_core::{x, y, z, PositionedPauliObservable}; |
| 24 | use proptest::prelude::*; |
| 25 | use rand::prelude::*; |
| 26 | use std::borrow::Borrow; |
| 27 | use std::ops::Range; |
| 28 | use std::str::FromStr; |
| 29 | |
| 30 | pub trait TestableClifford: |
| 31 | Clifford< |
| 32 | DensePauli: for<'life, 'life1> PartialEq<&'life [PositionedPauliObservable]> |
| 33 | + PartialEq |
| 34 | + std::fmt::Display |
| 35 | + std::fmt::Debug, |
| 36 | > + CliffordMutable<PhaseExponentValue = <Self as Clifford>::PhaseExponentValue> |
| 37 | + PartialEq |
| 38 | + Eq |
| 39 | + PreimageViews<PhaseExponentValue = <Self as Clifford>::PhaseExponentValue> |
| 40 | + MutablePreImages<PhaseExponentValue = <Self as Clifford>::PhaseExponentValue> |
| 41 | + FromStr<Err = CliffordStringParsingError> |
| 42 | + std::fmt::Display |
| 43 | + std::fmt::Debug |
| 44 | { |
| 45 | type SparsePauli: Pauli<PhaseExponentValue = <Self as Clifford>::PhaseExponentValue> |
| 46 | + for<'life> From<&'life [PositionedPauliObservable]> |
| 47 | + std::fmt::Display; |
| 48 | type DensePauli: Pauli<PhaseExponentValue = <Self as Clifford>::PhaseExponentValue> |
| 49 | + for<'life> PartialEq<&'life [PositionedPauliObservable]> |
| 50 | + std::fmt::Display; |
| 51 | } |
| 52 | |
| 53 | impl TestableClifford for CliffordUnitary { |
| 54 | type SparsePauli = SparsePauli; |
| 55 | type DensePauli = DensePauli; |
| 56 | } |
| 57 | |
| 58 | impl TestableClifford for CliffordUnitaryModPauli { |
| 59 | type SparsePauli = SparsePauliProjective; |
| 60 | type DensePauli = DensePauliProjective; |
| 61 | } |
| 62 | |
| 63 | fn is_pauli_x_up_to_phase(pauli: &impl Pauli, qubit_id: usize) -> bool { |
| 64 | pauli.z_bits().is_zero() && pauli.x_bits().weight() == 1 && pauli.x_bits().index(qubit_id) |
| 65 | } |
| 66 | |
| 67 | fn is_pauli_z_up_to_phase(pauli: &impl Pauli, qubit_id: usize) -> bool { |
| 68 | pauli.x_bits().is_zero() && pauli.z_bits().weight() == 1 && pauli.z_bits().index(qubit_id) |
| 69 | } |
| 70 | |
| 71 | fn are_identity_preimages_up_to_phase(clifford: &impl Clifford) -> bool { |
| 72 | for j in 0..clifford.num_qubits() { |
| 73 | if !is_pauli_x_up_to_phase(&clifford.preimage_x(j), j) { |
| 74 | return false; |
| 75 | } |
| 76 | if !is_pauli_z_up_to_phase(&clifford.preimage_z(j), j) { |
| 77 | return false; |
| 78 | } |
| 79 | } |
| 80 | true |
| 81 | } |
| 82 | |
| 83 | fn identity_preimages_with_dimension(dimension: usize) { |
| 84 | let id = CliffordUnitary::identity(dimension); |
| 85 | assert!(id.is_identity()); |
| 86 | let id_mod_pauli = CliffordUnitaryModPauli::identity(dimension); |
| 87 | assert!(are_identity_preimages_up_to_phase(&id_mod_pauli)); |
| 88 | } |
| 89 | |
| 90 | #[test] |
| 91 | fn identity_preimages() { |
| 92 | for dimension in 1..4 { |
| 93 | identity_preimages_with_dimension(dimension); |
| 94 | } |
| 95 | } |
| 96 | |
| 97 | proptest! { |
| 98 | #[test] |
| 99 | fn from_images(clifford in arbitrary_clifford(0..1)) { |
| 100 | let images = images_of(&clifford); |
| 101 | let from_images : CliffordUnitary = clifford_from_images(images.as_slice().iter()); |
| 102 | assert_eq!(images, images_of(&from_images)); |
| 103 | } |
| 104 | |
| 105 | #[test] |
| 106 | fn format_string_roundtrip(clifford in arbitrary_clifford(1..10)) { |
| 107 | format_string_roundtrip_generic_test(&clifford); |
| 108 | format_string_roundtrip_generic_test::<CliffordUnitaryModPauli>(&clifford.into()); |
| 109 | } |
| 110 | |
| 111 | #[test] |
| 112 | fn clone(clifford in arbitrary_clifford(0..10)) { |
| 113 | let cloned = clifford.clone(); |
| 114 | assert_eq!(images_of(&cloned), images_of(&clifford)); |
| 115 | } |
| 116 | |
| 117 | #[test] |
| 118 | fn pauli_exponent_multiply(clifford in arbitrary_clifford(0..10)) { |
| 119 | let pauli = pauli_random_order_two::<<paulimer::clifford::CliffordUnitary as Clifford>::DensePauli>(clifford.num_qubits(),&mut thread_rng()); |
| 120 | let mut product = clifford.clone(); |
| 121 | product.left_mul_pauli_exp(&pauli); |
| 122 | let ipauli = pauli.clone() * Phase::from_exponent(1u8); |
| 123 | |
| 124 | let assert_image = |indicator: PauliUnitary<Vec<bool>, u8>| { |
| 125 | let power_image = product.image(&indicator); |
| 126 | let clifford_image = clifford.image(&indicator); |
| 127 | // println!("indicator={}, pauli={}, power_image={}, clifford_image={}", indicator, pauli, power_image, clifford_image); |
| 128 | if commutes_with(&clifford_image,&pauli) { |
| 129 | assert_eq!(clifford_image, power_image); |
| 130 | } else { |
| 131 | assert_eq!(ipauli.clone() * &clifford_image, power_image); |
| 132 | } |
| 133 | }; |
| 134 | |
| 135 | for index in 0..clifford.num_qubits() { |
| 136 | assert_image(x_at(index, clifford.num_qubits())); |
| 137 | assert_image(z_at(index, clifford.num_qubits())); |
| 138 | } |
| 139 | } |
| 140 | |
| 141 | #[test] |
| 142 | fn controlled_pauli_multiply(clifford in arbitrary_clifford(2..3)) { |
| 143 | |
| 144 | assert!(clifford.num_qubits() >= 2); |
| 145 | let mut control : <paulimer::clifford::CliffordUnitary as Clifford>::DensePauli = pauli_random_order_two(clifford.num_qubits(),&mut thread_rng()); |
| 146 | while control.x_bits().is_zero() && control.z_bits().is_zero() { |
| 147 | control = pauli_random_order_two(clifford.num_qubits(),&mut thread_rng()); |
| 148 | } |
| 149 | let mut target : <paulimer::clifford::CliffordUnitary as Clifford>::DensePauli = pauli_random_order_two(clifford.num_qubits(),&mut thread_rng()); |
| 150 | while !commutes_with(&control,&target) || (control.x_bits().is_zero() && control.z_bits().is_zero()) { |
| 151 | target = pauli_random_order_two(clifford.num_qubits(),&mut thread_rng()); |
| 152 | } |
| 153 | |
| 154 | let mut product = clifford.clone(); |
| 155 | assert!(control.is_order_two()); |
| 156 | assert!(target.is_order_two()); |
| 157 | product.left_mul_controlled_pauli(&control,&target); |
| 158 | |
| 159 | let images = images_of(&clifford); |
| 160 | let product_images = images_of(&product); |
| 161 | for (image, product_image) in images.iter().zip(product_images.iter()) { |
| 162 | let mut expected_image = image.clone(); |
| 163 | if anti_commutes_with(image,&control) { |
| 164 | expected_image.mul_assign_right(&target); |
| 165 | } |
| 166 | if anti_commutes_with(image, &target) { |
| 167 | expected_image.mul_assign_left(&control); |
| 168 | } |
| 169 | // println!("Q={}, P1={}, P2={}, expected={}, actual={}", image, control, target, expected_image, *product_image); |
| 170 | assert_eq!(expected_image, *product_image); |
| 171 | } |
| 172 | } |
| 173 | |
| 174 | #[test] |
| 175 | fn pauli_multiply(clifford in arbitrary_clifford(0..1)) { |
| 176 | let pauli = arbitrary_pauli_of_length(clifford.num_qubits()); |
| 177 | let product = &pauli * clifford.clone(); |
| 178 | |
| 179 | let assert_image_sign = |indicator: PauliUnitary<Vec<bool>, u8>| { |
| 180 | let product_image = product.image(&indicator); |
| 181 | let clifford_image = clifford.image(&indicator); |
| 182 | // println!("indicator={}, pauli={}, product_image={}, clifford_image={}", indicator, pauli, product_image, clifford_image); |
| 183 | if commutes_with(&clifford_image, &pauli) { |
| 184 | assert_eq!(clifford_image, product_image); |
| 185 | } else { |
| 186 | assert_eq!(-clifford_image, product_image); |
| 187 | } |
| 188 | }; |
| 189 | |
| 190 | for index in 0..clifford.num_qubits() { |
| 191 | assert_image_sign(x_at(index, clifford.num_qubits())); |
| 192 | assert_image_sign(z_at(index, clifford.num_qubits())); |
| 193 | } |
| 194 | } |
| 195 | |
| 196 | #[test] |
| 197 | fn composition((left, right) in composable_cliffords(0..10)) { |
| 198 | let composed = left.multiply_with(&right); |
| 199 | for index in 0..left.num_qubits() { |
| 200 | let x = x_at(index, left.num_qubits()); |
| 201 | let z = z_at(index, left.num_qubits()); |
| 202 | assert_eq!(composed.preimage(&x), right.preimage(&left.preimage(&x))); |
| 203 | assert_eq!(composed.preimage(&z), right.preimage(&left.preimage(&z))); |
| 204 | } |
| 205 | } |
| 206 | |
| 207 | #[test] |
| 208 | fn right_swap(clifford in arbitrary_clifford(2..10), mut index0 in 0..10usize, mut index1 in 0..10usize) { |
| 209 | index0 %= clifford.num_qubits(); |
| 210 | index1 %= clifford.num_qubits(); |
| 211 | let swapped = clifford.clone() * Swap(index0, index1); |
| 212 | let clifford_images = images_of(&clifford); |
| 213 | let swapped_images = images_of(&swapped); |
| 214 | assert_eq!(swapped_images[2*index0], clifford_images[2*index1]); |
| 215 | assert_eq!(swapped_images[2*index0+1], clifford_images[2*index1+1]); |
| 216 | assert_eq!(swapped_images[2*index1], clifford_images[2*index0]); |
| 217 | assert_eq!(swapped_images[2*index1+1], clifford_images[2*index0+1]); |
| 218 | for index in 0..clifford.num_qubits() { |
| 219 | if index != index0 && index != index1 { |
| 220 | assert_eq!(swapped_images[2*index], clifford_images[2*index]); |
| 221 | assert_eq!(swapped_images[2*index+1], clifford_images[2*index+1]); |
| 222 | } |
| 223 | } |
| 224 | } |
| 225 | |
| 226 | #[test] |
| 227 | fn left_swap(clifford in arbitrary_clifford(2..3), mut index0 in 0..10usize, mut index1 in 0..10usize) { |
| 228 | index0 %= clifford.num_qubits(); |
| 229 | index1 %= clifford.num_qubits(); |
| 230 | let mut swapped = clifford.clone(); |
| 231 | swapped.left_mul_swap(index0, index1); |
| 232 | let clifford_images = preimages_of(&clifford); |
| 233 | let swapped_images = preimages_of(&swapped); |
| 234 | assert_eq!(swapped_images[2*index0], clifford_images[2*index1]); |
| 235 | assert_eq!(swapped_images[2*index0+1], clifford_images[2*index1+1]); |
| 236 | assert_eq!(swapped_images[2*index1], clifford_images[2*index0]); |
| 237 | assert_eq!(swapped_images[2*index1+1], clifford_images[2*index0+1]); |
| 238 | for index in 0..clifford.num_qubits() { |
| 239 | if index != index0 && index != index1 { |
| 240 | assert_eq!(swapped_images[2*index], clifford_images[2*index]); |
| 241 | assert_eq!(swapped_images[2*index+1], clifford_images[2*index+1]); |
| 242 | } |
| 243 | } |
| 244 | } |
| 245 | |
| 246 | #[test] |
| 247 | fn preimage_inverts_image(clifford in arbitrary_clifford(0..10)) { |
| 248 | let clifford = CliffordUnitary::identity(clifford.num_qubits()); |
| 249 | for index in 0..clifford.num_qubits() { |
| 250 | let x = &x_at(index, clifford.num_qubits()); |
| 251 | let z = &z_at(index, clifford.num_qubits()); |
| 252 | let x_image = clifford.image(x); |
| 253 | let z_image = clifford.image(z); |
| 254 | let x_image_preimage = clifford.preimage(&x_image); |
| 255 | let z_image_preimage = clifford.preimage(&z_image); |
| 256 | assert!( x == x_image_preimage); |
| 257 | assert!( z == z_image_preimage); |
| 258 | } |
| 259 | } |
| 260 | |
| 261 | #[test] |
| 262 | fn split_clifford(clifford1 in arbitrary_clifford(1..5), clifford2 in arbitrary_clifford(1..5)) { |
| 263 | let c1 = CliffordUnitaryModPauli::from(clifford1); |
| 264 | let c2 = CliffordUnitaryModPauli::from(clifford2); |
| 265 | let qubit_count = c1.num_qubits() + c2.num_qubits(); |
| 266 | let mut c3 = random_diagonal_clifford::<CliffordUnitaryModPauli>(qubit_count).multiply_with(&random_css_clifford(qubit_count)); |
| 267 | |
| 268 | let support = c1.qubits().collect::<Vec<_>>(); |
| 269 | let support_complement = (c1.num_qubits()..c3.num_qubits()).collect::<Vec<_>>(); |
| 270 | |
| 271 | c3.left_mul_clifford(&c1, &support); |
| 272 | c3.left_mul_clifford(&c2, &support_complement); |
| 273 | |
| 274 | if let Some((split_clifford1, split_clifford2)) = split_clifford_encoder_mod_pauli(&c3, &support, &support_complement) { |
| 275 | assert!(split_clifford1.is_valid()); |
| 276 | assert!(split_clifford2.is_valid()); |
| 277 | |
| 278 | assert_eq!(split_clifford1.num_qubits(), c1.num_qubits()); |
| 279 | assert_eq!(split_clifford2.num_qubits(), c2.num_qubits()); |
| 280 | |
| 281 | for qubit_index in split_clifford1.qubits() { |
| 282 | assert!(c3.preimage(&split_clifford1.image_z(qubit_index)).x_bits().is_zero()); |
| 283 | } |
| 284 | |
| 285 | // tensor product of split_clifford1, split_clifford2 encode the same state as c4 |
| 286 | let mut c4 = CliffordUnitaryModPauli::identity(qubit_count); |
| 287 | c4.left_mul_clifford(&split_clifford1, &support); |
| 288 | c4.left_mul_clifford(&split_clifford2, &support_complement); |
| 289 | for qubit_index in c4.qubits() { |
| 290 | assert!(c3.preimage(&c4.image_z(qubit_index)).x_bits().is_zero()); |
| 291 | } |
| 292 | |
| 293 | } |
| 294 | else { |
| 295 | panic!("Clifford should split") |
| 296 | } |
| 297 | } |
| 298 | |
| 299 | #[test] |
| 300 | fn identity_dimension(dimension in 0..1000usize) { |
| 301 | let identity = CliffordUnitary::identity(dimension); |
| 302 | assert_eq!(dimension, identity.num_qubits()); |
| 303 | } |
| 304 | |
| 305 | #[test] |
| 306 | fn identity_multiplication_is_trivial(clifford in arbitrary_clifford(0..10)) { |
| 307 | let identity = CliffordUnitary::identity(clifford.num_qubits()); |
| 308 | assert_eq!(clifford, clifford.multiply_with(&identity)); |
| 309 | assert_eq!(clifford, identity.multiply_with(&clifford)); |
| 310 | } |
| 311 | |
| 312 | #[test] |
| 313 | fn group_encoding_clifford_of_test(clifford in arbitrary_clifford(1..20), qubit_count in 1usize..20 ) { |
| 314 | let num_images = qubit_count.min(clifford.num_qubits()); |
| 315 | let images = (0 .. num_images).map(|id| clifford.image_z(id) ).collect::<Vec<_>>(); |
| 316 | let encoding_clifford = group_encoding_clifford_of(&images,clifford.num_qubits()); |
| 317 | for image in images { |
| 318 | let preimage = encoding_clifford.preimage(&image); |
| 319 | assert!(preimage.x_bits().is_zero()); |
| 320 | assert!(preimage.z_bits().max_bit_id().unwrap() < num_images); |
| 321 | assert_eq!(preimage.xz_phase_exponent(),0); |
| 322 | } |
| 323 | } |
| 324 | |
| 325 | #[test] |
| 326 | fn left_mul_root_and_apply_root_are_consistent(qubit_count in 1..10usize) { |
| 327 | check_left_mul_root_and_apply_root_are_consistent(qubit_count, <CliffordUnitary as CliffordMutable>::left_mul_root_x, apply_root_x::<DensePauli>); |
| 328 | check_left_mul_root_and_apply_root_are_consistent(qubit_count, <CliffordUnitary as CliffordMutable>::left_mul_root_y, apply_root_y::<DensePauli>); |
| 329 | check_left_mul_root_and_apply_root_are_consistent(qubit_count, <CliffordUnitary as CliffordMutable>::left_mul_root_z, apply_root_z::<DensePauli>); |
| 330 | } |
| 331 | |
| 332 | #[test] |
| 333 | fn left_mul_pauli_exp_and_apply_pauli_exp_are_consistent(clifford in arbitrary_clifford(1..20)) { |
| 334 | let identity = CliffordUnitary::identity(clifford.num_qubits()); |
| 335 | let mut pauli_exp = CliffordUnitary::identity(clifford.num_qubits()); |
| 336 | let exp = clifford.image_z(0); |
| 337 | pauli_exp.left_mul_pauli_exp(&exp); |
| 338 | for qubit_index in 0 .. clifford.num_qubits() { |
| 339 | let mut image_z = identity.image_z(qubit_index); |
| 340 | apply_pauli_exponent(&mut image_z, &exp); |
| 341 | assert_eq!(image_z, pauli_exp.image_z(qubit_index)); |
| 342 | |
| 343 | let mut image_x = identity.image_x(qubit_index); |
| 344 | apply_pauli_exponent(&mut image_x, &exp); |
| 345 | assert_eq!(image_x, pauli_exp.image_x(qubit_index)); |
| 346 | } |
| 347 | } |
| 348 | |
| 349 | #[test] |
| 350 | fn inverse(clifford in arbitrary_clifford(1..2)) { |
| 351 | let inverse = clifford.inverse(); |
| 352 | let identity = CliffordUnitary::identity(clifford.num_qubits()); |
| 353 | assert_eq!(identity, clifford.multiply_with(&inverse)); |
| 354 | } |
| 355 | |
| 356 | #[test] |
| 357 | fn is_diagonal(clifford in arbitrary_diagonal_clifford(1..15usize)) { |
| 358 | generic_diagonal_clifford_test::<CliffordUnitaryModPauli>(&clifford.clone().into()); |
| 359 | generic_diagonal_clifford_test::<CliffordUnitary>(&clifford); |
| 360 | |
| 361 | } |
| 362 | |
| 363 | #[test] |
| 364 | fn diagonal_resource_state_encoder_test(qubit_count in 1..15usize) { |
| 365 | assert!(prepare_all_plus(qubit_count).is_diagonal_resource_encoder(XOrZ::Z)); |
| 366 | assert!(prepare_all_zero(qubit_count).is_diagonal_resource_encoder(XOrZ::X)); |
| 367 | assert!(prepare_all_plus(qubit_count).unitary_from_diagonal_resource_state(XOrZ::Z).unwrap().is_identity()); |
| 368 | assert!(prepare_all_zero(qubit_count).unitary_from_diagonal_resource_state(XOrZ::X).unwrap().is_identity()); |
| 369 | } |
| 370 | |
| 371 | #[test] |
| 372 | fn is_css(clifford in arbitrary_css_clifford(2..10usize)) { |
| 373 | generic_is_css_clifford_test::<CliffordUnitary>(&clifford); |
| 374 | let clifford_mod_pauli: CliffordUnitaryModPauli = clifford.into(); |
| 375 | generic_is_css_clifford_test::<CliffordUnitaryModPauli>(&clifford_mod_pauli); |
| 376 | let qubit_count = clifford_mod_pauli.num_qubits(); |
| 377 | assert!(prepare_all_plus(qubit_count).is_diagonal_resource_encoder(XOrZ::Z)); |
| 378 | assert!(clifford_mod_pauli.multiply_with(&prepare_all_plus(qubit_count)).is_diagonal_resource_encoder(XOrZ::Z)); |
| 379 | assert!(clifford_mod_pauli.multiply_with(&prepare_all_zero(qubit_count)).is_diagonal_resource_encoder(XOrZ::X)); |
| 380 | } |
| 381 | |
| 382 | #[test] |
| 383 | fn is_phased_css_test( (css,diagonal) in composable_css_diagonal_cliffords(2..10usize)) { |
| 384 | let c1 : CliffordUnitaryModPauli = css.multiply_with(&diagonal).into(); |
| 385 | let c2 : CliffordUnitaryModPauli = diagonal.multiply_with(&css).into(); |
| 386 | assert!(split_phased_css(&css.clone().into()).is_some()); |
| 387 | assert!(split_phased_css(&diagonal.clone().into()).is_some()); |
| 388 | if let Some((diag,extracted_css)) = split_phased_css(&c2) { |
| 389 | assert_eq!(CliffordUnitaryModPauli::from(diagonal),diag); |
| 390 | assert_eq!(CliffordUnitaryModPauli::from(css),extracted_css); |
| 391 | } |
| 392 | assert!(split_phased_css(&c1).is_some()); |
| 393 | } |
| 394 | |
| 395 | #[test] |
| 396 | fn is_qubit_css_test( (css,qubit) in composable_css_qubit_cliffords(2..10usize)) { |
| 397 | let c2 : CliffordUnitaryModPauli = qubit.multiply_with(&css).into(); |
| 398 | assert!(split_qubit_cliffords_and_css(&css.clone().into()).is_some()); |
| 399 | assert!(split_qubit_cliffords_and_css(&qubit.clone().into()).is_some()); |
| 400 | if let Some((extracted_qubit,extracted_css)) = split_qubit_cliffords_and_css(&c2) { |
| 401 | assert_eq!(CliffordUnitaryModPauli::from(qubit),extracted_qubit); |
| 402 | assert_eq!(CliffordUnitaryModPauli::from(css),extracted_css); |
| 403 | } |
| 404 | } |
| 405 | |
| 406 | #[test] |
| 407 | fn qubit_cliffords_recognition_test( qubit_cliffords in arbitrary_qubit_cliffords(1..10usize)) { |
| 408 | let qubit_count = qubit_cliffords.num_qubits(); |
| 409 | let c : CliffordUnitaryModPauli = qubit_cliffords.into(); |
| 410 | let mut r = CliffordUnitaryModPauli::identity(qubit_count); |
| 411 | let plus = prepare_all_plus(qubit_count); |
| 412 | let zero = prepare_all_zero(qubit_count); |
| 413 | let plus_axes = split_qubit_tensor_product_encoder(&c.multiply_with(&plus)).unwrap(); |
| 414 | let zero_axes = split_qubit_tensor_product_encoder(&c.multiply_with(&zero)).unwrap(); |
| 415 | for (qubit_index,(zero,plus)) in std::iter::zip(zero_axes, plus_axes).enumerate() { |
| 416 | apply_qubit_clifford_by_axis(&mut r, qubit_index, zero, plus); |
| 417 | } |
| 418 | assert_eq!(c,r); |
| 419 | } |
| 420 | } |
| 421 | |
| 422 | prop_compose! { |
| 423 | fn arbitrary_clifford(dimension_range: Range<usize>)(dimension in dimension_range) -> CliffordUnitary { |
| 424 | arbitrary_clifford_of_dimension(dimension) |
| 425 | } |
| 426 | } |
| 427 | |
| 428 | prop_compose! { |
| 429 | fn arbitrary_css_clifford(dimension_range: Range<usize>)(dimension in dimension_range) -> CliffordUnitary { |
| 430 | let mut clifford: CliffordUnitary = random_css_clifford(dimension); |
| 431 | let pauli = pauli_random_order_two::<<paulimer::clifford::CliffordUnitary as Clifford>::DensePauli>(clifford.num_qubits(),&mut thread_rng()); |
| 432 | clifford.left_mul_pauli(&pauli); |
| 433 | clifford |
| 434 | } |
| 435 | } |
| 436 | |
| 437 | prop_compose! { |
| 438 | fn arbitrary_diagonal_clifford(dimension_range: Range<usize>)(dimension in dimension_range) -> CliffordUnitary { |
| 439 | let mut clifford: CliffordUnitary= random_diagonal_clifford(dimension); |
| 440 | let pauli = pauli_random_order_two::<<paulimer::clifford::CliffordUnitary as Clifford>::DensePauli>(clifford.num_qubits(),&mut thread_rng()); |
| 441 | clifford.left_mul_pauli(&pauli); |
| 442 | clifford |
| 443 | } |
| 444 | } |
| 445 | |
| 446 | prop_compose! { |
| 447 | fn composable_cliffords(dimension_range: Range<usize>)(dimension in dimension_range) -> (CliffordUnitary, CliffordUnitary) { |
| 448 | (arbitrary_clifford_of_dimension(dimension), arbitrary_clifford_of_dimension(dimension)) |
| 449 | } |
| 450 | } |
| 451 | |
| 452 | prop_compose! { |
| 453 | fn composable_css_diagonal_cliffords(dimension_range: Range<usize>)(dimension in dimension_range) -> (CliffordUnitary, CliffordUnitary) { |
| 454 | (arbitrary_css_clifford_of_dimension(dimension), arbitrary_diagonal_clifford_of_dimension(dimension)) |
| 455 | } |
| 456 | } |
| 457 | |
| 458 | prop_compose! { |
| 459 | fn composable_css_qubit_cliffords(dimension_range: Range<usize>)(dimension in dimension_range) -> (CliffordUnitary, CliffordUnitary) { |
| 460 | (arbitrary_css_clifford_of_dimension(dimension), arbitrary_qubit_cliffords_of_dimension(dimension)) |
| 461 | } |
| 462 | } |
| 463 | |
| 464 | prop_compose! { |
| 465 | fn arbitrary_qubit_cliffords(dimension_range: Range<usize>)(dimension in dimension_range) -> CliffordUnitary { |
| 466 | arbitrary_qubit_cliffords_of_dimension(dimension) |
| 467 | } |
| 468 | } |
| 469 | |
| 470 | prop_compose! { |
| 471 | fn arbitrary_images(max_dimension: usize)(dimension in 0..=max_dimension) -> Vec<PauliUnitary<BitVec, u8>> { |
| 472 | let images: Vec<PauliUnitary<BitVec, u8>> = std::iter::from_fn(|| Some(arbitrary_pauli_of_length(dimension))).take(dimension*2).collect(); |
| 473 | images |
| 474 | } |
| 475 | } |
| 476 | |
| 477 | prop_compose! { |
| 478 | fn arbitrary_pauli(max_dimension: usize)(dimension in 0..=max_dimension) -> PauliUnitary<BitVec, u8> { |
| 479 | arbitrary_pauli_of_length(dimension) |
| 480 | } |
| 481 | } |
| 482 | |
| 483 | fn arbitrary_clifford_of_dimension(dimension: usize) -> CliffordUnitary { |
| 484 | CliffordUnitary::random(dimension, &mut thread_rng()) |
| 485 | } |
| 486 | |
| 487 | fn arbitrary_css_clifford_of_dimension(dimension: usize) -> CliffordUnitary { |
| 488 | let mut clifford: CliffordUnitary = random_css_clifford(dimension); |
| 489 | let pauli = pauli_random_order_two::< |
| 490 | <paulimer::clifford::CliffordUnitary as Clifford>::DensePauli, |
| 491 | >(clifford.num_qubits(), &mut thread_rng()); |
| 492 | clifford.left_mul_pauli(&pauli); |
| 493 | clifford |
| 494 | } |
| 495 | |
| 496 | fn arbitrary_qubit_cliffords_of_dimension(dimension: usize) -> CliffordUnitary { |
| 497 | let mut clifford: CliffordUnitary = CliffordUnitary::identity(dimension); |
| 498 | for qubit_index in clifford.qubits() { |
| 499 | let qubit_random_clifford = arbitrary_clifford_of_dimension(1); |
| 500 | clifford.left_mul_clifford(&qubit_random_clifford, &[qubit_index]); |
| 501 | } |
| 502 | clifford |
| 503 | } |
| 504 | |
| 505 | fn arbitrary_diagonal_clifford_of_dimension(dimension: usize) -> CliffordUnitary { |
| 506 | let mut clifford: CliffordUnitary = random_diagonal_clifford(dimension); |
| 507 | let pauli = pauli_random_order_two::< |
| 508 | <paulimer::clifford::CliffordUnitary as Clifford>::DensePauli, |
| 509 | >(clifford.num_qubits(), &mut thread_rng()); |
| 510 | clifford.left_mul_pauli(&pauli); |
| 511 | clifford |
| 512 | } |
| 513 | |
| 514 | fn arbitrary_pauli_of_length(length: usize) -> PauliUnitary<BitVec, u8> { |
| 515 | pauli_random(length, &mut thread_rng()) |
| 516 | } |
| 517 | |
| 518 | fn images_of<CliffordLike: Clifford>(clifford: &CliffordLike) -> Vec<CliffordLike::DensePauli> { |
| 519 | let mut images = vec![]; |
| 520 | for qubit_index in clifford.qubits() { |
| 521 | images.push(clifford.image_x(qubit_index)); |
| 522 | images.push(clifford.image_z(qubit_index)); |
| 523 | } |
| 524 | images |
| 525 | } |
| 526 | |
| 527 | fn preimages_of<CliffordLike: Clifford>(clifford: &CliffordLike) -> Vec<CliffordLike::DensePauli> { |
| 528 | let mut preimages = vec![]; |
| 529 | for qubit_index in clifford.qubits() { |
| 530 | preimages.push(clifford.preimage_x(qubit_index)); |
| 531 | preimages.push(clifford.preimage_z(qubit_index)); |
| 532 | } |
| 533 | preimages |
| 534 | } |
| 535 | |
| 536 | fn x_at(index: usize, length: usize) -> PauliUnitary<Vec<bool>, u8> { |
| 537 | let zeros = vec![false; length]; |
| 538 | let mut bits = zeros.clone(); |
| 539 | bits[index] = true; |
| 540 | PauliUnitary::from_bits(bits, zeros, 0u8) |
| 541 | } |
| 542 | |
| 543 | fn z_at(index: usize, length: usize) -> PauliUnitary<Vec<bool>, u8> { |
| 544 | let zeros = vec![false; length]; |
| 545 | let mut bits = zeros.clone(); |
| 546 | bits[index] = true; |
| 547 | PauliUnitary::from_bits(zeros, bits, 0u8) |
| 548 | } |
| 549 | |
| 550 | /// One and two-qubit Clifford gates tests |
| 551 | macro_rules! generic_qubit_unitary_test_macro { |
| 552 | ($func:ident, $image_func:expr) => { |
| 553 | for num_qubits in 0..6 { |
| 554 | for qubit_index in 0..num_qubits { |
| 555 | generic_qubit_unitary_test( |
| 556 | num_qubits, |
| 557 | qubit_index, |
| 558 | CliffordUnitary::$func, |
| 559 | $image_func, |
| 560 | ); |
| 561 | generic_qubit_unitary_test( |
| 562 | num_qubits, |
| 563 | qubit_index, |
| 564 | CliffordUnitaryModPauli::$func, |
| 565 | $image_func, |
| 566 | ); |
| 567 | } |
| 568 | } |
| 569 | }; |
| 570 | } |
| 571 | |
| 572 | macro_rules! generic_two_qubit_unitary_test_macro { |
| 573 | ($func:ident, $image_func:expr) => { |
| 574 | for num_qubits in 0..6 { |
| 575 | for qubit_index1 in 0..num_qubits { |
| 576 | for qubit_index2 in 0..num_qubits { |
| 577 | if qubit_index1 != qubit_index2 { |
| 578 | generic_two_qubit_unitary_test( |
| 579 | num_qubits, |
| 580 | qubit_index1, |
| 581 | qubit_index2, |
| 582 | CliffordUnitary::$func, |
| 583 | $image_func, |
| 584 | ); |
| 585 | generic_two_qubit_unitary_test( |
| 586 | num_qubits, |
| 587 | qubit_index1, |
| 588 | qubit_index2, |
| 589 | CliffordUnitaryModPauli::$func, |
| 590 | $image_func, |
| 591 | ); |
| 592 | } |
| 593 | } |
| 594 | } |
| 595 | } |
| 596 | }; |
| 597 | } |
| 598 | |
| 599 | #[test] |
| 600 | fn hadamard_test() { |
| 601 | generic_qubit_unitary_test_macro!(left_mul_hadamard, h_images); |
| 602 | } |
| 603 | |
| 604 | #[test] |
| 605 | fn root_x_test() { |
| 606 | generic_qubit_unitary_test_macro!(left_mul_root_x, root_x_images); |
| 607 | generic_qubit_unitary_test_macro!(left_mul_root_x_inverse, root_x_inv_images); |
| 608 | } |
| 609 | |
| 610 | #[test] |
| 611 | fn root_z_test() { |
| 612 | generic_qubit_unitary_test_macro!(left_mul_root_z, root_z_images); |
| 613 | generic_qubit_unitary_test_macro!(left_mul_root_z_inverse, root_z_inv_images); |
| 614 | } |
| 615 | |
| 616 | #[test] |
| 617 | fn root_y_test() { |
| 618 | generic_qubit_unitary_test_macro!(left_mul_root_y, root_y_images); |
| 619 | generic_qubit_unitary_test_macro!(left_mul_root_y_inverse, root_y_inv_images); |
| 620 | } |
| 621 | |
| 622 | #[test] |
| 623 | fn xyz_test() { |
| 624 | generic_qubit_unitary_test_macro!(left_mul_x, x_images); |
| 625 | generic_qubit_unitary_test_macro!(left_mul_y, y_images); |
| 626 | generic_qubit_unitary_test_macro!(left_mul_z, z_images); |
| 627 | } |
| 628 | |
| 629 | #[test] |
| 630 | fn cx_test() { |
| 631 | generic_two_qubit_unitary_test_macro!(left_mul_cx, cx_images); |
| 632 | } |
| 633 | |
| 634 | #[test] |
| 635 | fn cz_test() { |
| 636 | generic_two_qubit_unitary_test_macro!(left_mul_cz, cz_images); |
| 637 | } |
| 638 | |
| 639 | #[test] |
| 640 | fn swap_test() { |
| 641 | generic_two_qubit_unitary_test_macro!(left_mul_swap, swap_images); |
| 642 | } |
| 643 | |
| 644 | #[test] |
| 645 | fn prepare_bell_test() { |
| 646 | generic_two_qubit_unitary_test_macro!(left_mul_prepare_bell, prepare_bell_images); |
| 647 | } |
| 648 | |
| 649 | type ImageTable = Vec<( |
| 650 | Vec<PositionedPauliObservable>, |
| 651 | Vec<PositionedPauliObservable>, |
| 652 | )>; |
| 653 | |
| 654 | fn cx_images(c: usize, t: usize) -> ImageTable { |
| 655 | vec![ |
| 656 | (vec![x(c)], vec![x(c), x(t)]), |
| 657 | (vec![z(c)], vec![z(c)]), |
| 658 | (vec![x(t)], vec![x(t)]), |
| 659 | (vec![z(t)], vec![z(c), z(t)]), |
| 660 | (vec![y(t)], vec![z(c), y(t)]), |
| 661 | (vec![y(c)], vec![y(c), x(t)]), |
| 662 | ] |
| 663 | } |
| 664 | |
| 665 | fn cz_images(c: usize, t: usize) -> ImageTable { |
| 666 | vec![ |
| 667 | (vec![x(c)], vec![x(c), z(t)]), |
| 668 | (vec![z(c)], vec![z(c)]), |
| 669 | (vec![x(t)], vec![z(c), x(t)]), |
| 670 | (vec![z(t)], vec![z(t)]), |
| 671 | (vec![y(t)], vec![z(c), y(t)]), |
| 672 | (vec![y(c)], vec![y(c), z(t)]), |
| 673 | ] |
| 674 | } |
| 675 | |
| 676 | fn swap_images(q1: usize, q2: usize) -> ImageTable { |
| 677 | vec![ |
| 678 | (vec![x(q1)], vec![x(q2)]), |
| 679 | (vec![z(q1)], vec![z(q2)]), |
| 680 | (vec![y(q1)], vec![y(q2)]), |
| 681 | (vec![-x(q1), z(q2)], vec![-x(q2), z(q1)]), |
| 682 | ] |
| 683 | } |
| 684 | |
| 685 | fn prepare_bell_images(q1: usize, q2: usize) -> ImageTable { |
| 686 | vec![ |
| 687 | (vec![z(q1)], vec![x(q1), x(q2)]), |
| 688 | (vec![x(q1)], vec![z(q1)]), |
| 689 | (vec![z(q2)], vec![z(q1), z(q2)]), |
| 690 | (vec![x(q2)], vec![x(q2)]), |
| 691 | (vec![z(q1), z(q2)], vec![-y(q1), y(q2)]), |
| 692 | ] |
| 693 | } |
| 694 | |
| 695 | fn x_images(q: usize) -> ImageTable { |
| 696 | vec![ |
| 697 | (vec![z(q)], vec![-z(q)]), |
| 698 | (vec![x(q)], vec![x(q)]), |
| 699 | (vec![y(q)], vec![-y(q)]), |
| 700 | ] |
| 701 | } |
| 702 | |
| 703 | fn y_images(q: usize) -> ImageTable { |
| 704 | vec![ |
| 705 | (vec![z(q)], vec![-z(q)]), |
| 706 | (vec![x(q)], vec![-x(q)]), |
| 707 | (vec![y(q)], vec![y(q)]), |
| 708 | ] |
| 709 | } |
| 710 | |
| 711 | fn z_images(q: usize) -> ImageTable { |
| 712 | vec![ |
| 713 | (vec![z(q)], vec![z(q)]), |
| 714 | (vec![x(q)], vec![-x(q)]), |
| 715 | (vec![y(q)], vec![-y(q)]), |
| 716 | ] |
| 717 | } |
| 718 | |
| 719 | fn h_images(q: usize) -> ImageTable { |
| 720 | vec![ |
| 721 | (vec![x(q)], vec![z(q)]), |
| 722 | (vec![z(q)], vec![x(q)]), |
| 723 | (vec![y(q)], vec![-y(q)]), |
| 724 | ] |
| 725 | } |
| 726 | |
| 727 | fn root_z_images(q: usize) -> ImageTable { |
| 728 | vec![ |
| 729 | (vec![z(q)], vec![z(q)]), |
| 730 | (vec![x(q)], vec![y(q)]), |
| 731 | (vec![y(q)], vec![-x(q)]), |
| 732 | ] |
| 733 | } |
| 734 | |
| 735 | fn root_z_inv_images(q: usize) -> ImageTable { |
| 736 | vec![ |
| 737 | (vec![z(q)], vec![z(q)]), |
| 738 | (vec![x(q)], vec![-y(q)]), |
| 739 | (vec![y(q)], vec![x(q)]), |
| 740 | ] |
| 741 | } |
| 742 | |
| 743 | fn root_x_images(q: usize) -> ImageTable { |
| 744 | vec![ |
| 745 | (vec![z(q)], vec![-y(q)]), |
| 746 | (vec![x(q)], vec![x(q)]), |
| 747 | (vec![y(q)], vec![z(q)]), |
| 748 | ] |
| 749 | } |
| 750 | |
| 751 | fn root_x_inv_images(q: usize) -> ImageTable { |
| 752 | vec![ |
| 753 | (vec![z(q)], vec![y(q)]), |
| 754 | (vec![x(q)], vec![x(q)]), |
| 755 | (vec![y(q)], vec![-z(q)]), |
| 756 | ] |
| 757 | } |
| 758 | |
| 759 | fn root_y_images(q: usize) -> ImageTable { |
| 760 | vec![ |
| 761 | (vec![z(q)], vec![x(q)]), |
| 762 | (vec![x(q)], vec![-z(q)]), |
| 763 | (vec![y(q)], vec![y(q)]), |
| 764 | ] |
| 765 | } |
| 766 | |
| 767 | fn root_y_inv_images(q: usize) -> ImageTable { |
| 768 | vec![ |
| 769 | (vec![z(q)], vec![-x(q)]), |
| 770 | (vec![x(q)], vec![z(q)]), |
| 771 | (vec![y(q)], vec![y(q)]), |
| 772 | ] |
| 773 | } |
| 774 | |
| 775 | fn check_images<CliffordLike: TestableClifford>(c: &CliffordLike, image_table: &ImageTable) { |
| 776 | let sparse = sparse::<CliffordLike>; |
| 777 | for (p, im_p) in image_table { |
| 778 | assert!(c.image(&sparse(p)) == im_p.as_slice()); |
| 779 | assert!(c.preimage(&sparse(im_p)) == p.as_slice()); |
| 780 | } |
| 781 | } |
| 782 | |
| 783 | fn generic_qubit_unitary_test<CliffordLike: TestableClifford>( |
| 784 | num_qubits: usize, |
| 785 | qubit_index: usize, |
| 786 | apply_transformation: impl FnOnce(&mut CliffordLike, usize), |
| 787 | images: impl Fn(usize) -> ImageTable, |
| 788 | ) { |
| 789 | let mut c = CliffordLike::identity(num_qubits); |
| 790 | apply_transformation(&mut c, qubit_index); |
| 791 | assert!(c.is_valid()); |
| 792 | check_images(&c, &images(qubit_index)); |
| 793 | for j in c.qubits() { |
| 794 | if j != qubit_index { |
| 795 | assert_identity_on(&c, j); |
| 796 | } |
| 797 | } |
| 798 | } |
| 799 | |
| 800 | fn generic_two_qubit_unitary_test<CliffordLike: TestableClifford>( |
| 801 | num_qubits: usize, |
| 802 | qubit_index1: usize, |
| 803 | qubit_index2: usize, |
| 804 | apply_transformation: impl FnOnce(&mut CliffordLike, usize, usize), |
| 805 | images: impl Fn(usize, usize) -> ImageTable, |
| 806 | ) { |
| 807 | let mut c = CliffordLike::identity(num_qubits); |
| 808 | apply_transformation(&mut c, qubit_index1, qubit_index2); |
| 809 | assert!(c.is_valid()); |
| 810 | check_images(&c, &images(qubit_index1, qubit_index2)); |
| 811 | for j in c.qubits() { |
| 812 | if j != qubit_index1 && j != qubit_index2 { |
| 813 | assert_identity_on(&c, j); |
| 814 | } |
| 815 | } |
| 816 | } |
| 817 | |
| 818 | fn assert_identity_on(c: &impl Clifford, qubit_index: usize) { |
| 819 | assert!(c.image_x(qubit_index).is_pauli_x(qubit_index)); |
| 820 | assert!(c.image_z(qubit_index).is_pauli_z(qubit_index)); |
| 821 | assert!(c.preimage_x(qubit_index).is_pauli_x(qubit_index)); |
| 822 | assert!(c.preimage_z(qubit_index).is_pauli_z(qubit_index)); |
| 823 | } |
| 824 | |
| 825 | fn generic_prepare_bell_states_test<CliffordLike: TestableClifford>() { |
| 826 | let c = clifford_to_prepare_bell_states::<CliffordLike>(1); |
| 827 | assert!(c.is_valid()); |
| 828 | assert!(c.image_z(0) == [x(0), x(1)].borrow()); |
| 829 | assert!(c.image_z(1) == [z(0), z(1)].borrow()); |
| 830 | } |
| 831 | |
| 832 | #[test] |
| 833 | fn clifford_to_prepare_bell_states_test() { |
| 834 | generic_prepare_bell_states_test::<CliffordUnitaryModPauli>(); |
| 835 | generic_prepare_bell_states_test::<CliffordUnitary>(); |
| 836 | } |
| 837 | |
| 838 | fn is_identity_by_images(clifford: &impl Clifford) -> bool { |
| 839 | for qubit_id in 0..clifford.num_qubits() { |
| 840 | if !clifford.image_z(qubit_id).is_pauli_z(qubit_id) { |
| 841 | return false; |
| 842 | } |
| 843 | if !clifford.image_x(qubit_id).is_pauli_x(qubit_id) { |
| 844 | return false; |
| 845 | } |
| 846 | } |
| 847 | true |
| 848 | } |
| 849 | |
| 850 | fn generic_clifford_identity_test<CliffordLike: Clifford>(max_qubits: usize) { |
| 851 | for j in 0..max_qubits { |
| 852 | let id = CliffordLike::identity(j); |
| 853 | assert!(id.is_valid()); |
| 854 | assert!(id.is_identity()); |
| 855 | assert!(is_identity_by_images(&id)); |
| 856 | } |
| 857 | } |
| 858 | |
| 859 | #[test] |
| 860 | fn clifford_identity_test() { |
| 861 | let max_qubits = 10usize; |
| 862 | generic_clifford_identity_test::<CliffordUnitaryModPauli>(max_qubits); |
| 863 | generic_clifford_identity_test::<CliffordUnitary>(max_qubits); |
| 864 | } |
| 865 | |
| 866 | fn two_qubit_clifford<CliffordLike: TestableClifford>( |
| 867 | transformation: impl FnOnce(&mut CliffordLike, usize, usize), |
| 868 | ) -> CliffordLike { |
| 869 | let mut res = CliffordLike::identity(2); |
| 870 | transformation(&mut res, 0, 1); |
| 871 | res |
| 872 | } |
| 873 | |
| 874 | fn one_qubit_clifford<CliffordLike: TestableClifford>( |
| 875 | transformation: impl FnOnce(&mut CliffordLike, usize), |
| 876 | ) -> CliffordLike { |
| 877 | let mut res = CliffordLike::identity(1); |
| 878 | transformation(&mut res, 0); |
| 879 | res |
| 880 | } |
| 881 | |
| 882 | fn clifford_examples<CliffordLike: TestableClifford>() -> Vec<CliffordLike> { |
| 883 | vec![ |
| 884 | one_qubit_clifford(CliffordLike::left_mul_x), |
| 885 | one_qubit_clifford(CliffordLike::left_mul_y), |
| 886 | one_qubit_clifford(CliffordLike::left_mul_z), |
| 887 | one_qubit_clifford(CliffordLike::left_mul_hadamard), |
| 888 | one_qubit_clifford(CliffordLike::left_mul_root_x), |
| 889 | one_qubit_clifford(CliffordLike::left_mul_root_y), |
| 890 | one_qubit_clifford(CliffordLike::left_mul_root_z), |
| 891 | one_qubit_clifford(CliffordLike::left_mul_root_x_inverse), |
| 892 | one_qubit_clifford(CliffordLike::left_mul_root_y_inverse), |
| 893 | one_qubit_clifford(CliffordLike::left_mul_root_z_inverse), |
| 894 | two_qubit_clifford(CliffordLike::left_mul_cx), |
| 895 | two_qubit_clifford(CliffordLike::left_mul_cz), |
| 896 | two_qubit_clifford(CliffordLike::left_mul_swap), |
| 897 | two_qubit_clifford(CliffordLike::left_mul_prepare_bell), |
| 898 | ] |
| 899 | } |
| 900 | |
| 901 | fn clifford_order2_examples<CliffordLike: TestableClifford>() -> Vec<CliffordLike> { |
| 902 | vec![ |
| 903 | one_qubit_clifford(CliffordLike::left_mul_x), |
| 904 | one_qubit_clifford(CliffordLike::left_mul_y), |
| 905 | one_qubit_clifford(CliffordLike::left_mul_z), |
| 906 | one_qubit_clifford(CliffordLike::left_mul_hadamard), |
| 907 | two_qubit_clifford(CliffordLike::left_mul_cx), |
| 908 | two_qubit_clifford(CliffordLike::left_mul_cz), |
| 909 | two_qubit_clifford(CliffordLike::left_mul_swap), |
| 910 | ] |
| 911 | } |
| 912 | |
| 913 | fn assert_images_consistent<CliffordLike: TestableClifford>(clifford: &CliffordLike) { |
| 914 | let sparse = sparse::<CliffordLike>; |
| 915 | for qubit_index in clifford.qubits() { |
| 916 | let im_x = clifford.image_x(qubit_index); |
| 917 | let im_z = clifford.image_z(qubit_index); |
| 918 | assert!(clifford.image_x_bits(&IndexSet::singleton(qubit_index)) == im_x); |
| 919 | assert!(clifford.image_z_bits(&IndexSet::singleton(qubit_index)) == im_z); |
| 920 | assert!(clifford.image(&sparse(&[x(qubit_index)])) == im_x); |
| 921 | assert!(clifford.image(&sparse(&[z(qubit_index)])) == im_z); |
| 922 | } |
| 923 | } |
| 924 | |
| 925 | fn assert_preimages_consistent<CliffordLike: TestableClifford>(clifford: &CliffordLike) { |
| 926 | let sparse = sparse::<CliffordLike>; |
| 927 | for qubit_index in clifford.qubits() { |
| 928 | let pre_im_x = clifford.preimage_x(qubit_index); |
| 929 | let pre_im_z = clifford.preimage_z(qubit_index); |
| 930 | assert!(clifford.preimage_x_bits(&IndexSet::singleton(qubit_index)) == pre_im_x); |
| 931 | assert!(clifford.preimage_z_bits(&IndexSet::singleton(qubit_index)) == pre_im_z); |
| 932 | assert!(clifford.preimage(&sparse(&[x(qubit_index)])) == pre_im_x); |
| 933 | assert!(clifford.preimage(&sparse(&[z(qubit_index)])) == pre_im_z); |
| 934 | } |
| 935 | } |
| 936 | |
| 937 | fn assert_inverse_and_multiply_are_consistent<CliffordLike: TestableClifford>( |
| 938 | clifford: &CliffordLike, |
| 939 | ) { |
| 940 | let inv = clifford.inverse(); |
| 941 | assert!(inv.multiply_with(clifford).is_identity()); |
| 942 | assert!(clifford.multiply_with(&inv).is_identity()); |
| 943 | } |
| 944 | |
| 945 | fn generic_consistency_test<CliffordLike: TestableClifford>() { |
| 946 | let test_cases = clifford_examples::<CliffordLike>(); |
| 947 | for c in test_cases { |
| 948 | assert!(c.is_valid()); |
| 949 | assert_images_consistent(&c); |
| 950 | assert_preimages_consistent(&c); |
| 951 | assert_inverse_and_multiply_are_consistent(&c); |
| 952 | } |
| 953 | } |
| 954 | |
| 955 | #[test] |
| 956 | pub fn clifford_consistency_test() { |
| 957 | generic_consistency_test::<CliffordUnitary>(); |
| 958 | generic_consistency_test::<CliffordUnitaryModPauli>(); |
| 959 | } |
| 960 | |
| 961 | fn generic_multiply_test<CliffordLike: TestableClifford>() { |
| 962 | let examples = clifford_order2_examples::<CliffordLike>(); |
| 963 | for clifford in examples { |
| 964 | let r = clifford.multiply_with(&clifford); |
| 965 | assert!(r.is_valid()); |
| 966 | assert!(r.is_identity()); |
| 967 | } |
| 968 | } |
| 969 | |
| 970 | #[test] |
| 971 | pub fn clifford_multiply_test() { |
| 972 | generic_multiply_test::<CliffordUnitary>(); |
| 973 | generic_multiply_test::<CliffordUnitaryModPauli>(); |
| 974 | } |
| 975 | |
| 976 | fn compare_clifford_transformations<CliffordLike: TestableClifford>( |
| 977 | num_qubits: usize, |
| 978 | apply_transformation1: impl FnOnce(&mut CliffordLike), |
| 979 | apply_transformation2: impl FnOnce(&mut CliffordLike), |
| 980 | ) { |
| 981 | let mut c1 = CliffordLike::identity(num_qubits); |
| 982 | let mut c2 = CliffordLike::identity(num_qubits); |
| 983 | apply_transformation1(&mut c1); |
| 984 | apply_transformation2(&mut c2); |
| 985 | assert!(c1.is_valid()); |
| 986 | assert!(c2.is_valid()); |
| 987 | assert!(c1 == c2); |
| 988 | } |
| 989 | |
| 990 | fn sparse<CliffordLike: TestableClifford>( |
| 991 | observable: &[PositionedPauliObservable], |
| 992 | ) -> <CliffordLike as TestableClifford>::SparsePauli { |
| 993 | CliffordLike::SparsePauli::from(observable) |
| 994 | } |
| 995 | |
| 996 | fn apply_exp_zz<CliffordLike: TestableClifford>(clifford: &mut CliffordLike) { |
| 997 | clifford.left_mul_pauli_exp(&sparse::<CliffordLike>(&[z(0), z(1)])); |
| 998 | } |
| 999 | |
| 1000 | fn apply_exp_xx<CliffordLike: TestableClifford>(clifford: &mut CliffordLike) { |
| 1001 | clifford.left_mul_pauli_exp(&sparse::<CliffordLike>(&[x(0), x(1)])); |
| 1002 | } |
| 1003 | |
| 1004 | fn apply_cz<CliffordLike: TestableClifford>(clifford: &mut CliffordLike) { |
| 1005 | clifford.left_mul_cz(0, 1); |
| 1006 | } |
| 1007 | |
| 1008 | fn apply_cz2<CliffordLike: TestableClifford>(clifford: &mut CliffordLike) { |
| 1009 | let z = |j| CliffordLike::SparsePauli::from(&[z(j)]); |
| 1010 | clifford.left_mul_controlled_pauli(&z(0), &z(1)); |
| 1011 | } |
| 1012 | |
| 1013 | fn apply_cz3<CliffordLike: TestableClifford>(clifford: &mut CliffordLike) { |
| 1014 | let sparse = sparse::<CliffordLike>; |
| 1015 | clifford.left_mul_pauli_exp(&sparse(&[-z(0)])); |
| 1016 | clifford.left_mul_pauli_exp(&sparse(&[z(0), z(1)])); |
| 1017 | clifford.left_mul_pauli_exp(&sparse(&[-z(1)])); |
| 1018 | } |
| 1019 | |
| 1020 | fn apply_exp_zz_via_cx(clifford: &mut impl TestableClifford) { |
| 1021 | clifford.left_mul_cx(1, 0); |
| 1022 | clifford.left_mul_root_z_inverse(0); |
| 1023 | clifford.left_mul_cx(1, 0); |
| 1024 | } |
| 1025 | |
| 1026 | fn apply_exp_xx_via_cx(clifford: &mut impl TestableClifford) { |
| 1027 | clifford.left_mul_cx(1, 0); |
| 1028 | clifford.left_mul_root_x_inverse(1); |
| 1029 | clifford.left_mul_cx(1, 0); |
| 1030 | } |
| 1031 | |
| 1032 | fn root_xyz_identities<CliffordLike: TestableClifford>() { |
| 1033 | let mut clifford = CliffordLike::identity(3); |
| 1034 | let sparse = sparse::<CliffordLike>; |
| 1035 | clifford.left_mul_pauli_exp(&sparse(&[-z(0)])); |
| 1036 | clifford.left_mul_root_z_inverse(0); |
| 1037 | assert!(clifford.is_identity()); |
| 1038 | clifford.left_mul_pauli_exp(&sparse(&[-x(1)])); |
| 1039 | clifford.left_mul_root_x_inverse(1); |
| 1040 | assert!(clifford.is_identity()); |
| 1041 | clifford.left_mul_pauli_exp(&sparse(&[-y(2)])); |
| 1042 | clifford.left_mul_root_y_inverse(2); |
| 1043 | assert!(clifford.is_identity()); |
| 1044 | clifford.left_mul_hadamard(2); |
| 1045 | clifford.left_mul_pauli_exp(&sparse(&[-z(2)])); |
| 1046 | clifford.left_mul_hadamard(2); |
| 1047 | clifford.left_mul_root_x_inverse(2); |
| 1048 | assert!(clifford.is_identity()); |
| 1049 | } |
| 1050 | |
| 1051 | fn generic_clifford_identities_test<CliffordLike: TestableClifford>() { |
| 1052 | compare_clifford_transformations::<CliffordLike>(2, apply_exp_zz_via_cx, apply_exp_zz); |
| 1053 | compare_clifford_transformations::<CliffordLike>(2, apply_exp_xx_via_cx, apply_exp_xx); |
| 1054 | compare_clifford_transformations::<CliffordLike>(2, apply_cz, apply_cz2); |
| 1055 | compare_clifford_transformations::<CliffordLike>(2, apply_cz, apply_cz3); |
| 1056 | root_xyz_identities::<CliffordLike>(); |
| 1057 | } |
| 1058 | |
| 1059 | fn controlled_pauli_via_pauli_exp_test( |
| 1060 | control: &[PositionedPauliObservable], |
| 1061 | target: &[PositionedPauliObservable], |
| 1062 | ) { |
| 1063 | let mut control_sparse: SparsePauli = control.into(); |
| 1064 | let mut target_sparse: SparsePauli = target.into(); |
| 1065 | |
| 1066 | let mut p1p2 = control_sparse.clone(); |
| 1067 | p1p2.mul_assign_right(&target_sparse); |
| 1068 | |
| 1069 | let num_qubits = |
| 1070 | std::cmp::max(control_sparse.max_qubit_id(), target_sparse.max_qubit_id()).unwrap() + 1; |
| 1071 | let mut clifford1 = CliffordUnitary::identity(num_qubits); |
| 1072 | let mut clifford2 = CliffordUnitary::identity(num_qubits); |
| 1073 | clifford1.left_mul_controlled_pauli(&control_sparse, &target_sparse); |
| 1074 | clifford2.left_mul_pauli_exp(&p1p2); |
| 1075 | control_sparse.add_assign_phase_exp(2); |
| 1076 | clifford2.left_mul_pauli_exp(&control_sparse); |
| 1077 | target_sparse.add_assign_phase_exp(2); |
| 1078 | clifford2.left_mul_pauli_exp(&target_sparse); |
| 1079 | assert_eq!(clifford1, clifford2); |
| 1080 | } |
| 1081 | |
| 1082 | #[test] |
| 1083 | fn clifford_identities_test() { |
| 1084 | controlled_pauli_via_pauli_exp_test(&[z(0)], &[z(1)]); |
| 1085 | controlled_pauli_via_pauli_exp_test(&[z(0)], &[x(1)]); |
| 1086 | controlled_pauli_via_pauli_exp_test(&[y(0), x(1)], &[z(0), z(1)]); |
| 1087 | controlled_pauli_via_pauli_exp_test(&[x(0), x(1)], &[z(0), z(1)]); |
| 1088 | generic_clifford_identities_test::<CliffordUnitaryModPauli>(); |
| 1089 | generic_clifford_identities_test::<CliffordUnitary>(); |
| 1090 | } |
| 1091 | |
| 1092 | fn generic_random_tensor_test<CliffordLike: TestableClifford>( |
| 1093 | num_qubits1: usize, |
| 1094 | num_qubits2: usize, |
| 1095 | ) { |
| 1096 | let id1 = CliffordLike::identity(num_qubits1); |
| 1097 | let id2 = CliffordLike::identity(num_qubits2); |
| 1098 | let r1 = CliffordLike::random(num_qubits1, &mut thread_rng()); |
| 1099 | let r2 = CliffordLike::random(num_qubits2, &mut thread_rng()); |
| 1100 | assert!((r1.tensor(&id2)).multiply_with(&(id1.tensor(&r2))) == r1.tensor(&r2)); |
| 1101 | } |
| 1102 | |
| 1103 | fn generic_tensor_test<CliffordLike: TestableClifford>() { |
| 1104 | let mut c1 = CliffordLike::identity(2); |
| 1105 | c1.left_mul_cx(0, 1); |
| 1106 | let mut c2 = CliffordLike::identity(2); |
| 1107 | c2.left_mul_cz(0, 1); |
| 1108 | let mut c1xc2 = CliffordLike::identity(4); |
| 1109 | c1xc2.left_mul_cx(0, 1); |
| 1110 | c1xc2.left_mul_cz(2, 3); |
| 1111 | assert!(c1xc2 == c1.tensor(&c2)); |
| 1112 | |
| 1113 | for _ in 0..10 { |
| 1114 | generic_random_tensor_test::<CliffordLike>(5, 10); |
| 1115 | } |
| 1116 | } |
| 1117 | |
| 1118 | #[test] |
| 1119 | fn tensor_test() { |
| 1120 | generic_tensor_test::<CliffordUnitary>(); |
| 1121 | generic_tensor_test::<CliffordUnitaryModPauli>(); |
| 1122 | } |
| 1123 | |
| 1124 | fn are_bits_equal_to_col(bitstring: &impl Bitwise, matrix: &BitMatrix, col: usize) -> bool { |
| 1125 | for j in 0..matrix.columncount() { |
| 1126 | if matrix[(j, col)] != bitstring.index(j) { |
| 1127 | return false; |
| 1128 | } |
| 1129 | } |
| 1130 | true |
| 1131 | } |
| 1132 | |
| 1133 | /// # Panics |
| 1134 | /// |
| 1135 | /// Will panic |
| 1136 | pub fn random_bitmatrix(rowcount: usize, columncount: usize) -> BitMatrix { |
| 1137 | let mut matrix = BitMatrix::with_shape(rowcount, columncount); |
| 1138 | let mut bits = std::iter::from_fn(move || Some(rand::Rng::gen::<bool>(&mut thread_rng()))); |
| 1139 | for row_index in 0..rowcount { |
| 1140 | for column_index in 0..columncount { |
| 1141 | matrix.set((row_index, column_index), bits.next().expect("boom")); |
| 1142 | } |
| 1143 | } |
| 1144 | matrix |
| 1145 | } |
| 1146 | |
| 1147 | #[test] |
| 1148 | fn css_clifford_test() { |
| 1149 | let mut num_tests = 0; |
| 1150 | while num_tests < 100 { |
| 1151 | let num_qubits = 10; |
| 1152 | let a = random_bitmatrix(num_qubits, num_qubits); |
| 1153 | if a.rank() == a.rowcount() { |
| 1154 | num_tests += 1; |
| 1155 | let a_inv_t = a.inverted().transposed(); |
| 1156 | let c = CliffordUnitary::from_css_preimage_indicators(&a, &a_inv_t); |
| 1157 | assert!(c.is_valid()); |
| 1158 | for k in c.qubits() { |
| 1159 | assert!(c.preimage_z(k).x_bits().is_zero()); |
| 1160 | assert!(c.preimage_z(k).z_bits() == &a_inv_t.row(k)); |
| 1161 | assert!(c.image_z(k).x_bits().is_zero()); |
| 1162 | assert!(are_bits_equal_to_col(c.image_z(k).z_bits(), &a, k)); |
| 1163 | |
| 1164 | assert!(c.preimage_x(k).z_bits().is_zero()); |
| 1165 | assert!(c.preimage_x(k).x_bits() == &a.row(k)); |
| 1166 | assert!(c.image_x(k).z_bits().is_zero()); |
| 1167 | assert!(are_bits_equal_to_col(c.image_x(k).x_bits(), &a_inv_t, k)); |
| 1168 | } |
| 1169 | } |
| 1170 | } |
| 1171 | } |
| 1172 | |
| 1173 | fn left_mul_clifford_generic_test<CliffordLike: TestableClifford>() { |
| 1174 | let mut clifford1 = CliffordLike::identity(4); |
| 1175 | let mut clifford2 = CliffordLike::identity(2); |
| 1176 | clifford1.left_mul_cx(1, 2); |
| 1177 | clifford2.left_mul_cx(0, 1); |
| 1178 | clifford1.left_mul_clifford(&clifford2, &[1, 2]); |
| 1179 | assert! {clifford1.is_identity()} |
| 1180 | clifford1.left_mul_cx(2, 3); |
| 1181 | clifford1.left_mul_clifford(&clifford2, &[2, 3]); |
| 1182 | } |
| 1183 | |
| 1184 | #[test] |
| 1185 | fn left_mul_clifford_test() { |
| 1186 | left_mul_clifford_generic_test::<CliffordUnitary>(); |
| 1187 | left_mul_clifford_generic_test::<CliffordUnitaryModPauli>(); |
| 1188 | } |
| 1189 | |
| 1190 | fn left_mul_permutation_generic_test<CliffordLike: TestableClifford>() { |
| 1191 | let mut clifford1 = CliffordLike::identity(3); |
| 1192 | clifford1.left_mul_swap(0, 1); |
| 1193 | clifford1.left_mul_swap(1, 2); |
| 1194 | clifford1.left_mul_permutation(&[2, 0, 1], &[0, 1, 2]); |
| 1195 | assert!(clifford1.is_identity()); |
| 1196 | } |
| 1197 | |
| 1198 | #[test] |
| 1199 | fn left_mul_permutation_test() { |
| 1200 | left_mul_permutation_generic_test::<CliffordUnitary>(); |
| 1201 | left_mul_permutation_generic_test::<CliffordUnitaryModPauli>(); |
| 1202 | } |
| 1203 | |
| 1204 | fn format_string_roundtrip_generic_test<CliffordLike: TestableClifford>(clifford: &CliffordLike) { |
| 1205 | let sparse_str = format!("{clifford}"); |
| 1206 | let dense_str = format!("{clifford:#}"); |
| 1207 | let clifford1 = sparse_str.parse::<CliffordLike>().expect(&sparse_str); |
| 1208 | let clifford2 = dense_str.parse::<CliffordLike>().expect(&dense_str); |
| 1209 | assert_eq!(clifford, &clifford1); |
| 1210 | assert_eq!(clifford, &clifford2); |
| 1211 | } |
| 1212 | |
| 1213 | fn random_diagonal_clifford<CliffordLike: TestableClifford>(qubit_count: usize) -> CliffordLike { |
| 1214 | let generators = diagonal_operations(qubit_count); |
| 1215 | random_clifford_via_operations_sampling(qubit_count, qubit_count * qubit_count, &generators) |
| 1216 | } |
| 1217 | |
| 1218 | fn random_css_clifford<CliffordLike: TestableClifford>(qubit_count: usize) -> CliffordLike { |
| 1219 | let generators = css_operations(qubit_count); |
| 1220 | random_clifford_via_operations_sampling(qubit_count, qubit_count * qubit_count, &generators) |
| 1221 | } |
| 1222 | |
| 1223 | fn generic_diagonal_clifford_test<CliffordLike: TestableClifford>(c: &CliffordLike) { |
| 1224 | use XOrZ::{X, Z}; |
| 1225 | assert!(c.is_diagonal(Z)); |
| 1226 | assert!(c.inverse().is_diagonal(Z)); |
| 1227 | |
| 1228 | let qubit_count = c.num_qubits(); |
| 1229 | let mut c2 = CliffordLike::identity(qubit_count); |
| 1230 | transverse_h(&mut c2); |
| 1231 | c2.left_mul_clifford(c, &c.qubits().collect::<Vec<_>>()); |
| 1232 | assert!(c2.is_diagonal_resource_encoder(Z)); |
| 1233 | let c3 = c2.unitary_from_diagonal_resource_state(Z).unwrap(); |
| 1234 | assert!(c3.is_valid()); |
| 1235 | assert!(c3.is_diagonal(Z)); |
| 1236 | for qubit_index in c3.qubits() { |
| 1237 | assert_eq!(c3.image_x(qubit_index), c2.image_z(qubit_index)); |
| 1238 | } |
| 1239 | |
| 1240 | transverse_h(&mut c2); |
| 1241 | assert!(c2.is_diagonal(X)); |
| 1242 | assert!(c2.inverse().is_diagonal(X)); |
| 1243 | assert!(c2.is_diagonal_resource_encoder(X)); |
| 1244 | let c4 = c2.unitary_from_diagonal_resource_state(X).unwrap(); |
| 1245 | assert!(c4.is_valid()); |
| 1246 | assert!(c4.is_diagonal(X)); |
| 1247 | for qubit_index in c4.qubits() { |
| 1248 | assert_eq!(c4.image_z(qubit_index), c2.image_z(qubit_index)); |
| 1249 | } |
| 1250 | } |
| 1251 | |
| 1252 | fn generic_is_css_clifford_test<CliffordLike: TestableClifford>(c: &CliffordLike) { |
| 1253 | assert!(c.is_css()); |
| 1254 | } |
| 1255 | |
| 1256 | fn transverse_h<CliffordLike: TestableClifford>(clifford: &mut CliffordLike) { |
| 1257 | for qubit_index in clifford.qubits() { |
| 1258 | clifford.left_mul_hadamard(qubit_index); |
| 1259 | } |
| 1260 | } |
| 1261 | |
| 1262 | fn check_left_mul_root_and_apply_root_are_consistent( |
| 1263 | qubit_count: usize, |
| 1264 | left_mul_root: fn(&mut CliffordUnitary, usize), |
| 1265 | apply_root: fn(&mut DensePauli, usize), |
| 1266 | ) { |
| 1267 | let mut clifford = CliffordUnitary::identity(qubit_count); |
| 1268 | for target_qubit in 0..qubit_count { |
| 1269 | let mut image = clifford.image_z(target_qubit); |
| 1270 | left_mul_root(&mut clifford, target_qubit); |
| 1271 | apply_root(&mut image, target_qubit); |
| 1272 | assert_eq!(image, clifford.image_z(target_qubit)); |
| 1273 | } |
| 1274 | } |