microsoft/qdk
Publicmirrored from https://github.com/microsoft/qdkAvailable
source/paulimer/src/pauli/algorithms.rs
128lines · modecode
| 1 | // Copyright (c) Microsoft Corporation. |
| 2 | // Licensed under the MIT License. |
| 3 | |
| 4 | use super::{anti_commutes_with, DensePauli, Pauli, PauliBinaryOps}; |
| 5 | use crate::{ |
| 6 | bits::{BitMatrix, Bitwise}, |
| 7 | setwise::complement, |
| 8 | NeutralElement, |
| 9 | }; |
| 10 | |
| 11 | /// # Panics |
| 12 | /// Will panic if the input `paulis` are not independent |
| 13 | pub fn complete_to_full_pauli_basis<PauliLike: Pauli>( |
| 14 | paulis: &[PauliLike], |
| 15 | qubit_count: usize, |
| 16 | ) -> Vec<DensePauli> |
| 17 | where |
| 18 | DensePauli: PauliBinaryOps<PauliLike>, |
| 19 | { |
| 20 | let mut paulis_as_bitmatrix = bitmatrix_from_paulis(paulis, qubit_count); |
| 21 | let rank_profile = paulis_as_bitmatrix.echelonize(); |
| 22 | assert_eq!(rank_profile.len(), paulis.len()); |
| 23 | let rank_profile_complement = complement(&rank_profile, 2 * qubit_count); |
| 24 | let mut result = Vec::new(); |
| 25 | for pauli in paulis { |
| 26 | let mut dense_pauli = DensePauli::neutral_element_of_size(qubit_count); |
| 27 | dense_pauli.assign(pauli); |
| 28 | result.push(dense_pauli); |
| 29 | } |
| 30 | for column_index in rank_profile_complement { |
| 31 | if column_index < qubit_count { |
| 32 | result.push(DensePauli::x(column_index, qubit_count)); |
| 33 | } else { |
| 34 | result.push(DensePauli::z(column_index - qubit_count, qubit_count)); |
| 35 | } |
| 36 | } |
| 37 | result |
| 38 | } |
| 39 | |
| 40 | pub fn bitmatrix_from_paulis<PauliLike: Pauli>( |
| 41 | paulis: &[PauliLike], |
| 42 | qubit_count: usize, |
| 43 | ) -> BitMatrix { |
| 44 | let mut result = BitMatrix::zeros(paulis.len(), 2 * qubit_count); |
| 45 | for (row_index, pauli) in paulis.iter().enumerate() { |
| 46 | for x_column_index in pauli.x_bits().support() { |
| 47 | result.set((row_index, x_column_index), true); |
| 48 | } |
| 49 | for z_column_index in pauli.z_bits().support() { |
| 50 | result.set((row_index, qubit_count + z_column_index), true); |
| 51 | } |
| 52 | } |
| 53 | result |
| 54 | } |
| 55 | |
| 56 | pub fn paulis_qubit_count<PauliLike: Pauli>(pauli: &[PauliLike]) -> usize { |
| 57 | pauli |
| 58 | .iter() |
| 59 | .map(super::Pauli::qubit_count) |
| 60 | .max() |
| 61 | .unwrap_or(0) |
| 62 | } |
| 63 | |
| 64 | pub fn are_the_same_group_up_to_phases<PauliLike1: Pauli, PauliLike2: Pauli>( |
| 65 | paulis_left: &[PauliLike1], |
| 66 | paulis_right: &[PauliLike2], |
| 67 | ) -> bool { |
| 68 | let qubit_count = paulis_qubit_count(paulis_left); |
| 69 | if paulis_qubit_count(paulis_right) != qubit_count { |
| 70 | return false; |
| 71 | } |
| 72 | let mut matrix_left = bitmatrix_from_paulis(paulis_left, qubit_count); |
| 73 | let mut matrix_right = bitmatrix_from_paulis(paulis_right, qubit_count); |
| 74 | let left_rank_profile = matrix_left.echelonize(); |
| 75 | let right_rank_profile = matrix_right.echelonize(); |
| 76 | let rank = left_rank_profile.len(); |
| 77 | if rank == right_rank_profile.len() { |
| 78 | matrix_left |
| 79 | .rows() |
| 80 | .take(rank) |
| 81 | .zip(matrix_right.rows().take(rank)) |
| 82 | .all(|(row_left, row_right)| row_left == row_right) |
| 83 | } else { |
| 84 | false |
| 85 | } |
| 86 | } |
| 87 | |
| 88 | pub fn are_mutually_commuting<PauliLike: Pauli>(paulis: &[PauliLike]) -> bool { |
| 89 | for i in 0..paulis.len() { |
| 90 | for j in 0..i { |
| 91 | if anti_commutes_with(&paulis[i], &paulis[j]) { |
| 92 | return false; |
| 93 | } |
| 94 | } |
| 95 | } |
| 96 | true |
| 97 | } |
| 98 | |
| 99 | pub fn apply_pauli_exponent<PauliLike: Pauli + PauliBinaryOps>( |
| 100 | target: &mut PauliLike, |
| 101 | exponent: &PauliLike, |
| 102 | ) { |
| 103 | if anti_commutes_with(target, exponent) { |
| 104 | target.mul_assign_left(exponent); |
| 105 | target.add_assign_phase_exp(1); |
| 106 | } |
| 107 | } |
| 108 | |
| 109 | pub fn apply_root_x<PauliLike: Pauli + PauliBinaryOps>(target: &mut PauliLike, qubit_index: usize) { |
| 110 | if target.z_bits().index(qubit_index) { |
| 111 | target.mul_assign_left_x(qubit_index); |
| 112 | target.add_assign_phase_exp(3); |
| 113 | } |
| 114 | } |
| 115 | |
| 116 | pub fn apply_root_y<PauliLike: Pauli + PauliBinaryOps>(target: &mut PauliLike, qubit_index: usize) { |
| 117 | if !(target.z_bits().index(qubit_index) & target.x_bits().index(qubit_index)) { |
| 118 | target.mul_assign_left_y(qubit_index); |
| 119 | target.add_assign_phase_exp(3); |
| 120 | } |
| 121 | } |
| 122 | |
| 123 | pub fn apply_root_z<PauliLike: Pauli + PauliBinaryOps>(target: &mut PauliLike, qubit_index: usize) { |
| 124 | if target.x_bits().index(qubit_index) { |
| 125 | target.mul_assign_left_z(qubit_index); |
| 126 | target.add_assign_phase_exp(3); |
| 127 | } |
| 128 | } |
| 129 | |