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crates/accelerate/src/synthesis/clifford/random_clifford.rs
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// This code is part of Qiskit. | ||
// | ||
// (C) Copyright IBM 2024 | ||
// | ||
// This code is licensed under the Apache License, Version 2.0. You may | ||
// obtain a copy of this license in the LICENSE.txt file in the root directory | ||
// of this source tree or at http://www.apache.org/licenses/LICENSE-2.0. | ||
// | ||
// Any modifications or derivative works of this code must retain this | ||
// copyright notice, and modified files need to carry a notice indicating | ||
// that they have been altered from the originals. | ||
|
||
use crate::synthesis::linear::utils::{ | ||
binary_matmul_inner, calc_inverse_matrix_inner, replace_row_inner, swap_rows_inner, | ||
}; | ||
use ndarray::{concatenate, s, Array1, Array2, ArrayView2, ArrayViewMut2, Axis}; | ||
use rand::{Rng, SeedableRng}; | ||
use rand_pcg::Pcg64Mcg; | ||
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/// Sample from the quantum Mallows distribution. | ||
fn sample_qmallows(n: usize, rng: &mut Pcg64Mcg) -> (Array1<bool>, Array1<usize>) { | ||
// Hadamard layer | ||
let mut had = Array1::from_elem(n, false); | ||
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// Permutation layer | ||
let mut perm = Array1::from_elem(n, 0); | ||
let mut inds: Vec<usize> = (0..n).collect(); | ||
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for i in 0..n { | ||
let m = n - i; | ||
let eps: f64 = 4f64.powi(-(m as i32)); | ||
let r: f64 = rng.gen(); | ||
let index: usize = -((r + (1f64 - r) * eps).log2().ceil() as isize) as usize; | ||
had[i] = index < m; | ||
let k = if index < m { index } else { 2 * m - index - 1 }; | ||
perm[i] = inds[k]; | ||
inds.remove(k); | ||
} | ||
(had, perm) | ||
} | ||
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/// Add symmetric random boolean value to off diagonal entries. | ||
fn fill_tril(mut mat: ArrayViewMut2<bool>, rng: &mut Pcg64Mcg, symmetric: bool) { | ||
let n = mat.shape()[0]; | ||
for i in 0..n { | ||
for j in 0..i { | ||
mat[[i, j]] = rng.gen(); | ||
if symmetric { | ||
mat[[j, i]] = mat[[i, j]]; | ||
} | ||
} | ||
} | ||
} | ||
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/// Invert a lower-triangular matrix with unit diagonal. | ||
fn inverse_tril(mat: ArrayView2<bool>) -> Array2<bool> { | ||
calc_inverse_matrix_inner(mat, false).unwrap() | ||
} | ||
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/// Generate a random Clifford tableau. | ||
/// | ||
/// The Clifford is sampled using the method of the paper "Hadamard-free circuits | ||
/// expose the structure of the Clifford group" by S. Bravyi and D. Maslov (2020), | ||
/// `https://arxiv.org/abs/2003.09412`__. | ||
/// | ||
/// The function returns a random clifford tableau. | ||
pub fn random_clifford_tableau_inner(num_qubits: usize, seed: Option<u64>) -> Array2<bool> { | ||
let mut rng = match seed { | ||
Some(seed) => Pcg64Mcg::seed_from_u64(seed), | ||
None => Pcg64Mcg::from_entropy(), | ||
}; | ||
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let (had, perm) = sample_qmallows(num_qubits, &mut rng); | ||
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let mut gamma1: Array2<bool> = Array2::from_elem((num_qubits, num_qubits), false); | ||
for i in 0..num_qubits { | ||
gamma1[[i, i]] = rng.gen(); | ||
} | ||
fill_tril(gamma1.view_mut(), &mut rng, true); | ||
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let mut gamma2: Array2<bool> = Array2::from_elem((num_qubits, num_qubits), false); | ||
for i in 0..num_qubits { | ||
gamma2[[i, i]] = rng.gen(); | ||
} | ||
fill_tril(gamma2.view_mut(), &mut rng, true); | ||
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let mut delta1: Array2<bool> = Array2::from_shape_fn((num_qubits, num_qubits), |(i, j)| i == j); | ||
fill_tril(delta1.view_mut(), &mut rng, false); | ||
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let mut delta2: Array2<bool> = Array2::from_shape_fn((num_qubits, num_qubits), |(i, j)| i == j); | ||
fill_tril(delta2.view_mut(), &mut rng, false); | ||
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// Compute stabilizer table | ||
let zero = Array2::from_elem((num_qubits, num_qubits), false); | ||
let prod1 = binary_matmul_inner(gamma1.view(), delta1.view()).unwrap(); | ||
let prod2 = binary_matmul_inner(gamma2.view(), delta2.view()).unwrap(); | ||
let inv1 = inverse_tril(delta1.view()).t().to_owned(); | ||
let inv2 = inverse_tril(delta2.view()).t().to_owned(); | ||
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let table1 = concatenate( | ||
Axis(0), | ||
&[ | ||
concatenate(Axis(1), &[delta1.view(), zero.view()]) | ||
.unwrap() | ||
.view(), | ||
concatenate(Axis(1), &[prod1.view(), inv1.view()]) | ||
.unwrap() | ||
.view(), | ||
], | ||
) | ||
.unwrap(); | ||
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let table2 = concatenate( | ||
Axis(0), | ||
&[ | ||
concatenate(Axis(1), &[delta2.view(), zero.view()]) | ||
.unwrap() | ||
.view(), | ||
concatenate(Axis(1), &[prod2.view(), inv2.view()]) | ||
.unwrap() | ||
.view(), | ||
], | ||
) | ||
.unwrap(); | ||
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// Compute the full stabilizer tableau | ||
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// The code below is identical to the Python implementation, but is based on the original | ||
// code in the paper. | ||
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let mut table = Array2::from_elem((2 * num_qubits, 2 * num_qubits), false); | ||
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// Apply qubit permutation | ||
for i in 0..num_qubits { | ||
replace_row_inner(table.view_mut(), i, table2.slice(s![i, ..])); | ||
replace_row_inner( | ||
table.view_mut(), | ||
perm[i] + num_qubits, | ||
table2.slice(s![perm[i] + num_qubits, ..]), | ||
); | ||
} | ||
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// Apply layer of Hadamards | ||
for i in 0..num_qubits { | ||
if had[i] { | ||
swap_rows_inner(table.view_mut(), i, i + num_qubits); | ||
} | ||
} | ||
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// Apply table | ||
let random_symplectic_mat = binary_matmul_inner(table1.view(), table.view()).unwrap(); | ||
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// Generate random phases | ||
let random_phases: Array2<bool> = Array2::from_shape_fn((2 * num_qubits, 1), |_| rng.gen()); | ||
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let random_tableau: Array2<bool> = concatenate( | ||
Axis(1), | ||
&[random_symplectic_mat.view(), random_phases.view()], | ||
) | ||
.unwrap(); | ||
random_tableau | ||
} |
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