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gate_matrix.rs
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// This code is part of Qiskit.
//
// (C) Copyright IBM 2023
//
// 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 num_complex::Complex64;
use std::f64::consts::FRAC_1_SQRT_2;
// num-complex exposes an equivalent function but it's not a const function
// so it's not compatible with static definitions. This is a const func and
// just reduces the amount of typing we need.
#[inline(always)]
const fn c64(re: f64, im: f64) -> Complex64 {
Complex64::new(re, im)
}
pub static ONE_QUBIT_IDENTITY: [[Complex64; 2]; 2] =
[[c64(1., 0.), c64(0., 0.)], [c64(0., 0.), c64(1., 0.)]];
#[inline]
pub fn rx_gate(theta: f64) -> [[Complex64; 2]; 2] {
let half_theta = theta / 2.;
let cos = c64(half_theta.cos(), 0.);
let isin = c64(0., -half_theta.sin());
[[cos, isin], [isin, cos]]
}
#[inline]
pub fn ry_gate(theta: f64) -> [[Complex64; 2]; 2] {
let half_theta = theta / 2.;
let cos = c64(half_theta.cos(), 0.);
let sin = c64(half_theta.sin(), 0.);
[[cos, -sin], [sin, cos]]
}
#[inline]
pub fn rz_gate(theta: f64) -> [[Complex64; 2]; 2] {
let ilam2 = c64(0., 0.5 * theta);
[[(-ilam2).exp(), c64(0., 0.)], [c64(0., 0.), ilam2.exp()]]
}
pub static H_GATE: [[Complex64; 2]; 2] = [
[c64(FRAC_1_SQRT_2, 0.), c64(FRAC_1_SQRT_2, 0.)],
[c64(FRAC_1_SQRT_2, 0.), c64(-FRAC_1_SQRT_2, 0.)],
];
pub static CX_GATE: [[Complex64; 4]; 4] = [
[c64(1., 0.), c64(0., 0.), c64(0., 0.), c64(0., 0.)],
[c64(0., 0.), c64(0., 0.), c64(0., 0.), c64(1., 0.)],
[c64(0., 0.), c64(0., 0.), c64(1., 0.), c64(0., 0.)],
[c64(0., 0.), c64(1., 0.), c64(0., 0.), c64(0., 0.)],
];
pub static SX_GATE: [[Complex64; 2]; 2] = [
[c64(0.5, 0.5), c64(0.5, -0.5)],
[c64(0.5, -0.5), c64(0.5, 0.5)],
];
pub static SXDG_GATE: [[Complex64; 2]; 2] = [
[c64(0.5, -0.5), c64(0.5, 0.5)],
[c64(0.5, 0.5), c64(0.5, -0.5)],
];
pub static X_GATE: [[Complex64; 2]; 2] = [[c64(0., 0.), c64(1., 0.)], [c64(1., 0.), c64(0., 0.)]];
pub static Z_GATE: [[Complex64; 2]; 2] = [[c64(1., 0.), c64(0., 0.)], [c64(0., 0.), c64(-1., 0.)]];
pub static Y_GATE: [[Complex64; 2]; 2] = [[c64(0., 0.), c64(0., -1.)], [c64(0., 1.), c64(0., 0.)]];
pub static CZ_GATE: [[Complex64; 4]; 4] = [
[c64(1., 0.), c64(0., 0.), c64(0., 0.), c64(0., 0.)],
[c64(0., 0.), c64(1., 0.), c64(0., 0.), c64(0., 0.)],
[c64(0., 0.), c64(0., 0.), c64(1., 0.), c64(0., 0.)],
[c64(0., 0.), c64(0., 0.), c64(0., 0.), c64(-1., 0.)],
];
pub static CY_GATE: [[Complex64; 4]; 4] = [
[c64(1., 0.), c64(0., 0.), c64(0., 0.), c64(0., 0.)],
[c64(0., 0.), c64(0., 0.), c64(0., 0.), c64(0., -1.)],
[c64(0., 0.), c64(0., 0.), c64(1., 0.), c64(0., 0.)],
[c64(0., 0.), c64(0., 1.), c64(0., 0.), c64(0., 0.)],
];
pub static CCX_GATE: [[Complex64; 8]; 8] = [
[
c64(1., 0.),
c64(0., 0.),
c64(0., 0.),
c64(0., 0.),
c64(0., 0.),
c64(0., 0.),
c64(0., 0.),
c64(0., 0.),
],
[
c64(0., 0.),
c64(1., 0.),
c64(0., 0.),
c64(0., 0.),
c64(0., 0.),
c64(0., 0.),
c64(0., 0.),
c64(0., 0.),
],
[
c64(0., 0.),
c64(0., 0.),
c64(1., 0.),
c64(0., 0.),
c64(0., 0.),
c64(0., 0.),
c64(0., 0.),
c64(0., 0.),
],
[
c64(0., 0.),
c64(0., 0.),
c64(0., 0.),
c64(0., 0.),
c64(0., 0.),
c64(0., 0.),
c64(0., 0.),
c64(1., 0.),
],
[
c64(0., 0.),
c64(0., 0.),
c64(0., 0.),
c64(0., 0.),
c64(1., 0.),
c64(0., 0.),
c64(0., 0.),
c64(0., 0.),
],
[
c64(0., 0.),
c64(0., 0.),
c64(0., 0.),
c64(0., 0.),
c64(0., 0.),
c64(1., 0.),
c64(0., 0.),
c64(0., 0.),
],
[
c64(0., 0.),
c64(0., 0.),
c64(0., 0.),
c64(0., 0.),
c64(0., 0.),
c64(0., 0.),
c64(1., 0.),
c64(0., 0.),
],
[
c64(0., 0.),
c64(0., 0.),
c64(0., 0.),
c64(1., 0.),
c64(0., 0.),
c64(0., 0.),
c64(0., 0.),
c64(0., 0.),
],
];
pub static ECR_GATE: [[Complex64; 4]; 4] = [
[
c64(0., 0.),
c64(FRAC_1_SQRT_2, 0.),
c64(0., 0.),
c64(0., FRAC_1_SQRT_2),
],
[
c64(FRAC_1_SQRT_2, 0.),
c64(0., 0.),
c64(0., -FRAC_1_SQRT_2),
c64(0., 0.),
],
[
c64(0., 0.),
c64(0., FRAC_1_SQRT_2),
c64(0., 0.),
c64(FRAC_1_SQRT_2, 0.),
],
[
c64(0., -FRAC_1_SQRT_2),
c64(0., 0.),
c64(FRAC_1_SQRT_2, 0.),
c64(0., 0.),
],
];
pub static SWAP_GATE: [[Complex64; 4]; 4] = [
[c64(1., 0.), c64(0., 0.), c64(0., 0.), c64(0., 0.)],
[c64(0., 0.), c64(0., 0.), c64(1., 0.), c64(0., 0.)],
[c64(0., 0.), c64(1., 0.), c64(0., 0.), c64(0., 0.)],
[c64(0., 0.), c64(0., 0.), c64(0., 0.), c64(1., 0.)],
];
pub static ISWAP_GATE: [[Complex64; 4]; 4] = [
[c64(1., 0.), c64(0., 0.), c64(0., 0.), c64(0., 0.)],
[c64(0., 0.), c64(0., 0.), c64(0., 1.), c64(0., 0.)],
[c64(0., 0.), c64(0., 1.), c64(0., 0.), c64(0., 0.)],
[c64(0., 0.), c64(0., 0.), c64(0., 0.), c64(1., 0.)],
];
pub static S_GATE: [[Complex64; 2]; 2] = [[c64(1., 0.), c64(0., 0.)], [c64(0., 0.), c64(0., 1.)]];
pub static SDG_GATE: [[Complex64; 2]; 2] =
[[c64(1., 0.), c64(0., 0.)], [c64(0., 0.), c64(0., -1.)]];
pub static T_GATE: [[Complex64; 2]; 2] = [
[c64(1., 0.), c64(0., 0.)],
[c64(0., 0.), c64(FRAC_1_SQRT_2, FRAC_1_SQRT_2)],
];
pub static TDG_GATE: [[Complex64; 2]; 2] = [
[c64(1., 0.), c64(0., 0.)],
[c64(0., 0.), c64(FRAC_1_SQRT_2, -FRAC_1_SQRT_2)],
];
#[inline]
pub fn global_phase_gate(theta: f64) -> [[Complex64; 1]; 1] {
[[c64(0., theta).exp()]]
}
#[inline]
pub fn phase_gate(lam: f64) -> [[Complex64; 2]; 2] {
[
[c64(1., 0.), c64(0., 0.)],
[c64(0., 0.), c64(0., lam).exp()],
]
}
#[inline]
pub fn u_gate(theta: f64, phi: f64, lam: f64) -> [[Complex64; 2]; 2] {
let cos = (theta / 2.).cos();
let sin = (theta / 2.).sin();
[
[c64(cos, 0.), (-c64(0., lam).exp()) * sin],
[c64(0., phi).exp() * sin, c64(0., phi + lam).exp() * cos],
]
}
#[inline]
pub fn xx_minus_yy_gate(theta: f64, beta: f64) -> [[Complex64; 4]; 4] {
let cos = (theta / 2.).cos();
let sin = (theta / 2.).sin();
[
[
c64(cos, 0.),
c64(0., 0.),
c64(0., 0.),
c64(0., -sin) * c64(0., -beta).exp(),
],
[c64(0., 0.), c64(1., 0.), c64(0., 0.), c64(0., 0.)],
[c64(0., 0.), c64(0., 0.), c64(1., 0.), c64(0., 0.)],
[
c64(0., -sin) * c64(0., beta).exp(),
c64(0., 0.),
c64(0., 0.),
c64(cos, 0.),
],
]
}
#[inline]
pub fn u1_gate(lam: f64) -> [[Complex64; 2]; 2] {
[
[c64(1., 0.), c64(0., 0.)],
[c64(0., 0.), c64(0., lam).exp()],
]
}
#[inline]
pub fn u2_gate(phi: f64, lam: f64) -> [[Complex64; 2]; 2] {
[
[
c64(FRAC_1_SQRT_2, 0.),
(-c64(0., lam).exp()) * FRAC_1_SQRT_2,
],
[
c64(0., phi).exp() * FRAC_1_SQRT_2,
c64(0., phi + lam).exp() * FRAC_1_SQRT_2,
],
]
}
#[inline]
pub fn u3_gate(theta: f64, phi: f64, lam: f64) -> [[Complex64; 2]; 2] {
let cos = (theta / 2.).cos();
let sin = (theta / 2.).sin();
[
[c64(cos, 0.), -(c64(0., lam).exp()) * sin],
[c64(0., phi).exp() * sin, c64(0., phi + lam).exp() * cos],
]
}
#[inline]
pub fn xx_plus_yy_gate(theta: f64, beta: f64) -> [[Complex64; 4]; 4] {
let cos = (theta / 2.).cos();
let sin = (theta / 2.).sin();
[
[c64(1., 0.), c64(0., 0.), c64(0., 0.), c64(0., 0.)],
[
c64(0., 0.),
c64(cos, 0.),
c64(0., -sin) * c64(0., -beta).exp(),
c64(0., 0.),
],
[
c64(0., 0.),
c64(0., -sin) * c64(0., beta).exp(),
c64(cos, 0.),
c64(0., 0.),
],
[c64(0., 0.), c64(0., 0.), c64(0., 0.), c64(1., 0.)],
]
}