Add partial implementation of xx-decomposer in Rust

crates/accelerate/src/gates.rs

@@ -0,0 +1,50 @@
+// 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, ComplexFloat};
+use num_complex::Complex64;
+use ndarray::prelude::*;
+// For Complex64::zero()
+// use num_traits::Zero;
+use qiskit_circuit::util::{c64, C_ZERO};
+
+pub(crate) fn rz_matrix(theta: f64) -> Array2<Complex64> {
+    let ilam2 = c64(0., 0.5 * theta);
+    array![[(-ilam2).exp(), C_ZERO], [C_ZERO, ilam2.exp()]]
+}
+
+pub(crate) fn rxx_matrix(theta: f64) -> Array2<Complex64> {
+    let theta2 = theta / 2.0;
+//    let cos = c64::new(theta2.cos(), 0.0);
+    let cos = c64(theta2.cos(), 0.0);    
+    let isin = c64(0.0, theta2.sin());
+    let cz = C_ZERO;
+    array![
+        [cos, cz, cz, -isin],
+        [cz, cos, -isin, cz],
+        [cz, -isin, cos, cz],
+        [-isin, cz, cz, cos],
+        ]
+}
+
+pub(crate) fn ryy_matrix(theta: f64) -> Array2<Complex64> {
+    let theta2 = theta / 2.0;
+    let cos = Complex64::new(theta2.cos(), 0.0);
+    let isin = Complex64::new(0.0, theta2.sin());
+    let cz = C_ZERO;
+    array![
+        [cos, cz, cz, isin],
+        [cz, cos, -isin, cz],
+        [cz, -isin, cos, cz],
+        [isin, cz, cz, cos],
+        ]
+}

crates/accelerate/src/lib.rs

@@ -45,6 +45,8 @@ pub mod two_qubit_decompose;
 pub mod uc_gate;
 pub mod utils;
 pub mod vf2_layout;
+mod gates;
+mod xx_decompose;
 
 mod rayon_ext;
 #[cfg(test)]

crates/accelerate/src/two_qubit_decompose.rs

@@ -46,6 +46,7 @@ use crate::euler_one_qubit_decomposer::{
 };
 use crate::utils;
 use crate::QiskitError;
+use crate::gates::{rz_matrix};
 
 use rand::prelude::*;
 use rand_distr::StandardNormal;
@@ -144,7 +145,7 @@ pub trait TraceToFidelity {
 
 impl TraceToFidelity for Complex64 {
     fn trace_to_fid(self) -> f64 {
-        (4.0 + self.abs().powi(2)) / 20.0
+        (4.0 + self.norm_sqr()) / 20.0
     }
 }
 
@@ -296,10 +297,10 @@ fn ry_matrix(theta: f64) -> Array2<Complex64> {
     array![[cos, -sin], [sin, cos]]
 }
 
-fn rz_matrix(theta: f64) -> Array2<Complex64> {
-    let ilam2 = c64(0., 0.5 * theta);
-    array![[(-ilam2).exp(), C_ZERO], [C_ZERO, ilam2.exp()]]
-}
+// fn rz_matrix(theta: f64) -> Array2<Complex64> {
+//     let ilam2 = c64(0., 0.5 * theta);
+//     array![[(-ilam2).exp(), C_ZERO], [C_ZERO, ilam2.exp()]]
+// }
 
 fn compute_unitary(sequence: &TwoQubitSequenceVec, global_phase: f64) -> Array2<Complex64> {
     let identity = aview2(&ONE_QUBIT_IDENTITY);

crates/accelerate/src/xx_decompose/circuits.rs

@@ -0,0 +1,173 @@
+use std::f64::consts::PI;
+use ndarray::prelude::*;
+use ndarray::linalg::kron;
+use qiskit_circuit::circuit_data::CircuitData;
+use crate::xx_decompose::utilities::{safe_acos, Square, EPSILON};
+use crate::xx_decompose::weyl;
+use crate::gates::{rz_matrix, rxx_matrix, ryy_matrix};
+use crate::xx_decompose::types::{GateData, Coordinate};
+
+const PI2 : f64 = PI / 2.0;
+
+fn decompose_xxyy_into_xxyy_xx(
+    a_target: f64,
+    b_target: f64,
+    a_source: f64,
+    b_source: f64,
+    interaction: f64,
+) -> [f64; 6] {
+    let cplus = (a_source + b_source).cos();
+    let cminus = (a_source - b_source).cos();
+    let splus = (a_source + b_source).sin();
+    let sminus = (a_source - b_source).sin();
+    let ca = interaction.cos();
+    let sa = interaction.sin();
+
+    let uplusv =
+        1. / 2. *
+        safe_acos(cminus.sq() * ca.sq() + sminus.sq() * sa.sq() - (a_target - b_target).cos().sq(),
+                  2. * cminus * ca * sminus * sa);
+
+    let uminusv =
+        1. / 2.
+        * safe_acos(
+            cplus.sq() * ca.sq() + splus.sq() * sa.sq() - (a_target + b_target).cos().sq(),
+            2. * cplus * ca * splus * sa,
+        );
+
+    let (u, v) = ((uplusv + uminusv) / 2., (uplusv - uminusv) / 2.);
+
+    let middle_matrix = rxx_matrix(2. * a_source)
+        .dot(&ryy_matrix(2. * b_source))
+        .dot(&kron(&rz_matrix(2. * u), &rz_matrix(2. * v)))
+        .dot(&rxx_matrix(2. * interaction));
+
+    let phase_solver = {
+        let q = 1. / 4.;
+        let mq = - 1. / 4.;
+        array![
+            [q, q, q, q],
+            [q, mq, mq, q],
+            [q, q, mq, mq],
+            [q, mq, q, mq],
+        ]
+    };
+    let inner_phases = array![
+        middle_matrix[[0, 0]].arg(), middle_matrix[[1, 1]].arg(),
+        middle_matrix[[1, 2]].arg() + PI2,
+        middle_matrix[[0, 3]].arg() + PI2,
+    ];
+    let [mut r, mut s, mut x, mut y] = {
+        let p = phase_solver.dot(&inner_phases);
+        [p[0],p[1],p[2],p[3]]
+    };
+
+    let generated_matrix =
+        kron(&rz_matrix(2. * r), &rz_matrix(2. * s))
+        .dot(&middle_matrix)
+        .dot(&kron(&rz_matrix(2. * x), &rz_matrix(2. * y)));
+
+    // If there's a phase discrepancy, need to conjugate by an extra Z/2 (x) Z/2.
+    if ((generated_matrix[[3, 0]].arg().abs() - PI2) < 0.01
+        && a_target > b_target)
+        || ((generated_matrix[[3, 0]].arg().abs() + PI2) < 0.01
+            && a_target < b_target) {
+            x += PI / 4.;
+            y += PI / 4.;
+            r -= PI / 4.;
+            s -= PI / 4.;
+        }
+    [r, s, u, v, x, y]
+}
+
+// Builds a single step in an XX-based circuit.
+//
+// `source` and `target` are positive canonical coordinates; `strength` is the interaction strength
+// at this step in the circuit as a canonical coordinate (so that CX = RZX(pi/2) corresponds to
+// pi/4); and `embodiment` is a Qiskit circuit which enacts the canonical gate of the prescribed
+// interaction `strength`.
+fn xx_circuit_step(source: &Coordinate, strength: f64, target: &Coordinate,
+                   embodiment: CircuitData) -> Result<(), String> {
+
+    let mut permute_source_for_overlap: Option<Vec<GateData>> = None;
+    let mut permute_target_for_overlap: Option<Vec<GateData>> = None;
+
+    for reflection_name in &weyl::REFLECTION_NAMES {
+        let (reflected_source_coord, source_reflection, reflection_phase_shift) = weyl::apply_reflection(*reflection_name, source);
+        for source_shift_name in &weyl::SHIFT_NAMES {
+            let (shifted_source_coord, source_shift, shift_phase_shift) = weyl::apply_shift(
+                *source_shift_name, &reflected_source_coord);
+
+            // check for overlap, back out permutation
+            let (mut source_shared, mut target_shared) = (None, None);
+            for (i, j) in [(0, 0), (0, 1), (0, 2), (1, 0), (1, 1), (1, 2), (2, 0), (2, 1), (2, 2)] {
+                if shifted_source_coord.distance(target, i, j) < EPSILON ||
+                    shifted_source_coord.distance(target, j, i) < EPSILON
+                {
+                    (source_shared, target_shared) = (Some(i), Some(j));
+                    break;
+                }
+            }
+            if source_shared.is_none() {
+                continue;
+            }
+            // Return [0, 1, 2] with `iex` deleted.
+            fn exclude_one(iex: i32) -> [usize; 2] {
+                let mut pair = [-1, -1];
+                let mut j = 0;
+                for i in 0..3 {
+                    if i != iex {
+                        pair[j] = i;
+                        j += 1;
+                    }
+                }
+                [pair[0] as usize, pair[1] as usize]
+            } // exclude_one
+
+            let [source_first, source_second] = exclude_one(source_shared.unwrap());
+            let [target_first, target_second] = exclude_one(target_shared.unwrap());
+
+            let decomposed_coords = decompose_xxyy_into_xxyy_xx(
+                target[target_first],
+                target[target_second],
+                shifted_source_coord[source_first],
+                shifted_source_coord[source_second],
+                strength,
+            );
+
+            if decomposed_coords.iter().any(|val| val.is_nan()) {
+                continue;
+            }
+
+            let [r, s, u, v, x, y] = decomposed_coords;
+            // OK: this combination of things works.
+            // save the permutation which rotates the shared coordinate into ZZ.
+            permute_source_for_overlap = weyl::canonical_rotation_circuit(source_first, source_second);
+            permute_target_for_overlap = weyl::canonical_rotation_circuit(target_first, target_second);
+            break;
+        } // for source_shift_name
+
+        if permute_source_for_overlap.is_some() {
+            break;
+        }
+    } // for reflection_name
+
+    if permute_source_for_overlap.is_none() {
+        // TODO: Decide which error to return.
+        return Err(format!("Error during RZX decomposition: Could not find a suitable Weyl reflection to match {:?} to {:?} along {:?}.",
+                    source, target, strength
+        ));
+    }
+
+// the basic formula we're trying to work with is:
+// target^p_t_f_o =
+//     rs * (source^s_reflection * s_shift)^p_s_f_o * uv * operation * xy
+// but we're rearranging it into the form
+//   target = affix source prefix
+// and computing just the prefix / affix circuits.
+
+
+    return Ok(())
+}
+
+// fn canonical_xx_circuit(target, strength_sequence, basis_embodiments):

crates/accelerate/src/xx_decompose/decomposer.rs

@@ -0,0 +1,28 @@
+use crate::xx_decompose::utilities::Square;
+
+struct Point {
+    a: f64,
+    b: f64,
+    c: f64,
+}
+
+/// Computes the infidelity distance between two points p, q expressed in positive canonical
+/// coordinates.
+fn _average_infidelity(p: Point, q: Point) -> f64 {
+    let Point {
+        a: a0,
+        b: b0,
+        c: c0,
+    } = p;
+    let Point {
+        a: a1,
+        b: b1,
+        c: c1,
+    } = q;
+
+    1. - 1. / 20.
+        * (4.
+            + 16.
+                * ((a0 - a1).cos().sq() * (b0 - b1).cos().sq() * (c0 - c1).cos().sq()
+                    + (a0 - a1).sin().sq() * (b0 - b1).sin().sq() * (c0 - c1).sin().sq()))
+}

crates/accelerate/src/xx_decompose/mod.rs

@@ -0,0 +1,18 @@
+// This code is part of Qiskit.
+//
+// (C) Copyright IBM 2022
+//
+// 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.
+
+pub mod circuits;
+pub mod decomposer;
+pub mod utilities;
+mod types;
+mod weyl;
+mod polytopes;