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use crate::StabilizerCHForm;
use crate::error::Result;
use crate::form::types::PhaseFactor;
impl StabilizerCHForm {
pub(crate) fn _resolve_superposition(
&mut self,
vec_t: &ndarray::Array1<bool>,
vec_u: &ndarray::Array1<bool>,
delta: PhaseFactor,
) -> Result<()> {
if vec_t == vec_u {
self.handle_same_vecs_case(delta, vec_t);
return Ok(());
}
let (diff_indices_0, diff_indices_1) = self.get_differing_indices(vec_t, vec_u);
let pivot = self.apply_basis_transform_circuit(&diff_indices_0, &diff_indices_1)?;
// if t_q == 1, (y_q, z_q) = (1,0)
// if t_q == 0, (y_q, z_q) = (0,1)
if vec_t[pivot] {
self.vec_s.assign(vec_u);
match delta {
PhaseFactor::PLUS_ONE => {
// H(|1> + |0>) = |0>
// |1> + |0> = H|0>
self.vec_s[pivot] = false;
self.vec_v[pivot] = !self.vec_v[pivot];
}
PhaseFactor::MINUS_ONE => {
// H(|1> - |0>) = -|1>
// |1> - |0> = -H|1>
self.vec_s[pivot] = true;
self.vec_v[pivot] = !self.vec_v[pivot];
self.phase_factor.flip_sign();
}
PhaseFactor::PLUS_I => {
if self.vec_v[pivot] {
// H(|1> + i|0>) = e^{iπ/4}SH|0>
self.phase_factor *= PhaseFactor::EXP_I_PI_4;
self.vec_s[pivot] = false;
self.right_multiply_s(pivot)?;
} else {
// |1> + i|0> = iSH|1>
self.vec_s[pivot] = true;
self.vec_v[pivot] = true;
self.right_multiply_s(pivot)?;
self.phase_factor *= PhaseFactor::PLUS_I;
}
}
PhaseFactor::MINUS_I => {
if self.vec_v[pivot] {
// H(|1> - i|0>) = e^{-iπ/4}SH|1>
self.phase_factor *= PhaseFactor::EXP_I_7PI_4;
self.vec_s[pivot] = true;
self.right_multiply_s(pivot)?;
} else {
// |1> - i|0> = -iSH|0>
self.vec_s[pivot] = false;
self.vec_v[pivot] = true;
self.right_multiply_s(pivot)?;
self.phase_factor *= PhaseFactor::MINUS_I;
}
}
_ => unreachable!(),
}
} else {
self.vec_s.assign(vec_t);
match delta {
PhaseFactor::PLUS_ONE => {
// H(|0> + |1>) = |0>
// |0> + |1> = H|0>
self.vec_s[pivot] = false;
self.vec_v[pivot] = !self.vec_v[pivot];
}
PhaseFactor::MINUS_ONE => {
// H(|0> - |1>) = -|1>
// |0> - |1> = -H|1>
self.vec_s[pivot] = true;
self.vec_v[pivot] = !self.vec_v[pivot];
}
PhaseFactor::PLUS_I => {
if self.vec_v[pivot] {
// H(|0> + i|1>) = e^{iπ/4}SH|1>
self.phase_factor *= PhaseFactor::EXP_I_PI_4;
self.vec_s[pivot] = true;
self.right_multiply_s(pivot)?;
} else {
// |0> + i|1> = SH|0>
self.vec_s[pivot] = false;
self.vec_v[pivot] = true;
self.right_multiply_s(pivot)?;
}
}
PhaseFactor::MINUS_I => {
if self.vec_v[pivot] {
// H(|0> - i|1>) = e^{-iπ/4}SH|0>
self.phase_factor *= PhaseFactor::EXP_I_7PI_4;
self.vec_s[pivot] = false;
self.right_multiply_s(pivot)?;
} else {
// |0> - i|1> = SH|1>
self.vec_s[pivot] = true;
self.vec_v[pivot] = true;
self.right_multiply_s(pivot)?;
}
}
_ => unreachable!(),
}
}
Ok(())
}
fn handle_same_vecs_case(&mut self, delta: PhaseFactor, vec_t: &ndarray::Array1<bool>) {
match delta {
PhaseFactor::PLUS_ONE => {
self.vec_s = vec_t.clone();
}
PhaseFactor::MINUS_ONE => {
panic!("Inconsistent state: superposition with -1 coefficient.");
}
PhaseFactor::PLUS_I => {
self.vec_s = vec_t.clone();
self.phase_factor *= PhaseFactor::EXP_I_PI_4;
}
PhaseFactor::MINUS_I => {
self.vec_s = vec_t.clone();
self.phase_factor *= PhaseFactor::EXP_I_7PI_4;
}
_ => unreachable!(),
}
}
fn get_differing_indices(
&self,
vec_t: &ndarray::Array1<bool>,
vec_u: &ndarray::Array1<bool>,
) -> (Vec<usize>, Vec<usize>) {
let mut diff_indices_0 = Vec::new();
let mut diff_indices_1 = Vec::new();
for i in 0..self.n {
if vec_t[i] != vec_u[i] {
if self.vec_v[i] {
diff_indices_1.push(i);
} else {
diff_indices_0.push(i);
}
}
}
(diff_indices_0, diff_indices_1)
}
fn apply_basis_transform_circuit(
&mut self,
diff_indices_0: &[usize],
diff_indices_1: &[usize],
) -> Result<usize> {
if diff_indices_0.is_empty() {
let pivot = diff_indices_1[0];
for &i in &diff_indices_1[1..] {
self.right_multiply_cx(i, pivot)?;
}
Ok(pivot)
} else {
let pivot = diff_indices_0[0];
for &i in &diff_indices_0[1..] {
self.right_multiply_cx(pivot, i)?;
}
for &i in diff_indices_1 {
self.right_multiply_cz(pivot, i)?;
}
Ok(pivot)
}
}
}