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// Copyright (c) Microsoft Corporation.
// Licensed under the MIT License.
//! Public implementations and crate-private functions for applying processes
//! in each different representation.
use itertools::Itertools;
use ndarray::{Array, Array2, Array3, ArrayView2, Axis};
use rand::{distributions::WeightedIndex, prelude::Distribution, thread_rng};
use crate::{
chp_decompositions::ChpOperation, linalg::ConjBy, log, log_as_err, Pauli, Process,
ProcessData::*, State, StateData::*, Tableau, C64,
};
use super::promote_pauli_channel;
impl Process {
/// Applies this process to a quantum register with a given
/// state, returning the new state of that register.
pub fn apply(&self, state: &State) -> Result<State, String> {
if state.n_qubits != self.n_qubits {
return Err(format!(
"Channel acts on {} qubits, but was applied to {}-qubit state.",
self.n_qubits, state.n_qubits
));
}
match &self.data {
Unitary(u) => apply_unitary(&u, state),
KrausDecomposition(ks) => apply_kraus_decomposition(&ks, state),
MixedPauli(paulis) => apply_pauli_channel(&paulis, state),
Sequence(processes) => {
// TODO[perf]: eliminate the extraneous clone here.
let mut acc_state = state.clone();
for process in processes {
acc_state = process.apply(state)?;
}
Ok(acc_state)
}
ChpDecomposition(_operations) => todo!(),
Unsupported => Err("Unsupported quantum process.".to_string()),
}
}
/// Applies this process to the given qubits in a register with a given
/// state, returning the new state of that register.
pub fn apply_to(&self, idx_qubits: &[usize], state: &State) -> Result<State, String> {
// If we have a sequence, we can apply each in turn and exit early.
if let Sequence(channels) = &self.data {
// TODO[perf]: eliminate the extraneous clone here.
let mut acc_state = state.clone();
for channel in channels {
acc_state = channel.apply_to(idx_qubits, &acc_state)?;
}
return Ok(acc_state);
}
// Fail if there's not enough qubits.
if state.n_qubits < self.n_qubits {
return log_as_err(format!(
"Channel acts on {} qubits, but a state on only {} qubits was given.\n\nChannel:\n{:?}\n\nState:\n{:?}",
self.n_qubits, state.n_qubits, self, state
));
}
// Fail if any indices are repeated.
if idx_qubits.iter().unique().count() < idx_qubits.len() {
return log_as_err(format!(
"List of qubit indices {:?} contained repeated elements.",
idx_qubits
));
}
// Make sure that there are only as many indices as qubits that this
// channel acts upon.
if idx_qubits.len() != self.n_qubits {
return log_as_err(format!(
"Qubit indices were specified as {:?}, but this channel only acts on {} qubits.",
idx_qubits, self.n_qubits
));
}
// At this point we know that idx_qubits has self.n_qubits many unique
// indices, such that we can meaningfully apply the channel to the
// qubits described by idx_qubits.
//
// To do so in general, we can proceed to make a new channel
// that expands this channel to act on the full register and then use
// the ordinary apply method.
//
// In some cases, however, we can do so more efficiently by working
// with the small channel directly, so we check for those cases first
// before falling through to the general case.
// TODO[perf]: For larger systems, we could add another "fast path" using
// matrix multiplication kernels to avoid extending
// channels to larger Hilbert spaces.
// For smaller systems, extending channels and possibly
// caching them is likely to be more performant; need to
// tune to find crossover point.
if let ChpDecomposition(operations) = &self.data {
if let Stabilizer(tableau) = &state.data {
return apply_chp_decomposition_to(operations, state.n_qubits, idx_qubits, tableau);
}
}
// Having tried fast paths above, we now fall back to the most general
// case.
match self.n_qubits {
1 => {
if state.n_qubits == 1 {
self.apply(state)
} else {
self.extend_one_to_n(idx_qubits[0], state.n_qubits)
.apply(state)
}
}
// TODO[perf]: If the size of the register matches the size of the
// channel, permute rather than expanding.
2 => self
.extend_two_to_n(idx_qubits[0], idx_qubits[1], state.n_qubits)
.apply(state),
_ => {
log(&format!(
"Expanding {}-qubit channels is not yet implemented.",
self.n_qubits
));
unimplemented!("");
}
}
}
}
fn apply_chp_decomposition_to(
operations: &[ChpOperation],
n_qubits: usize,
idx_qubits: &[usize],
tableau: &Tableau,
) -> Result<State, String> {
let mut new_tableau = tableau.clone();
for operation in operations {
match *operation {
ChpOperation::Phase(idx) => new_tableau.apply_s_mut(idx_qubits[idx]),
ChpOperation::AdjointPhase(idx) => new_tableau.apply_s_adj_mut(idx_qubits[idx]),
ChpOperation::Hadamard(idx) => new_tableau.apply_h_mut(idx_qubits[idx]),
ChpOperation::Cnot(idx_control, idx_target) => {
new_tableau.apply_cnot_mut(idx_qubits[idx_control], idx_qubits[idx_target])
}
};
}
Ok(State {
n_qubits,
data: Stabilizer(new_tableau),
})
}
pub(crate) fn apply_unitary(u: &Array2<C64>, state: &State) -> Result<State, String> {
Ok(State {
n_qubits: state.n_qubits,
data: match &state.data {
Pure(psi) => Pure(u.dot(psi)),
Mixed(rho) => Mixed(rho.conjugate_by(&u.into())),
Stabilizer(_tableau) => {
return Err(
"TODO: Promote stabilizer state to state vector and recurse.".to_string(),
)
}
},
})
}
pub(crate) fn apply_kraus_decomposition(ks: &Array3<C64>, state: &State) -> Result<State, String> {
Ok(State {
n_qubits: state.n_qubits,
data: match &state.data {
Pure(psi) => {
// We can't apply a channel with more than one Kraus operator (Choi rank > 1) to a
// pure state directly, so if the Choi rank is bigger than 1, promote to
// Mixed and recurse.
if ks.shape()[0] == 1 {
Pure({
let k: ArrayView2<C64> = ks.slice(s![0, .., ..]);
k.dot(psi)
})
} else {
apply_kraus_decomposition(ks, &state.to_mixed())?.data
}
}
Mixed(rho) => Mixed({
let mut sum: Array2<C64> = Array::zeros((rho.shape()[0], rho.shape()[1]));
for k in ks.axis_iter(Axis(0)) {
sum = sum + rho.conjugate_by(&k);
}
sum
}),
Stabilizer(_tableau) => {
return Err(
"TODO: Promote stabilizer state to state vector and recurse.".to_string(),
)
}
},
})
}
pub(crate) fn apply_pauli_channel(
paulis: &[(f64, Vec<Pauli>)],
state: &State,
) -> Result<State, String> {
Ok(State {
n_qubits: state.n_qubits,
data: match &state.data {
Pure(_) | Mixed(_) => {
// Promote and recurse.
let promoted = promote_pauli_channel(paulis);
return promoted.apply(state);
}
Stabilizer(tableau) => {
// TODO[perf]: Introduce an apply_mut method to
// avoid extraneous cloning.
let mut new_tableau = tableau.clone();
// Sample a Pauli and apply it.
let weighted = WeightedIndex::new(paulis.iter().map(|(pr, _)| pr)).unwrap();
let idx = weighted.sample(&mut thread_rng());
let pauli = &(&paulis)[idx].1;
// TODO: Consider moving the following to a method
// on Tableau itself.
for (idx_qubit, p) in pauli.iter().enumerate() {
match p {
Pauli::I => (),
Pauli::X => new_tableau.apply_x_mut(idx_qubit),
Pauli::Y => new_tableau.apply_y_mut(idx_qubit),
Pauli::Z => new_tableau.apply_z_mut(idx_qubit),
}
}
Stabilizer(new_tableau)
}
},
})
}