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use crate::errors::{CircuitError, CircuitResult};
use crate::types::Precision;
use num_complex::Complex;
use num_rational::Rational64;
use num_traits::{One, Zero};
use std::fmt::Debug;
use std::num::NonZeroUsize;
/// Standard functions needed by registers containing multiple qubits.
pub trait QubitRegister {
/// Size of the register in qubits.
fn n(&self) -> usize;
/// Size of the register in qubits.
fn n_nonzero(&self) -> NonZeroUsize {
NonZeroUsize::new(self.n()).unwrap()
}
/// Absolute indices represented by the register.
fn indices(&self) -> &[usize];
}
/// Result of splitting a register in two.
#[derive(Debug)]
pub enum SplitResult<R: QubitRegister + Debug> {
/// All registers were selected
SELECTED(R),
/// None of the registers were selected
UNSELECTED(R),
/// Some registers were selected, some were not selected.
SPLIT(R, R),
}
/// Result of splitting a register into multiple registers.
#[derive(Debug)]
pub enum SplitManyResult<R: QubitRegister + Debug> {
/// All registers were selected.
AllSelected(Vec<R>),
/// Some were selected, remaining were not.
Remaining(Vec<R>, R),
}
impl<R: QubitRegister + Debug> SplitManyResult<R> {
/// Returns select and unselected registers.
pub fn get_all_selected(self) -> Result<Vec<R>, Vec<R>> {
match self {
SplitManyResult::AllSelected(v) => Ok(v),
SplitManyResult::Remaining(v, _) => Err(v),
}
}
/// Returns select registers, throws out remaining.
pub fn get_selected(self) -> Vec<R> {
match self {
SplitManyResult::AllSelected(v) => v,
SplitManyResult::Remaining(v, _) => v,
}
}
}
/// A base-level circuit builder trait, requiring definitions of registers, base circuit objects,
/// and end-result quantum state.
pub trait CircuitBuilder {
/// The register type used for the circuit.
type Register: QubitRegister + Debug;
/// The struct used to represent circuit objects.
type CircuitObject;
/// Return type for state calculations.
type StateCalculation;
/// Number of qubits in circuit.
fn n(&self) -> usize;
/// Construct a single qubit.
fn qubit(&mut self) -> Self::Register {
self.register(NonZeroUsize::new(1).unwrap())
}
/// Construct a register with multiple qubits. Fails if n=0.
fn qudit(&mut self, n: usize) -> Option<Self::Register> {
NonZeroUsize::new(n).map(|n| self.register(n))
}
/// Construct a register with multiple qubits.
fn register(&mut self, n: NonZeroUsize) -> Self::Register;
/// Construct a register with multiple qubits. Fails if n=0.
fn try_register(&mut self, n: usize) -> Option<Self::Register> {
self.qudit(n)
}
/// Merge two registers into a single register with first the r1 indices, then the r2 indices.
fn merge_two_registers(&mut self, r1: Self::Register, r2: Self::Register) -> Self::Register;
/// Merge multiple registers together into a single register, returns None if none given.
fn merge_registers<It>(&mut self, rs: It) -> Option<Self::Register>
where
It: IntoIterator<Item = Self::Register>,
{
rs.into_iter().fold(None, |acc, r1| match acc {
Some(r2) => Some(self.merge_two_registers(r2, r1)),
None => Some(r1),
})
}
/// Split a register into two, selecting the relative indices from the `indices` iterator.
fn split_register_relative<It>(
&mut self,
r: Self::Register,
indices: It,
) -> SplitResult<Self::Register>
where
It: IntoIterator<Item = usize>;
/// Split a register into two, selecting the indices from the `indices` iterator.
fn split_register_absolute<It>(
&mut self,
r: Self::Register,
indices: It,
) -> SplitResult<Self::Register>
where
It: IntoIterator<Item = usize>,
{
let r_indices = r.indices().to_vec();
let r_rel_indices = indices.into_iter().filter_map(move |abs_index| {
// Ok to use n^2 since n must be small.
r_indices.iter().cloned().find(|i| *i == abs_index)
});
self.split_register_relative(r, r_rel_indices)
}
/// Split the register into `r.n()` individual registers of 1 qubit each.
fn split_all_register(&mut self, r: Self::Register) -> Vec<Self::Register> {
split_helper(self, r, vec![])
}
/// Split off the first qubit from the register, returns the optional remaining registers
/// and the first qubit.
fn split_first_qubit(&mut self, r: Self::Register) -> (Option<Self::Register>, Self::Register) {
match self.split_register_relative(r, [0]) {
SplitResult::SELECTED(r) => (None, r),
SplitResult::SPLIT(ra, rb) => (Some(ra), rb),
SplitResult::UNSELECTED(_) => unreachable!(),
}
}
/// Similar to [split_first_qubit] but the last qubit.
fn split_last_qubit(&mut self, r: Self::Register) -> (Self::Register, Option<Self::Register>) {
let n = r.n();
match self.split_register_relative(r, [n - 1]) {
SplitResult::SELECTED(r) => (r, None),
SplitResult::SPLIT(ra, rb) => (rb, Some(ra)),
SplitResult::UNSELECTED(_) => unreachable!(),
}
}
/// Split into multiple qubits, each with relative indices given by the sub-iterators.
///
/// # Example
/// ```
/// # use qip::prelude::*;
///
/// # fn main() {
/// let mut b = LocalBuilder::<f64>::default();
/// let ra = b.qudit(5).expect("5 is non-negative");
/// let rb = b.qudit(5).expect("5 is non-negative");
/// assert_eq!(ra.indices(), &[0,1,2,3,4]);
/// let split_res = b.split_relative_index_groups(rb, [[0,1], [2,3]]);
/// if let SplitManyResult::Remaining(groups, remaining) = split_res {
/// assert_eq!(groups[0].indices(), &[5, 6]);
/// assert_eq!(groups[1].indices(), &[7, 8]);
/// assert_eq!(remaining.indices(), &[9])
/// } else {
/// assert!(false);
/// };
///
/// # }
/// ```
fn split_relative_index_groups<
It: IntoIterator<Item = Itt>,
Itt: IntoIterator<Item = usize>,
>(
&mut self,
r: Self::Register,
indices: It,
) -> SplitManyResult<Self::Register> {
let mut rs = self
.split_all_register(r)
.into_iter()
.map(Some)
.collect::<Vec<_>>();
let selected_rs = indices
.into_iter()
.flat_map(|is| {
let subrs = is.into_iter().map(|i| rs[i].take().unwrap());
self.merge_registers(subrs)
})
.collect();
let remaining_rs = self.merge_registers(rs.into_iter().flatten());
match remaining_rs {
None => SplitManyResult::AllSelected(selected_rs),
Some(r) => SplitManyResult::Remaining(selected_rs, r),
}
}
/// Apply a circuit object to the circuit directly.
fn apply_circuit_object(
&mut self,
r: Self::Register,
c: Self::CircuitObject,
) -> CircuitResult<Self::Register>;
/// Calculate the quantum state at the end of the circuit, using |0> as input.
fn calculate_state(&mut self) -> Self::StateCalculation {
self.calculate_state_with_init(None)
}
/// Calculate the state at the end of the circuit using an initial state given by each register
/// and the classical state in that register.
fn calculate_state_with_init<'a, It>(&mut self, it: It) -> Self::StateCalculation
where
Self::Register: 'a,
It: IntoIterator<Item = (&'a Self::Register, usize)>;
}
fn split_helper<CB>(cb: &mut CB, r: CB::Register, mut acc: Vec<CB::Register>) -> Vec<CB::Register>
where
CB: CircuitBuilder + ?Sized,
{
match cb.split_register_relative(r, Some(0)) {
SplitResult::SELECTED(r) => {
acc.push(r);
acc
}
SplitResult::SPLIT(r0, r) => {
acc.push(r0);
split_helper(cb, r, acc)
}
SplitResult::UNSELECTED(_) => unreachable!(),
}
}
/// Standard functions for building unitary circuits.
pub trait UnitaryBuilder<P: Precision>: CircuitBuilder {
/// Apply an arbitrary matrix to the circuit given by a vector.
fn apply_vec_matrix(
&mut self,
r: Self::Register,
data: Vec<Complex<P>>,
) -> CircuitResult<Self::Register> {
let n = r.n();
self.apply_circuit_object(r, Self::vec_matrix_to_circuitobject(n, data))
}
/// Apply an arbitrary matrix to the circuit given by an array.
fn apply_matrix<const N: usize>(
&mut self,
r: Self::Register,
data: [Complex<P>; N],
) -> CircuitResult<Self::Register> {
let n = r.n();
self.apply_circuit_object(r, Self::matrix_to_circuitobject(n, data))
}
/// Single qubit matrices can be applied to each qubit in a register unambiguously.
/// Matrix is organized as |0><0|, |0><1|, |1><0|, |1><1|
fn broadcast_single_qubit_matrix(
&mut self,
r: Self::Register,
data: [Complex<P>; 4],
) -> Self::Register {
let n = r.n();
self.apply_circuit_object(r, Self::matrix_to_circuitobject(n, data))
.unwrap()
}
/// Make a circuit object out of an arbitrary matrix
/// Single Qubit matrix is organized as |0><0|, |0><1|, |1><0|, |1><1|
fn matrix_to_circuitobject<const N: usize>(
n: usize,
data: [Complex<P>; N],
) -> Self::CircuitObject {
Self::vec_matrix_to_circuitobject(n, data.to_vec())
}
/// Make a circuit object out of an arbitrary matrix
/// Single Qubit matrix is organized as |0><0|, |0><1|, |1><0|, |1><1|
fn vec_matrix_to_circuitobject(n: usize, data: Vec<Complex<P>>) -> Self::CircuitObject;
}
/// A Builder which can construct Clifford Circuit Elements.
pub trait CliffordTBuilder<P: Precision>: UnitaryBuilder<P> {
/// Make a circuit object representing the X gate on a single qubit.
/// Equivalent to calling `matrix_to_circuitobject` with \[0, 1, 1, 0\]
fn make_x(&self) -> Self::CircuitObject {
Self::matrix_to_circuitobject(
1,
[
Complex::zero(),
Complex::one(),
Complex::one(),
Complex::zero(),
],
)
}
/// Make a circuit object representing the Y gate on a single qubit.
/// Equivalent to calling `matrix_to_circuitobject` with \[0, -i, i, 0\]
fn make_y(&self) -> Self::CircuitObject {
Self::matrix_to_circuitobject(
1,
[
Complex::zero(),
-Complex::i(),
Complex::i(),
Complex::zero(),
],
)
}
/// Make a circuit object representing the Z gate on a single qubit.
/// Equivalent to calling `matrix_to_circuitobject` with \[1, 0, 0, -1\]
fn make_z(&self) -> Self::CircuitObject {
Self::matrix_to_circuitobject(
1,
[
Complex::one(),
Complex::zero(),
Complex::zero(),
-Complex::one(),
],
)
}
/// Make a circuit object representing the H gate on a single qubit.
/// Equivalent to calling `matrix_to_circuitobject` with \[1, 1, 1, -1\]/sqrt(2)
fn make_h(&self) -> Self::CircuitObject {
let l = Complex::one() * P::from(std::f64::consts::FRAC_1_SQRT_2).unwrap();
Self::matrix_to_circuitobject(1, [l, l, l, -l])
}
/// Make a circuit object representing the S (phase) gate on a single qubit.
/// Equivalent to calling `matrix_to_circuitobject` with \[1, 0, 0, -i\]
fn make_s(&self) -> Self::CircuitObject {
Self::matrix_to_circuitobject(
1,
[
Complex::one(),
Complex::zero(),
Complex::zero(),
Complex::i(),
],
)
}
/// Make a circuit object representing the T gate on a single qubit.
/// Equivalent to calling `matrix_to_circuitobject` with \[1, 0, 0, e^{i pi / 4} \]
fn make_t(&self) -> Self::CircuitObject {
Self::matrix_to_circuitobject(
1,
[
Complex::one(),
Complex::zero(),
Complex::zero(),
Complex::from_polar(P::one(), P::from(std::f64::consts::FRAC_PI_4).unwrap()),
],
)
}
/// Make a circuit object representing the CNOT gate on a pair of qubits
/// Equivalent to calling `matrix_to_circuitobject` with \[ I, 0, 0, X \]
/// where I is the identity matrix and X is the x-gate.
fn make_cnot(&self) -> Self::CircuitObject {
let l = Complex::one();
let o = Complex::zero();
Self::matrix_to_circuitobject(2, [l, o, o, o, o, l, o, o, o, o, o, l, o, o, l, o])
}
/// Create and apply an NOT (or X) gate circuit object.
fn not(&mut self, r: Self::Register) -> Self::Register {
self.x(r)
}
/// Create and apply an X (or NOT) gate circuit object.
fn x(&mut self, r: Self::Register) -> Self::Register {
self.apply_circuit_object(r, self.make_x()).unwrap()
}
/// Create and apply a Y gate circuit object.
fn y(&mut self, r: Self::Register) -> Self::Register {
self.apply_circuit_object(r, self.make_y()).unwrap()
}
/// Create and apply a Z gate circuit object.
fn z(&mut self, r: Self::Register) -> Self::Register {
self.apply_circuit_object(r, self.make_z()).unwrap()
}
/// Create and apply an H gate circuit object.
fn h(&mut self, r: Self::Register) -> Self::Register {
self.apply_circuit_object(r, self.make_h()).unwrap()
}
/// Create and apply a T gate circuit object.
fn t(&mut self, r: Self::Register) -> Self::Register {
self.apply_circuit_object(r, self.make_t()).unwrap()
}
/// Create and apply a T^\dagger gate circuit object.
fn t_dagger(&mut self, r: Self::Register) -> Self::Register {
let r = self.s_dagger(r);
self.t(r)
}
/// Create and apply an S gate circuit object.
fn s(&mut self, r: Self::Register) -> Self::Register {
self.apply_circuit_object(r, self.make_s()).unwrap()
}
/// Create and apply an S^\dagger gate circuit object.
fn s_dagger(&mut self, r: Self::Register) -> Self::Register {
let r = self.z(r);
self.s(r)
}
/// Create and apply a CNOT gate circuit object.
fn cnot(
&mut self,
cr: Self::Register,
r: Self::Register,
) -> Result<(Self::Register, Self::Register), CircuitError> {
if cr.n() > 1 {
Err(CircuitError::new(
"Clifford CNOT can only have a single control qubit.",
))
} else {
let rs = self.split_all_register(r);
let (cr, rs) = rs.into_iter().try_fold((cr, vec![]), |(cr, mut acc), r| {
let r = self.merge_two_registers(cr, r);
let circuit_object = self.make_cnot();
let r = self.apply_circuit_object(r, circuit_object)?;
let (cr, r) = match self.split_register_relative(r, Some(0)) {
SplitResult::SPLIT(cr, r) => (cr, r),
SplitResult::SELECTED(_) => unreachable!(),
SplitResult::UNSELECTED(_) => unreachable!(),
};
acc.push(r);
Ok((cr, acc))
})?;
let r = self.merge_registers(rs).unwrap();
Ok((cr, r))
}
}
/// Apply the SWAP gate to a pair of registers of equal sizes.
fn swap(
&mut self,
ra: Self::Register,
rb: Self::Register,
) -> Result<(Self::Register, Self::Register), CircuitError> {
if ra.n() == rb.n() {
let ras = self.split_all_register(ra);
let rbs = self.split_all_register(rb);
let (ras, rbs): (Vec<_>, Vec<_>) = ras
.into_iter()
.zip(rbs.into_iter())
.map(|(ra, rb)| {
assert_eq!(ra.n(), 1);
assert_eq!(rb.n(), 1);
self.cnot(ra, rb)
.and_then(|(ra, rb)| self.cnot(rb, ra))
.and_then(|(rb, ra)| self.cnot(ra, rb))
.unwrap()
})
.unzip();
let ra = self.merge_registers(ras).unwrap();
let rb = self.merge_registers(rbs).unwrap();
Ok((ra, rb))
} else {
Err(CircuitError::new(
"Swap must be between registers of the same size.",
))
}
}
}
/// A Builder which can construct temporary qudits.
pub trait TemporaryRegisterBuilder: CircuitBuilder {
/// Make a temporary qubit, initialized to zero.
fn make_zeroed_temp_qubit(&mut self) -> Self::Register;
/// Make a register of multiple qubits, initialized to zero.
fn make_zeroed_temp_register(&mut self, n: NonZeroUsize) -> Self::Register {
let rs = (0..usize::from(n))
.map(|_| self.make_zeroed_temp_qubit())
.collect::<Vec<_>>();
self.merge_registers(rs).unwrap()
}
/// Return a register which has been reset to zero.
fn return_zeroed_temp_register(&mut self, r: Self::Register);
}
/// A builder which can construct more advanced gates using temporary qudits.
pub trait AdvancedCircuitBuilder<P: Precision>:
CliffordTBuilder<P> + TemporaryRegisterBuilder
{
/// Applies a NOT gate to `r` for the two qubit control state `cr = 11`.
fn basic_toffoli(
&mut self,
cr: Self::Register,
r: Self::Register,
) -> Result<(Self::Register, Self::Register), CircuitError> {
if cr.n() == 2 {
if let SplitResult::SPLIT(cra, crb) = self.split_register_relative(cr, [0]) {
// Manually implement toffoli gate using CNOT
let r = self.h(r);
let (crb, r) = self.cnot(crb, r).unwrap();
let r = self.t_dagger(r);
let (cra, r) = self.cnot(cra, r).unwrap();
let r = self.t(r);
let (crb, r) = self.cnot(crb, r).unwrap();
let r = self.t_dagger(r);
let (cra, r) = self.cnot(cra, r).unwrap();
let crb = self.t(crb);
let r = self.t(r);
let (cra, crb) = self.cnot(cra, crb).unwrap();
let r = self.h(r);
let cra = self.t(cra);
let crb = self.t_dagger(crb);
let (cra, crb) = self.cnot(cra, crb).unwrap();
let cr = self.merge_two_registers(cra, crb);
Ok((cr, r))
} else {
unreachable!()
}
} else {
Err(CircuitError::new(
"Basic Toffoli can only be applied to two control qubits.",
))
}
}
/// Applies NOT to `r` if all qubits in `cr` are `1`.
fn toffoli(
&mut self,
cr: Self::Register,
r: Self::Register,
) -> Result<(Self::Register, Self::Register), CircuitError> {
if cr.n() == 1 {
self.cnot(cr, r)
} else if cr.n() == 2 {
self.basic_toffoli(cr, r)
} else if let SplitResult::SPLIT(crhead, crtail) = self.split_register_relative(cr, [0, 1])
{
let tr = self.make_zeroed_temp_qubit();
let (crhead, tr) = self.toffoli(crhead, tr).unwrap();
let cr = self.merge_two_registers(crtail, tr);
let (cr, r) = self.toffoli(cr, r).unwrap();
let (crtail, tr) = self.split_last_qubit(cr);
let tr = tr.unwrap();
let (crhead, tr) = self.toffoli(crhead, tr).unwrap();
self.return_zeroed_temp_register(tr);
Ok((self.merge_two_registers(crhead, crtail), r))
} else {
unreachable!()
}
}
}
/// A Builder which can construct arbitrary rotations around axes.
pub trait RotationsBuilder<P: Precision>: CliffordTBuilder<P> {
/// Rotate around z.
fn rz(&mut self, r: Self::Register, theta: P) -> Self::Register;
/// Rotate around x.
fn rx(&mut self, r: Self::Register, theta: P) -> Self::Register {
let r = self.h(r);
let r = self.rz(r, theta);
self.h(r)
}
/// Rotate around y.
fn ry(&mut self, r: Self::Register, theta: P) -> Self::Register {
let r = self.s_dagger(r);
let r = self.h(r);
let r = self.rz(r, -theta);
let r = self.h(r);
self.s(r)
}
/// Rotate around z.
fn rz_ratio(&mut self, r: Self::Register, theta: Rational64) -> CircuitResult<Self::Register> {
Ok(self.rz(r, P::from(theta).unwrap()))
}
/// Rotate around z.
fn rx_ratio(&mut self, r: Self::Register, theta: Rational64) -> CircuitResult<Self::Register> {
let r = self.h(r);
let r = self.rz_ratio(r, theta)?;
Ok(self.h(r))
}
/// Rotate around z.
fn ry_ratio(&mut self, r: Self::Register, theta: Rational64) -> CircuitResult<Self::Register> {
let r = self.s(r);
let r = self.h(r);
let r = self.rz_ratio(r, -theta)?;
let r = self.h(r);
Ok(self.s_dagger(r))
}
/// Rotate around z by pi/m
fn rz_pi_by(&mut self, r: Self::Register, m: i64) -> CircuitResult<Self::Register> {
self.rz_ratio(r, Rational64::new(1, m))
}
/// Rotate around x by pi/m
fn rx_pi_by(&mut self, r: Self::Register, m: i64) -> CircuitResult<Self::Register> {
self.rx_ratio(r, Rational64::new(1, m))
}
/// Rotate around y by pi/m
fn ry_pi_by(&mut self, r: Self::Register, m: i64) -> CircuitResult<Self::Register> {
self.ry_ratio(r, Rational64::new(1, m))
}
}
/// A builder that can take destructive measurements.
pub trait MeasurementBuilder: CircuitBuilder {
/// Handle which points to measurements.
type MeasurementHandle;
/// Take a measurement of `r`, return `r` and a handle to fetch the result later.
fn measure(&mut self, r: Self::Register) -> (Self::Register, Self::MeasurementHandle);
}
/// A builder that can take nondestructive measurements.
pub trait StochasticMeasurementBuilder: CircuitBuilder {
/// Handle which points to measurements.
type StochasticMeasurementHandle;
/// Take a measurement of `r`, return `r` and a handle to fetch the result later.
fn measure_stochastic(
&mut self,
r: Self::Register,
) -> (Self::Register, Self::StochasticMeasurementHandle);
}
/// A builder which can export its circuit for use later, and can apply a circuit to itself.
pub trait Subcircuitable: CircuitBuilder {
/// The export type for the circuit.
type Subcircuit;
/// Export the circuit as a subcircuit if able.
fn make_subcircuit(&self) -> CircuitResult<Self::Subcircuit>;
/// Append the subcircuit to the register `r`.
fn apply_subcircuit(
&mut self,
sc: Self::Subcircuit,
r: Self::Register,
) -> CircuitResult<Self::Register>;
}
/// Create a circuit for the circuit given by `r`.
pub fn make_circuit_matrix<CB, P, F>(cb: &mut CB, r: &CB::Register, f: F) -> Vec<Vec<Complex<P>>>
where
CB: CircuitBuilder,
P: Precision,
F: Fn(CB::StateCalculation) -> Vec<Complex<P>>,
{
(0..1 << r.n())
.map(|indx| f(cb.calculate_state_with_init(Some((r, indx)))))
.collect()
}