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//! Probability distributions over computational basis states.
//!
//! [`Probabilities`] serves dense vectors and lazily factored per-block
//! marginals through one interface.
/// Marginal distribution of one independent subsystem: `mask` marks its global
/// qubit positions and `probs` holds its `2^k` entries.
#[derive(Debug, Clone)]
pub struct FactoredBlock {
pub probs: Vec<f64>,
pub mask: u64,
}
/// Distribution over basis states: a dense `2^n` vector, or the per-block
/// marginals of a decomposed run, multiplied on demand so the `2^n` Kronecker
/// product is built only when asked for.
#[derive(Debug, Clone)]
#[non_exhaustive]
pub enum Probabilities {
/// Full probability vector of length 2^n.
Dense(Vec<f64>),
/// Lazy Kronecker product of independent block distributions.
Factored {
blocks: Vec<FactoredBlock>,
total_qubits: usize,
},
}
impl Probabilities {
/// Number of basis states (2^n).
pub fn len(&self) -> usize {
match self {
Probabilities::Dense(v) => v.len(),
Probabilities::Factored { total_qubits, .. } => 1 << total_qubits,
}
}
/// Always false, a probability distribution has at least one state.
pub fn is_empty(&self) -> bool {
false
}
/// Per-qubit `(P(0), P(1))`, summed from the distribution already held.
/// Query APIs can still choose faster direct marginal algorithms before
/// producing a joint distribution.
pub fn marginals(&self) -> Vec<(f64, f64)> {
match self {
Probabilities::Dense(v) => {
let n = v.len().ilog2() as usize;
let mut marginals = vec![(0.0f64, 0.0f64); n];
for (idx, &p) in v.iter().enumerate() {
for (q, m) in marginals.iter_mut().enumerate() {
if (idx >> q) & 1 == 0 {
m.0 += p;
} else {
m.1 += p;
}
}
}
marginals
}
Probabilities::Factored {
blocks,
total_qubits,
} => {
let mut marginals = vec![(0.0f64, 0.0f64); *total_qubits];
for block in blocks {
let mut qubits = Vec::new();
let mut mask = block.mask;
while mask != 0 {
qubits.push(mask.trailing_zeros() as usize);
mask &= mask.wrapping_sub(1);
}
for (idx, &p) in block.probs.iter().enumerate() {
for (local_bit, &qubit) in qubits.iter().enumerate() {
if (idx >> local_bit) & 1 == 0 {
marginals[qubit].0 += p;
} else {
marginals[qubit].1 += p;
}
}
}
}
marginals
}
}
}
/// Joint distribution over `qubits`, `2^k` entries with `qubits[0]` in the
/// lowest bit, the index order [`ReducedDensityMatrix::data`] states.
///
/// The factored arm sums each block over the qubits it holds and multiplies
/// the block marginals into place, so the cost is `2^k` per block rather
/// than the `2^n` a walk over the joint distribution would pay.
///
/// # Panics
/// Panics if a qubit index is out of range for the distribution.
///
/// [`ReducedDensityMatrix::data`]: crate::sim::ReducedDensityMatrix::data
pub fn subset_marginal(&self, qubits: &[usize]) -> Vec<f64> {
let width = 1usize << qubits.len();
match self {
Probabilities::Dense(v) => {
let mut out = vec![0.0f64; width];
for (index, &p) in v.iter().enumerate() {
out[gather_bits(index, qubits)] += p;
}
out
}
Probabilities::Factored { blocks, .. } => {
let mut out = vec![1.0f64; width];
for block in blocks {
let picks: Vec<(usize, usize)> = qubits
.iter()
.enumerate()
.filter(|&(_, &q)| block.mask >> q & 1 == 1)
.map(|(out_bit, &q)| (local_bit(block.mask, q), out_bit))
.collect();
if picks.is_empty() {
continue;
}
let mut block_marginal = vec![0.0f64; 1usize << picks.len()];
for (index, &p) in block.probs.iter().enumerate() {
let local = picks
.iter()
.enumerate()
.fold(0usize, |acc, (bit, &(source, _))| {
acc | (index >> source & 1) << bit
});
block_marginal[local] += p;
}
for (state, slot) in out.iter_mut().enumerate() {
let local = picks
.iter()
.enumerate()
.fold(0usize, |acc, (bit, &(_, source))| {
acc | (state >> source & 1) << bit
});
*slot *= block_marginal[local];
}
}
out
}
}
}
/// Probability of a single computational basis state. O(1) for dense,
/// O(K) for factored where K is the number of independent blocks.
///
/// # Panics
/// Panics if `index >= self.len()`.
pub fn get(&self, index: usize) -> f64 {
match self {
Probabilities::Dense(v) => v[index],
Probabilities::Factored { blocks, .. } => {
let mut p = 1.0;
for block in blocks {
let local = extract_block_bits(index, block.mask);
p *= block.probs[local];
}
p
}
}
}
/// Iterate over all basis-state probabilities in order. `Dense` iterates
/// the slice; `Factored` computes each entry on the fly in O(K).
pub fn iter(&self) -> ProbabilitiesIter<'_> {
match self {
Probabilities::Dense(v) => ProbabilitiesIter {
inner: ProbabilitiesIterInner::Dense(v.iter().copied()),
},
Probabilities::Factored {
blocks,
total_qubits,
} => ProbabilitiesIter {
inner: ProbabilitiesIterInner::Factored {
blocks,
next: 0,
len: 1usize << total_qubits,
},
},
}
}
/// Materialize the full probability vector: a clone for dense, O(K x 2^N)
/// for factored. Prefer [`Probabilities::get`] for spot-checking.
pub fn to_vec(&self) -> Vec<f64> {
match self {
Probabilities::Dense(v) => v.clone(),
Probabilities::Factored {
blocks,
total_qubits,
} => {
let n = 1usize << total_qubits;
let mut result = vec![0.0f64; n];
#[cfg(feature = "parallel")]
{
const MIN_PAR_STATES: usize = 1 << 14;
if n >= MIN_PAR_STATES {
use rayon::prelude::*;
crate::backend::init_thread_pool();
result.par_iter_mut().enumerate().for_each(|(i, slot)| {
let mut p = 1.0;
for block in blocks {
let local = extract_block_bits(i, block.mask);
p *= block.probs[local];
}
*slot = p;
});
return result;
}
}
for (i, slot) in result.iter_mut().enumerate() {
let mut p = 1.0;
for block in blocks {
let local = extract_block_bits(i, block.mask);
p *= block.probs[local];
}
*slot = p;
}
result
}
}
}
}
/// Pack the bits `index` holds at `qubits` into a dense index, `qubits[0]`
/// lowest.
fn gather_bits(index: usize, qubits: &[usize]) -> usize {
qubits
.iter()
.enumerate()
.fold(0usize, |acc, (bit, &q)| acc | (index >> q & 1) << bit)
}
/// Position of global qubit `q` within a block's local index, which counts the
/// block's qubits below it.
fn local_bit(mask: u64, q: usize) -> usize {
(mask & ((1u64 << q) - 1)).count_ones() as usize
}
/// Concrete iterator for [`Probabilities::iter`].
pub struct ProbabilitiesIter<'a> {
inner: ProbabilitiesIterInner<'a>,
}
enum ProbabilitiesIterInner<'a> {
Dense(std::iter::Copied<std::slice::Iter<'a, f64>>),
Factored {
blocks: &'a [FactoredBlock],
next: usize,
len: usize,
},
}
impl Iterator for ProbabilitiesIter<'_> {
type Item = f64;
fn next(&mut self) -> Option<Self::Item> {
match &mut self.inner {
ProbabilitiesIterInner::Dense(iter) => iter.next(),
ProbabilitiesIterInner::Factored { blocks, next, len } => {
if *next >= *len {
return None;
}
let index = *next;
*next += 1;
let mut p = 1.0;
for block in *blocks {
let local = extract_block_bits(index, block.mask);
p *= block.probs[local];
}
Some(p)
}
}
}
fn size_hint(&self) -> (usize, Option<usize>) {
match &self.inner {
ProbabilitiesIterInner::Dense(iter) => iter.size_hint(),
ProbabilitiesIterInner::Factored { next, len, .. } => {
let remaining = len.saturating_sub(*next);
(remaining, Some(remaining))
}
}
}
}
impl ExactSizeIterator for ProbabilitiesIter<'_> {}
/// Extract the bits of `global_index` at positions set in `mask`,
/// packing them into contiguous low bits.
#[inline]
fn extract_block_bits(global_index: usize, mask: u64) -> usize {
#[cfg(target_arch = "x86_64")]
{
if is_x86_feature_detected!("bmi2") {
// SAFETY: BMI2 availability is checked immediately before this call.
return unsafe { core::arch::x86_64::_pext_u64(global_index as u64, mask) as usize };
}
}
let mut result = 0usize;
let mut bit = 0;
let mut m = mask;
while m != 0 {
let pos = m.trailing_zeros() as usize;
if global_index & (1 << pos) != 0 {
result |= 1 << bit;
}
bit += 1;
m &= m.wrapping_sub(1);
}
result
}
#[cfg(test)]
mod tests {
use super::*;
fn factored_2x3() -> Probabilities {
Probabilities::Factored {
blocks: vec![
FactoredBlock {
probs: vec![0.25, 0.75],
mask: 0b001,
},
FactoredBlock {
probs: vec![0.1, 0.2, 0.3, 0.4],
mask: 0b110,
},
],
total_qubits: 3,
}
}
#[test]
fn dense_basic_accessors() {
let p = Probabilities::Dense(vec![0.1, 0.2, 0.3, 0.4]);
assert_eq!(p.len(), 4);
assert!(!p.is_empty());
assert_eq!(p.get(2), 0.3);
assert_eq!(p.get(3), 0.4);
assert_eq!(p.to_vec(), vec![0.1, 0.2, 0.3, 0.4]);
let collected: Vec<f64> = p.iter().collect();
assert_eq!(collected, vec![0.1, 0.2, 0.3, 0.4]);
}
#[test]
fn factored_get_matches_to_vec() {
let p = factored_2x3();
assert_eq!(p.len(), 8);
let dense = p.to_vec();
for (i, d) in dense.iter().enumerate() {
assert!((p.get(i) - d).abs() < 1e-12);
}
let sum: f64 = dense.iter().sum();
assert!((sum - 1.0).abs() < 1e-12);
}
#[test]
fn factored_iter_matches_to_vec() {
let p = factored_2x3();
let dense = p.to_vec();
let iter_vec: Vec<f64> = p.iter().collect();
assert_eq!(iter_vec.len(), dense.len());
for (a, b) in iter_vec.iter().zip(dense.iter()) {
assert!((a - b).abs() < 1e-12);
}
}
#[test]
fn factored_iter_size_hint_exact() {
let p = factored_2x3();
let mut it = p.iter();
assert_eq!(it.size_hint(), (8, Some(8)));
assert_eq!(it.len(), 8);
it.next();
assert_eq!(it.size_hint(), (7, Some(7)));
for _ in 0..7 {
it.next();
}
assert_eq!(it.size_hint(), (0, Some(0)));
assert!(it.next().is_none());
}
#[test]
fn dense_iter_size_hint_exact() {
let p = Probabilities::Dense(vec![0.5, 0.5]);
let it = p.iter();
assert_eq!(it.size_hint(), (2, Some(2)));
}
#[test]
fn extract_block_bits_scalar_via_get() {
let blocks = vec![FactoredBlock {
probs: vec![0.0, 0.0, 0.0, 1.0],
mask: 0b1010,
}];
let p = Probabilities::Factored {
blocks,
total_qubits: 4,
};
assert!((p.get(0b1010) - 1.0).abs() < 1e-12);
assert!(p.get(0b0010).abs() < 1e-12);
assert!(p.get(0b1000).abs() < 1e-12);
}
#[cfg(feature = "parallel")]
#[test]
fn factored_to_vec_parallel_path() {
let mut blocks = Vec::new();
for i in 0..5 {
blocks.push(FactoredBlock {
probs: vec![0.125; 8],
mask: 0b111u64 << (3 * i),
});
}
let p = Probabilities::Factored {
blocks,
total_qubits: 15,
};
let v = p.to_vec();
assert_eq!(v.len(), 1 << 15);
let sum: f64 = v.iter().sum();
assert!((sum - 1.0).abs() < 1e-9);
for (i, val) in v.iter().enumerate() {
assert!((p.get(i) - val).abs() < 1e-12);
}
}
}