Clifford+T Simulation

Circuits that mix Clifford gates with a modest number of T gates sit between the efficient stabilizer regime and the exponential statevector regime. PRISM-Q offers three strategies. The right one depends on your T-count, qubit count, and whether you need exact answers or can tolerate Monte Carlo error.

These route through the Clifford+T strategies before the standard dispatch tree when the T-count permits.

Stabilizer rank (src/sim/stabilizer_rank.rs)

Exact probability output remains capped because it returns a dense vector with 2^n entries. Shot sampling uses coherent weighted MPS branches instead of a dense statevector fallback. Clifford gates mutate each branch state, T and Tdg split branches, and measurement computes outcome probabilities from the weighted branch ensemble before projecting every branch to the sampled outcome. This removes the hard qubit-count cap from run_stabilizer_rank_shots; practical scaling is governed by branch count, MPS bond growth, and measurement count.

The dense probability path maintains a weighted sum of stabilizer states. Each T gate doubles the term count via the T = alpha*I + beta*Z decomposition. Clifford gates are O(n²) per term and weighted amplitudes are accumulated for exact probabilities.

Stochastic Pauli Propagation (src/sim/unified_pauli.rs)

Backward-propagates measurement observables as Pauli strings. Clifford gates conjugate in O(1). T gates branch stochastically into two Pauli paths with appropriate weights. Per-path cost O(d×n/64), independent of T-gate count. Returns marginal probabilities via Monte Carlo estimation.

#![allow(unused)]
fn main() {
run_spp(circuit, num_samples, seed) // -> SppResult
}

Deterministic Sparse Pauli Dynamics (src/sim/unified_pauli.rs)

Backward-propagates as a weighted sum of Pauli strings stored in a HashMap. T gates deterministically branch X/Y terms. Identical strings auto-merge. Optional ε-truncation for approximate mode. Exact for small T-counts, approximate with bounded error for larger ones.

#![allow(unused)]
fn main() {
run_spd(circuit, epsilon, max_terms) // -> SpdResult
}

You can also build Clifford+T test circuits directly with clifford_t_circuit.