[ruslan-splynx]

Closes #556.

Each noisy trajectory used to build six state-sized probability/alias buffers for one terminal draw. CPU AoS FP64, SoA FP64 and FP32 now fully validate the state without materializing probabilities, then use one cumulative draw; zero shots validate with no allocations/RNG consumption. Two or more shots keep the alias algorithm, allocation requirements and seeded mapping.

The single-shot seed-to-outcome mapping intentionally changes. Both algorithms consume one RNG u64, so absolute noisy shot seeds, gate/channel ordering and subsequent readout RNG position are preserved. Shared validation retains normalization budgets and FP32 widening, rejects late NaN/Inf and malformed layouts before drawing, skips zero bins and handles endpoint rounding with the last positive bin. No production unsafe code, dependency, fusion or noisy-worker/state-reuse change is introduced.

Paired Criterion A/B/B/A on Intel i5-13500, logical CPU0 / one Rayon worker, shared services untouched, two repeats × 10 samples per cell:

Public API case	Baseline	Candidate	Speedup
FP64 AoS sample n=20 / 1 shot	10.366 ms	0.820 ms	12.65×
FP64 SoA sample n=20 / 1 shot	10.308 ms	0.964 ms	10.69×
FP32 sample n=20 / 1 shot	10.212 ms	0.849 ms	12.03×
noisy n=4 / 1024 trajectories	536.0 µs	414.7 µs	1.29×
noisy n=16 / 64 trajectories	96.39 ms	83.80 ms	1.15×
noisy n=20 / 8 trajectories	366.65 ms	274.84 ms	1.33×

At n=20 single-shot, all CPU layouts drop from 7 allocations / 36 MiB scratch peak to 1 allocation / 8 result bytes. Full one-worker noisy n=20/8 additional live-heap peak drops 52 → 16 MiB; this is requested Rust heap, not RSS. Many-shot allocations match baseline exactly. Initial tiny 1024-shot regressions motivated an isolated inline(never) low-shot helper; final tiny 2–4-shot cells retain up to 5.3% (roughly 3–6 ns) overhead. No many-shot speedup or wider optimal streaming threshold is claimed.

Validation: 346 SV unit/property tests; six stored Aer noise/readout oracles; three noisy-driver tests; public analytic single/many-shot distributions through all three layouts; 1/2/4-worker noisy determinism with Pauli/Kraus/readout; million-shot convergence and FP32 equivalence. Workspace all-target clippy, final SV clippy, rustfmt and diff checks passed. Linux final release: all six noisy Aer oracles plus both public sampler/worker-invariance tests passed.

docs/perf/p8-06-single-shot-sampling.md documents seeds, limits, commands and noise-model identity. Data includes all 48 cases × 4 Criterion repeats with confidence intervals/raw samples, allocation counters, provenance and the valid initial helper campaign. An invalid shared-Cargo-target pilot returned identical binaries; allocation preflight caught it, pilot timings were discarded, and accepted builds use independent targets and distinct hashes. Benchmark/memory evidence is from actual public Rust APIs; no Python/GPU/Metal performance claim.

Draft pending CI and final review. #557 trajectory reuse/concurrency/sparse results and draft #569 Metal timings remain separate.