wai-quantum 0.3.27: Gaussian boson sampling, exactly #145

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2026-10-04

Transaction Science

wai-quantum 0.3.27: Gaussian boson sampling, exactly ...

A photonic sampler's outcome probabilities are hafnians (photon-number
detection) or torontonians (threshold detection) of its Gaussian state.
quantum_gbs computes both exactly and reproducibly.

- hafnian: power traces, a sum over 2^{n/2} pair subsets, each the
  lambda^{n/2} coefficient of exp(sum tr(B^k) lambda^k / 2k). The traces come
  from a Householder Hessenberg reduction, La Budde's characteristic
  polynomial and Newton's identities: O(n^3 2^{n/2}).
- torontonian: inclusion-exclusion over the 2^m clicked-mode subsets.
- Both sums run in 64 fixed chunks, threaded natively and sequential on WASI,
  added in chunk order, so the bits do not depend on threading.
- GaussianState: squeezed vacua through an interferometer with uniform loss,
  as the complex covariance in the (a, a-dagger) basis.
- click_probability, photon_probability: exact pattern probabilities.
- sample_clicks: exact samples, drawn mode by mode from marginal
  torontonians.
- click_marginals, check_samples: the one- and two-mode click statistics
  every sampler of the state must reproduce, polynomial in the modes, and a
  z-score check of observed patterns against them.

Against an independent implementation:
- click probabilities of three lossy states, every pattern: 1.1e-10;
- photon probabilities up to four photons: 2.3e-13;
- hafnians: 1.5e-12 up to 20x20 and 4.5e-8 at 36x36, where the alternating
  sum loses precision on either side. A 36x36 hafnian takes under 2 s.

Tests:
- hafnians match exhaustion over matchings, and (2k-1)!!;
- squeezed vacuum reproduces its textbook click and photon statistics;
- click probabilities sum to one with loss;
- exact samples reproduce marginals and full-pattern frequencies, and pass
  the check, while a different interferometer fails it.
Mutating the hafnian sign, La Budde's recurrence, Newton's identities, the
torontonian sign or the loss channel fails a named test. bit_identity pins a
24x24 hafnian and a 14-click torontonian (threaded natively, sequential under
WASI), probabilities, samples and marginals, on both targets.

CLI: wai-quantum gbs --squeezing ... [--eta --seed | --unitary] [--sample K |
--check FILE] [--json], byte-identical natively and under wasm32-wasip2.

Co-Authored-By: Claude Opus 5.5 <[email protected]>

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