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Gaussian boson sampling

Platform-specific

Photonic quantum-advantage benchmark: sample photon-number patterns from squeezed light sent through a large random interferometer, a task whose probabilities are #P-hard matrix hafnians.

Measures
Ability to sample from a squeezed-light random interferometer's photon-number distribution, reported as detected photons and modes, sampling speed, and estimated classical-simulation cost
Introduced by
Hamilton, Kruse, Sansoni, Barkhofen, Silberhorn & Jex (2016)
Also known as
GBS

Gaussian boson sampling (GBS) is the flagship quantum-computational-advantage benchmark for photonic platforms, the photonic counterpart of the random-circuit sampling scored by cross-entropy benchmarking. Proposed by Hamilton and colleagues in 2016, it replaces the single-photon inputs of Aaronson–Arkhipov boson sampling with squeezed vacuum, which photon sources produce far more readily, and swaps matrix permanents for matrix hafnians. It underpins the advantage claims of USTC’s Jiuzhang machines and Xanadu’s Borealis.

How it works

Squeezed-vacuum states are injected into the modes of a large random interferometer and photon numbers are counted at the outputs. The probability of each detection pattern is the hafnian of a submatrix of a matrix fixed by the squeezing and the interferometer, #P-hard to compute (threshold-detector experiments like Jiuzhang sample the related Torontonian; Borealis used photon-number-resolving detectors). Full-size probabilities cannot be computed, so instead of a single score, experiments report detected-photon and mode counts and sampling speed, validate small instances against exact simulation, run statistical tests to reject classical spoofing hypotheses (thermal, distinguishable-photon, uniform samplers), and estimate the classical cost of simulation.

Strengths and limitations

GBS deliberately scales past the classical-verification wall that caps benchmarks like Quantum Volume, but the same fact makes validation contestable. Loss-exploiting tensor-network spoofers (Oh et al. 2023; Nature Physics 2024) sampled closer to the ideal distribution than the original Jiuzhang and Borealis experiments themselves. GBS machines are special-purpose, non-universal samplers, so results do not translate into gate-model metrics, and proposed applications (vibronic spectra, dense-subgraph and graph-similarity problems, molecular docking) remain heuristic, with no proven speedup.

Notable results

Jiuzhang’s 2020 run (76 detected photons) was the first photonic advantage claim; Borealis (2022) made the interferometer programmable, detecting up to 219 photons. The arms race with classical simulation continues: Jiuzhang 4.0 (2025) reports 1024 squeezed states across 8176 modes with up to 3050 detected photons, engineered explicitly to outrun tensor-network spoofers. Xanadu’s The Walrus remains maintained (v0.22.0, May 2025); Strawberry Fields was archived in January 2026.

Key papers

Reference implementations

  • Cross-Entropy Benchmarking : Estimates circuit fidelity by checking how often a device samples the high-probability bitstrings of random quantum circuits, the metric behind Google's quantum supremacy claim.