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Quantum

Sample-efficient benchmarking of shallow all-to-all random quantum circuits

Gregory Bentsen, Bill Fefferman, Soumik Ghosh, Michael J. Gullans, Yinchen Liu

Featured May 26, 2026

Original Paper

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Simply

Scientists found two new ways to prove quantum computers are truly powerful, even when noisy: one uses a nonlinear score that works for simple quantum circuits, and another uses a 'heavy output' trick that needs very few tries to tell real quantum machines from fakes.

In depth
The paper introduces two novel benchmarks to certify quantum advantage in shallow-depth all-to-all random quantum circuits against classical spoofers. They demonstrate that the nonlinear cross-entropy (log XEB), previously deemed sample-inefficient, is robust to noise and sample-efficient in this regime. Additionally, they develop a heavy output generation (HOG) binary classifier that achieves logarithmic sample complexity, requiring exponentially fewer samples to distinguish quantum hardware from classical spoofers.

Key Takeaways

  • 1
    The nonlinear cross-entropy (log XEB) is established as a sample-efficient benchmark for shallow-depth all-to-all random quantum circuits, overcoming the classical spoofing vulnerabilities of linear XEB.
  • 2
    A novel heavy output generation (HOG) binary classifier is introduced, featuring logarithmic sample complexity () for distinguishing quantum samplers from classical spoofers.
  • 3
    The analytical framework leverages Brownian random circuit ensembles and replica tricks, enabling exact calculations of high-order moments of output probability distributions, which is challenging for discrete circuits.

Conceptual Flow

HIGH LEVEL
1
Methodology: How to tell real quantum from fakes?

The paper uses special math to understand how quantum circuits behave, then creates two new tests: one measures a 'nonlinear score' and another looks for 'heavy outputs' to spot real quantum computers.

Quantum Circuit
Classical Spoofer
Analyze Behavior
Nonlinear Score Test
Heavy Output Test
2
Results: What did they find?

The new tests can reliably tell noisy quantum computers apart from fakes, with one test needing far fewer samples than before, making it much faster to prove quantum advantage.

Noisy Quantum
Classical Spoofer
Distinguish Reliably
Quantum Advantage Certified
Few Samples Needed