Tight Query Lower Bounds for Quantum Sampling, with an Application to Certified Randomness
Tight quantum query bounds show high XEB scores certify near-ideal randomness from untrusted samplers.
The paper studies what a high linear cross-entropy benchmark (XEB) score certifies about an untrusted device in random circuit sampling. In the quantum query model, exceeding the honest sampler's ideal score by a constant requires Ω(N^{1/3}) queries for Haar and Fourier ensembles with N outcomes, and the bound is tight. A polynomial-query device scoring within o(1) of ideal retains n−O(log n) bits of smooth min-entropy even against an entangled adversary who later learns the oracle. Sampling the collision distribution has query complexity Θ(N^{1/3}).
- Beating the ideal XEB score by a constant needs Ω(N^{1/3}) queries.
- The bound is tight for Haar-random states and Fourier sampling.
- Near-ideal scores leave n−O(log n) bits of smooth min-entropy.
- Collision-distribution sampling has query complexity Θ(N^{1/3}).
From the original article
1 min read at arxiv.orgRandom circuit sampling experiments, the leading demonstrations of quantum computational advantage, are tested with the linear cross-entropy benchmark (XEB), which scores outcomes by their ideal probabilities. We study what a high XEB score certifies about an untrusted quantum device.
By Keshav Bhateja · arxiv.org
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