A Phase Transition in Linear Cross-Entropy Benchmarking
summary
Shows that the linear cross-entropy benchmark (XEB) stops tracking fidelity as noise crosses a sharp phase transition: XEB ≈ fidelity for εN ≪ 1 but breaks down above a threshold scaling like C/N (numerics for all-to-all give εN ≈ 0.92). Method maps averaged two-copy quantities to a statistical-mechanics model, analyzes the transfer-matrix eigenvalue spectrum, and verifies results with tensor-network simulations (and Markov checks) of the Hamming-symmetric subspace; above threshold XEB decay becomes noise‑independent while fidelity falls to q^−N.
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chapters (21)
- 0:00Intro
- 0:37Comparing architectures
- 2:01Benchmarking
- 4:13Estimating fidelity
- 6:48Claims about XEB
- 8:04Outline
- 8:30White-noise approximation
- 9:35Statistical mechanical mapping
- 10:36Prior results
- 13:10Main claim
- 14:53Stat.mech. model mapping
- 17:21XEB observable
- 17:59Update rules of stat. mech. model
- 20:35Physics of the model
- 22:42Decay of fidelity and XEB
- 27:20Hamming symmetry
- 30:59Numerical results: fidelity
- 31:57Numerical results: XEB
- 35:45Is there a transition here?
- 36:47Noise-induced transition in complexity?
- 39:46Outlook
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