A Phase Transition in Linear Cross-Entropy Benchmarking

Explore a comprehensive lecture on the phase transition phenomenon in linear cross-entropy benchmarking (XEB) for quantum computational advantage and quantum processor benchmarks. Delve into the critical question of whether XEB accurately approximates quantum state preparation fidelity. Examine previous research findings on XEB's fidelity approximation in low noise rate regimes and its breakdown at higher noise rates. Discover the sharp phase transition that occurs at a critical noise rate value, dependent on circuit architecture and two-qubit gate properties. Investigate the phase transition using statistical mechanics models mapped from average two-copy quantities in random quantum circuit architectures. Gain insights into the transfer matrix's spectral properties and their role in explaining the phase transition behavior. Identify two-qubit gate sets exhibiting the highest noise robustness in this context.