A sharp phase transition in linear crossentropy benchmarking
Abstract
Demonstrations of quantum computational advantage and benchmarks of quantum processors via quantum random circuit sampling are based on evaluating the linear crossentropy benchmark (XEB). A key question in the theory of XEB is whether it approximates the fidelity of the quantum state preparation. Previous works have shown that the XEB generically approximates the fidelity in a regime where the noise rate per qudit $\varepsilon$ satisfies $\varepsilon N \ll 1$ for a system of $N$ qudits and that this approximation breaks down at large noise rates. Here, we show that the breakdown of XEB as a fidelity proxy occurs as a sharp phase transition at a critical value of $\varepsilon N$ that depends on the circuit architecture and properties of the twoqubit gates, including in particular their entangling power. We study the phase transition using a mapping of average twocopy quantities to statistical mechanics models in random quantum circuit architectures with full or onedimensional connectivity. We explain the phase transition behavior in terms of spectral properties of the transfer matrix of the statistical mechanics model and identify twoqubit gate sets that exhibit the largest noise robustness.
 Publication:

arXiv eprints
 Pub Date:
 May 2023
 DOI:
 10.48550/arXiv.2305.04954
 arXiv:
 arXiv:2305.04954
 Bibcode:
 2023arXiv230504954W
 Keywords:

 Quantum Physics;
 Condensed Matter  Statistical Mechanics
 EPrint:
 17 pages, 8 figures