A sharp phase transition in linear cross-entropy benchmarking

Understand

Demonstrations of quantum computational advantage and benchmarks of quantum processors via quantum random circuit sampling are based on evaluating the linear cross-entropy 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 two-qubit gates, including in particular their entangling power.