A sharp phase transition in linear cross-entropy benchmarking
- URL: http://arxiv.org/abs/2305.04954v1
- Date: Mon, 8 May 2023 18:00:05 GMT
- Title: A sharp phase transition in linear cross-entropy benchmarking
- Authors: Brayden Ware, Abhinav Deshpande, Dominik Hangleiter, Pradeep Niroula,
Bill Fefferman, Alexey V. Gorshkov, Michael J. Gullans
- Abstract summary: 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 $varepsilon N ll 1$.
Here, we show that the breakdown of XEB as a fidelity proxy occurs as a sharp phase transition at a critical value of $varepsilon N$.
- Score: 1.4841630983274847
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: 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. We study the phase transition using a
mapping of average two-copy quantities to statistical mechanics models in
random quantum circuit architectures with full or one-dimensional connectivity.
We explain the phase transition behavior in terms of spectral properties of the
transfer matrix of the statistical mechanics model and identify two-qubit gate
sets that exhibit the largest noise robustness.
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