Phase Transitions in Random Circuit Sampling

Published

October 9, 2024

Author(s)

Sergio Boixo, Rene Peralta

Abstract

Undesired coupling to the surrounding environment destroys long-range correlations on quantum processors and hinders the coherent evolution in the nominally available computational space. This noise is an outstanding challenge to leverage the computation power of near-term quantum processors [1]. It has been shown that benchmarking Random Circuit Sampling (RCS) with Cross-Entropy Benchmarking (XEB) can provide an estimate of the effective size of the Hilbert space coherently available [2–8]. Nevertheless, quantum algorithms' outputs can be trivialized by noise, making them susceptible to classical computation spoofing. Here, by implementing an RCS algorithm we demonstrate experimentally that there are two phase transitions observable with XEB, which we explain theoretically with a statistical model. The first is a dynamical transition as a function of the number of cycles and is the continuation of the anti-concentration point in the noiseless case. The second is a quantum phase transition controlled by the error per cycle; to identify it analytically and experimentally, we create a weak link model which allows varying the strength of noise versus coherent evolution. Furthermore, by presenting an RCS experiment in the weak noise phase with 67 qubits at 32 cycles, we demonstrate that the computational cost of our experiment is beyond the capabilities of existing classical supercomputers. Our experimental and theoretical work establishes the existence of transitions to a stable computationally complex phase that is reachable with current quantum processors.

Citation

Nature

Issue

634

Pub Type

Journals

Download Paper

https://doi.org/10.1038/s41586-024-07998-6

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Keywords

quantum computation, quantum circuit

Citation

Boixo, S. and Peralta, R. (2024), Phase Transitions in Random Circuit Sampling, Nature, [online], https://doi.org/10.1038/s41586-024-07998-6, https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=958703 (Accessed December 26, 2024)