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Governing asymptotic regime of classical RCS difficulty in the experimental noise regime

Ascertain which asymptotic results—noiseless exponential hardness versus fixed‑noise asymptotic easiness—govern the empirical classical difficulty of random circuit sampling within experimentally accessible ranges of qubit number N and gate error rate ε, and delineate the thresholds and regimes where each behavior dominates.

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Background

The authors review theory showing noiseless RCS is exponentially hard for classical simulation, alongside recent results that RCS becomes asymptotically easy at fixed noise rates under certain assumptions. They point out that these do not conclusively determine the behavior at realistic system sizes and error rates.

They explicitly state uncertainty about which theoretical regime controls classical RCS difficulty in the experimentally accessible parameter space, framing a concrete open question about identifying the governing asymptotics and thresholds.

References

Ultimately, which set of results control the behavior of classical RCS in the range of system sizes and error rates accessible to experiments is unclear, but one thing is clear: The larger one can make a quantum computer while continuing to push down error rates (for example, in a manner that maintains overall circuit fidelities while increasing N), the more likely it is that we will find tasks at which non-error-corrected quantum computers dramatically outperform the best classical algorithms.

— The computational power of random quantum circuits in arbitrary geometries (2406.02501 - DeCross et al., 4 Jun 2024) in Outlook