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Empirical evidence for a gap between the computational powers of classical and quantum computers has been provided by experiments that sample the output distributions of two-dimensional quantum circuits.
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It is worth noting that the classical approach to RCS used to show N N -asymptotic easiness at fixed noise rate in Ref. Aharonov et al. 2023 scales exponentially with the inverse of the gate error rate, leaving open the possibility that the window of system sizes controlled by noiseless asymptotics may be quite large even at modest gate error rates
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