A classical polynomial-time sampler exists for the output distribution of amplitude-damped IQP circuits with logarithmic depth and arbitrary l-local diagonal gates.
Since the unitary gates are diagonal in the computational basis, their action is limited to introducing phase factors in the coefficients
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Efficient simulation of noisy IQP circuits with amplitude-damping noise
A classical polynomial-time sampler exists for the output distribution of amplitude-damped IQP circuits with logarithmic depth and arbitrary l-local diagonal gates.