Efficient simulation of noisy IQP circuits with amplitude-damping noise

TL;DR

This paper introduces a polynomial-time classical algorithm for simulating the output of amplitude-damped IQP circuits, addressing a gap in the simulation of non-unital noise without randomness.

Contribution

It presents the first efficient classical simulation method for amplitude-damped IQP circuits with certain local gates and noise conditions.

Findings

The algorithm efficiently samples from noisy IQP circuit outputs.

It applies to circuits with arbitrary local diagonal gates and logarithmic depth.

The method handles constant amplitude-damping noise without requiring randomness.

Abstract

Efficient classical simulation of noisy intermediate-scale quantum (NISQ) circuits has been a topic of intense study over the past few years. The majority of results on efficient simulation assume that the circuits undergo some variant of unital noise or involve sufficient randomness. However, there are limited results for circuits undergoing non-unital noise in the absence of randomness. In this work, we present a polynomial-time classical algorithm to sample from the output distributions of amplitude-damped instantaneous quantum polynomial (IQP) circuits. Our algorithm works for circuits generated by arbitrary $l$-local diagonal gates with depth $d = \Omega(\log(n))$, undergoing constant amplitude-damping noise.