Sampling from the output distributions of quantum computations comprising only commuting gates, known as instantaneous quantum polynomial (IQP) computations, is believed to be intractable for classical computers, and hence this task has become a leading candidate for testing the capabilities of quantum devices. Here we demonstrate that for an arbitrary IQP circuit undergoing dephasing or depolarizing noise, whose depth is greater than a critical $O(1)$ threshold, the output distribution can be efficiently sampled by a classical computer. Unlike other simulation algorithms for quantum supremacy tasks, we do not require assumptions on the circuit's architecture, on anti-concentration properties, nor do we require $\Omega(\log(n))$ circuit depth. We take advantage of the fact that IQP circuits have deep sections of diagonal gates, which allows the noise to build up predictably and induce a large-scale breakdown of entanglement within the circuit. Our results suggest that quantum supremacy experiments based on IQP circuits may be more susceptible to classical simulation than previously thought.

翻译：仅由对易门构成的量子计算（称为瞬时量子多项式（IQP）计算）的输出分布采样，被认为对经典计算机是难以处理的，因此该任务已成为测试量子设备能力的主要候选方案。本文证明，对于经历退相位或退极化噪声的任意IQP电路，当其深度超过一个关键的$O(1)$阈值时，其输出分布可由经典计算机高效采样。与其他量子霸权任务的模拟算法不同，我们既不要求对电路架构或反集中性性质进行假设，也不要求电路深度达到$\Omega(\log(n))$。我们利用了IQP电路具有较深的对角门层段这一事实，这使得噪声能够以可预测的方式累积，并在电路内部引发大规模纠缠崩溃。我们的结果表明，基于IQP电路的量子霸权实验可能比先前认为的更容易受到经典模拟的影响。