Simulating quantum systems is one of the most promising avenues to harness the computational power of quantum computers. However, hardware errors in noisy near-term devices remain a major obstacle for applications. Ideas based on the randomization of Suzuki-Trotter product formulas have been shown to be a powerful approach to reducing the errors of quantum simulation and lowering the gate count. In this paper, we study the performance of non-unitary simulation channels and consider the error structure of channels constructed from a weighted average of unitary circuits. We show that averaging over just a few simulation circuits can significantly reduce the Trotterization error for both single-step short-time and multi-step long-time simulations. We focus our analysis on two approaches for constructing circuit ensembles for averaging: (i) permuting the order of the terms in the Hamiltonian and (ii) applying a set of global symmetry transformations. We compare our analytical error bounds to empirical performance and show that empirical error reduction surpasses our analytical estimates in most cases. Finally, we test our method on an IonQ trapped-ion quantum computer accessed via the Amazon Braket cloud platform, and benchmark the performance of the averaging approach.

翻译：模拟量子系统是利用量子计算机计算能力最有前景的途径之一。然而，近期含噪设备中的硬件错误仍是应用的主要障碍。基于 Suziki-Trotter 乘积公式随机化的思想已被证明是减少量子模拟错误并降低门数量的强大方法。在本文中，我们研究了非幺正模拟通道的性能，并考虑了由幺正电路加权平均构建的通道的错误结构。我们表明，仅对少量模拟电路进行平均就能显著减少单步短时和多步长时模拟中的 Trotterization 误差。我们的分析聚焦于两种构建电路集合以进行平均的方法：(i) 置换哈密顿量中各项的顺序；(ii) 应用一组全局对称性变换。我们将解析误差界限与实证性能进行比较，发现大多数情况下实证误差减少超过了解析估计。最后，我们在通过 Amazon Braket 云平台访问的 IonQ 离子阱量子计算机上测试了该方法，并对平均方法的性能进行了基准测试。