  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.
