Trotterization-based, iterative approaches to quantum simulation (QS) are restricted to simulation times less than the coherence time of the quantum computer (QC), which limits their utility in the near term. Here, we present a hybrid quantum-classical algorithm, called variational fast forwarding (VFF), for decreasing the quantum circuit depth of QSs. VFF seeks an approximate diagonalization of a short-time simulation to enable longer-time simulations using a constant number of gates. Our error analysis provides two results: (1) the simulation error of VFF scales at worst linearly in the fast-forwarded simulation time, and (2) our cost function’s operational meaning as an upper bound on average-case simulation error provides a natural termination condition for VFF. We implement VFF for the Hubbard, Ising, and Heisenberg models on a simulator. In addition, we implement VFF on Rigetti’s QC to demonstrate simulation beyond the coherence time. Finally, we show how to estimate energy eigenvalues using VFF.

基于量子化的基于迭代的迭代方法（QS）的仿真时间小于量子计算机（QC）的相干时间，这在短期内限制了它们的实用性。在这里，我们提出了一种混合量子经典算法，称为变分快速转发（VFF），用于减小QSs的量子电路深度。VFF寻求短时间仿真的近似对角化，以使用恒定数量的门进行较长时间的仿真。我们的误差分析提供了两个结果：（1）在快速前进的模拟时间内，VFF标度的模拟误差在最坏的线性范围内；（2）我们的成本函数的操作含义是平均情况下模拟误差的上限提供了自然终止VFF的条件。我们在模拟器上为Hubbard，Ising和Heisenberg模型实现VFF。此外，我们在Rigetti的QC上实现了VFF，以演示超出相干时间的仿真。最后，我们展示了如何使用VFF估算能量本征值。