Quantum simulation promises to address many challenges in fields ranging from quantum chemistry to material science and high-energy physics, and could be implemented in noisy intermediate-scale quantum devices. A challenge in building good digital quantum simulators is the fidelity of the engineered dynamics given a finite set of elementary operations. Here we present a framework for optimizing the order of operations based on a geometric picture, thus abstracting from the operation details and achieving computational efficiency. Based on this geometric framework, we provide two alternative second-order Trotter expansions: one with optimal fidelity at a short timescale, and the second robust at a long timescale. Thanks to the improved fidelity at different timescales, the two expansions we introduce can form the basis for experimental-constrained digital quantum simulation.

中文翻译：

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用于数字量子模拟的高保真Trotter公式

量子仿真有望解决从量子化学到材料科学和高能物理领域的许多挑战，并且可以在嘈杂的中型量子设备中实现。在给定有限的基本操作集的情况下，构建好的数字量子模拟器所面临的挑战是工程动力学的保真度。在这里，我们提出了一个基于几何图形优化操作顺序的框架，从而从操作细节中抽象出来并实现了计算效率。在此几何框架的基础上，我们提供了两种可选的二阶Trotter扩展：一种在短时间范围内具有最佳保真度，另一种在长时间范围内具有鲁棒性。由于在不同时间范围内保真度的提高，