With quantum computers of significant size now on the horizon, we should understand how to best exploit their initially limited abilities. To this end, we aim to identify a practical problem that is beyond the reach of current classical computers, but that requires the fewest resources for a quantum computer. We consider quantum simulation of spin systems, which could be applied to understand condensed matter phenomena. We synthesize explicit circuits for three leading quantum simulation algorithms, using diverse techniques to tighten error bounds and optimize circuit implementations. Quantum signal processing appears to be preferred among algorithms with rigorous performance guarantees, whereas higher-order product formulas prevail if empirical error estimates suffice. Our circuits are orders of magnitude smaller than those for the simplest classically infeasible instances of factoring and quantum chemistry, bringing practical quantum computation closer to reality.

随着即将出现的大型量子计算机，我们应该了解如何最好地利用其最初有限的能力。为此，我们旨在确定一个实际问题，这是当前经典计算机无法解决的，但是对于量子计算机而言，它需要最少的资源。我们考虑了自旋系统的量子模拟，该模拟可用于理解凝聚态现象。我们使用三种技术来收紧误差范围并优化电路实现，从而为三种领先的量子仿真算法合成显式电路。在具有严格性能保证的算法中，似乎首选量子信号处理，而如果经验误差估计足够，则采用高阶乘积公式。