The standard approach to universal fault-tolerant quantum computing is to develop a general purpose quantum error correction mechanism that can implement a universal set of logical gates fault-tolerantly. Given such a scheme, any quantum algorithm can be realized fault-tolerantly by composing the relevant logical gates from this set. However, we know that quantum computers provide a significant quantum advantage only for specific quantum algorithms. Hence, a universal quantum computer can likely gain from compiling such specific algorithms using tailored quantum error correction schemes. In this work, we take the first steps towards such algorithm-tailored quantum fault-tolerance. We consider Trotter circuits in quantum simulation, which is an important application of quantum computing. We develop a solve-and-stitch algorithm to systematically synthesize physical realizations of Clifford Trotter circuits on the well-known $[\![ n,n-2,2 ]\!]$ error-detecting code family. Our analysis shows that this family implements Trotter circuits with optimal depth, thereby serving as an illuminating example of tailored quantum error correction. We achieve fault-tolerance for these circuits using flag gadgets, which add minimal overhead. The solve-and-stitch algorithm has the potential to scale beyond this specific example and hence provide a principled approach to tailored fault-tolerance in quantum computing.

翻译：实现通用容错量子计算的标准方法是开发一种通用量子纠错机制，使其能够容错地实现通用逻辑门集合。基于此类方案，任何量子算法均可通过组合该集合中的相关逻辑门来容错实现。然而，我们知道量子计算机仅在特定量子算法上具有显著的量子优势。因此，通用量子计算机很可能需要通过定制化的量子纠错方案来编译这些特定算法。在本工作中，我们迈出了实现这种算法定制化量子容错的第一步。我们重点研究了量子模拟中的Trotter线路——这是量子计算的重要应用之一。我们开发了一种"求解-拼接"(solve-and-stitch)算法，用于在著名的$[\![ n,n-2,2 ]\!]$错误检测码族上系统化地合成Clifford Trotter线路的物理实现。分析表明，该码族能以最优深度实现Trotter线路，从而成为定制化量子纠错的一个典型范例。我们通过使用旗标(flag)器件实现这些线路的容错性，且仅增加极小的开销。该求解-拼接算法具有超越此特定示例的可扩展潜力，因此为量子计算中的定制化容错提供了一种系统性方法。