Tailoring Fault-Tolerance to Quantum Algorithms
<|reference_start|>Tailoring Fault-Tolerance to Quantum Algorithms: 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.<|reference_end|>
@article{chen2024tailoring,
    title={Tailoring Fault-Tolerance to Quantum Algorithms},
    author={Zhuangzhuang Chen and Narayanan Rengaswamy},
    journal={arXiv preprint arXiv:2404.11953},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.11953},
    primaryClass={quant-ph cs.IT math.IT}
}