Focus beyond Quadratic Speedups for Error-Corrected Quantum Advantage

R. Babbush, J. McClean, M. Newman, C. Gidney, S. Boixo, H. Neven
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引用次数: 93

Abstract

We discuss conditions under which it would be possible for a modest fault-tolerant quantum computer to realize a runtime advantage by executing a quantum algorithm with only a small polynomial speedup over the best classical alternative. The challenge is that the computation must finish within a reasonable amount of time while being difficult enough that the small quantum scaling advantage would compensate for the large constant factor overheads associated with error-correction. We compute several examples of such runtimes using state-of-the-art surface code constructions for superconducting qubits under a variety of assumptions. We conclude that quadratic speedups will not enable quantum advantage on early generations of such fault-tolerant devices unless there is a significant improvement in how we would realize quantum error-correction. While this conclusion persists even if we were to increase the rate of logical gates in the surface code by more than an order of magnitude, we also repeat this analysis for speedups by other polynomial degrees and find that quartic speedups look significantly more practical.
超越二次加速,聚焦纠错量子优势
我们讨论了一些条件,在这些条件下,适度的容错量子计算机可以通过执行量子算法来实现运行时优势,而量子算法的速度只比最佳的经典替代算法加快一个小的多项式。挑战在于计算必须在合理的时间内完成,同时足够困难,小量子缩放优势将补偿与纠错相关的大常数因子开销。我们使用最先进的超导量子比特表面代码结构在各种假设下计算了几个这样的运行时示例。我们得出的结论是,除非我们在如何实现量子纠错方面有重大改进,否则二次加速将无法在早期几代此类容错设备上实现量子优势。虽然即使我们要将表面代码中的逻辑门的速率提高一个数量级以上,这个结论仍然存在,但我们也对其他多项式度的加速重复此分析,并发现四次加速看起来更加实用。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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