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arXiv 2007.07391quant-ph
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组合优化容错量子启发式算法的编译

Compilation of Fault-Tolerant Quantum Heuristics for Combinatorial Optimization

Yuval R. Sanders, Dominic W. Berry, Pedro C. S. Costa, Louis W. Tessler, Nathan Wiebe, Craig Gidney, Hartmut Neven, Ryan Babbush

备注：
77 pages, 19 figures, 9 tables. v2 contains new appendix on in-place binary to unary conversion
发表信息：
PRX Quantum 1, 020312 (2020)
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摘要：

在这里，我们将探讨哪些启发式量子算法的组合优化可能是最实用的尝试在一个小型的容错量子计算机。我们编译电路的几个变种的量子加速模拟退火，包括那些使用qubitization或Szegedy散步，以避免经典的马尔可夫链和那些模拟的频谱间隙放大的哈密顿编码吉布斯状态。我们还优化了绝热算法，量子增强的人口转移，量子近似优化算法和其他方法的容错实现。这些方法中的许多方法都是通过调用相同的子程序来检查的;因此，无论哪种启发式方法在实践中最有效，都应该对这些原语的优化电路感兴趣。我们编译这些瓶颈的几个家庭的优化问题，并报告多久，什么规模的系统可以执行这些算法在表面码给定的资源预算范围。我们的研究结果不鼓励的概念，任何量子优化启发式实现只有二次加速将实现一个优势，在适度的超导量子位表面码处理器上的经典算法没有显着改善的表面码的实施。例如，在量子有利的假设下（例如，我们的分析表明，量子加速模拟退火将需要大约一天和一百万个物理量子比特来优化自旋玻璃，而经典模拟退火可以在大约四个CPU分钟内解决。

英文摘要：

Here we explore which heuristic quantum algorithms for combinatorial optimization might be most practical to try out on a small fault-tolerant quantum computer. We compile circuits for several variants of quantum accelerated simulated annealing including those using qubitization or Szegedy walks to quantize classical Markov chains and those simulating spectral gap amplified Hamiltonians encoding a Gibbs state. We also optimize fault-tolerant realizations of the adiabatic algorithm, quantum enhanced population transfer, the quantum approximate optimization algorithm, and other approaches. Many of these methods are bottlenecked by calls to the same subroutines; thus, optimized circuits for those primitives should be of interest regardless of which heuristic is most effective in practice. We compile these bottlenecks for several families of optimization problems and report for how long and for what size systems one can perform these heuristics in the surface code given a range of resource budgets. Our results discourage the notion that any quantum optimization heuristic realizing only a quadratic speedup will achieve an advantage over classical algorithms on modest superconducting qubit surface code processors without significant improvements in the implementation of the surface code. For instance, under quantum-favorable assumptions (e.g., that the quantum algorithm requires exactly quadratically fewer steps), our analysis suggests that quantum accelerated simulated annealing would require roughly a day and a million physical qubits to optimize spin glasses that could be solved by classical simulated annealing in about four CPU-minutes.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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