量子计算的最优布局综合
Optimal Layout Synthesis for Quantum Computing
AI总结：
本文提出最优和近似两种量子布局综合器，通过基于时空的变量编码降低复杂度，在门成本、保真度及QAOA深度和成本上显著优于现有方法。
摘要：
近年来，量子计算发展迅速。世界各地的研究者迫切希望运行规模越来越大的量子算法，这些算法有望实现任何经典算法都无法达到的加速。然而，现有的量子计算机仍然具有易失性和易出错的特点。因此，将量子程序转换为满足这些硬件限制的布局综合是实现量子计算的关键步骤。本文提出了两种综合器：一种是最优综合器，另一种是近似但接近最优的综合器。尽管已有一些针对该问题的最优方法发表，但我们的最优综合器探索了更大的解空间，因此在更强的意义上是最优的。此外，与一些领先的最优方法相比，它在时间和空间复杂度上实现了指数级的降低。这一成功的关键在于一种更高效的基于时空的变量编码方式，将布局综合问题编码为数学规划问题。通过略微改变我们的公式化表示，我们得到了一个更高效的近似综合器，在一组全面的基准程序和架构上，与一些领先的启发式方法相比，其在额外门成本方面最多可降低100%，在保真度方面最多可提升10倍。对于名为QAOA的一类特定量子程序，它被认为是近期量子计算机的一个有前景的应用，我们进一步通过考虑交换性来调整近似综合器，与领先QAOA研究中使用的工具相比，在深度上最多减少75%，在额外成本上最多减少65%。
英文摘要：
Recent years have witnessed the fast development of quantum computing. Researchers around the world are eager to run larger and larger quantum algorithms that promise speedups impossible to any classical algorithm. However, the available quantum computers are still volatile and error-prone. Thus, layout synthesis, which transforms quantum programs to meet these hardware limitations, is a crucial step in the realization of quantum computing. In this paper, we present two synthesizers, one optimal and one approximate but nearly optimal. Although a few optimal approaches to this problem have been published, our optimal synthesizer explores a larger solution space, thus is optimal in a stronger sense. In addition, it reduces time and space complexity exponentially compared to some leading optimal approaches. The key to this success is a more efficient spacetime-based variable encoding of the layout synthesis problem as a mathematical programming problem. By slightly changing our formulation, we arrive at an approximate synthesizer that is even more efficient and outperforms some leading heuristic approaches, in terms of additional gate cost, by up to 100%, and also fidelity by up to 10x on a comprehensive set of benchmark programs and architectures. For a specific family of quantum programs named QAOA, which is deemed to be a promising application for near-term quantum computers, we further adjust the approximate synthesizer by taking commutation into consideration, achieving up to 75% reduction in depth and up to 65% reduction in additional cost compared to the tool used in a leading QAOA study.
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