分而治之：用于组合优化与分布式量子计算
Divide and Conquer for Combinatorial Optimization and Distributed Quantum Computation
AI总结：
本文提出量子分而治之算法（QDCA），结合图划分与量子电路切割，将大型组合优化问题映射到分布式量子架构，在最大独立集问题上优于经典算法，并实验验证可缓解噪声，实现超越单机规模的协同计算。
摘要：
扩展单片量子计算机系统的规模是一项艰巨的任务。随着设备内量子比特数量的增加，多种因素会导致良率和性能的下降。为应对这一挑战，由众多联网量子计算机组成的分布式架构已被提出，作为实现可扩展性的可行路径。此类系统将需要针对其分布式架构量身定制的算法和编译器。在这项工作中，我们引入了量子分而治之算法（QDCA），这是一种混合变分方法，用于将大型组合优化问题映射到分布式量子架构上。这是通过结合使用图划分和量子电路切割来实现的。QDCA是应用-编译器协同设计的一个例子，它改变了变分拟设的结构，以驯服量子电路切割所带来的指数级编译开销。这种跨层协同设计的结果是一个高度灵活的算法，可以根据可用的经典或量子计算资源量进行调优，并且可以应用于近期和长期的分布式量子架构。我们在最大独立集问题的实例上模拟了QDCA，发现它能够胜过类似的经典算法。我们还在超导量子计算机上评估了一个8量子比特的QDCA拟设，并表明电路切割有助于减轻噪声的影响。我们的工作展示了众多小规模量子计算机如何协同解决比其自身量子比特数大85%的问题，从而推动了大规模分布式量子计算的发展和潜力。
英文摘要：
Scaling the size of monolithic quantum computer systems is a difficult task. As the number of qubits within a device increases, a number of factors contribute to decreases in yield and performance. To meet this challenge, distributed architectures composed of many networked quantum computers have been proposed as a viable path to scalability. Such systems will need algorithms and compilers that are tailored to their distributed architectures. In this work we introduce the Quantum Divide and Conquer Algorithm (QDCA), a hybrid variational approach to mapping large combinatorial optimization problems onto distributed quantum architectures. This is achieved through the combined use of graph partitioning and quantum circuit cutting. The QDCA, an example of application-compiler co-design, alters the structure of the variational ansatz to tame the exponential compilation overhead incurred by quantum circuit cutting. The result of this cross-layer co-design is a highly flexible algorithm which can be tuned to the amount of classical or quantum computational resources that are available, and can be applied to both near- and long-term distributed quantum architectures. We simulate the QDCA on instances of the Maximum Independent Set problem and find that it is able to outperform similar classical algorithms. We also evaluate an 8-qubit QDCA ansatz on a superconducting quantum computer and show that circuit cutting can help to mitigate the effects of noise. Our work demonstrates how many small-scale quantum computers can work together to solve problems $85\%$ larger than their own qubit count, motivating the development and potential of large-scale distributed quantum computing.
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