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arXiv 2210.09321quant-phcs.DM
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量子电路映射的最优子架构研究

On Optimal Subarchitectures for Quantum Circuit Mapping

Tom Peham, Lukas Burgholzer, Robert Wille

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19 pages, 9 figures, 3 tables
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AI总结：

本文反驳了量子电路映射中仅需考虑与电路等规模子架构的猜想，提出判断更大部分架构是否带来更优解的标准，并给出两种计算近最优子架构集合的方法，在IBM、Google和Rigetti量子计算机上验证了其优势。

摘要：

将高层量子电路编译为可在最先进量子计算机上执行的低层描述，是量子计算软件栈中的关键环节。量子电路映射是编译过程中的一个步骤，其目标是对电路进行变换，使其符合目标设备有限的量子比特连通性约束。由于量子电路映射的搜索空间随量子比特数量呈指数增长，因此在该过程中应尽可能少地考虑设备的物理量子比特。此前的研究推测，仅考虑由电路中使用的量子比特数量构成的量子计算机子架构就足够了。在本工作中，我们反驳了这一猜想，并建立了判断标准，用于评估考虑架构中更大规模的部分是否可能为映射问题带来更优解。我们证明，确定最小规模的子架构——即在不丢失某些量子电路最优映射解的前提下无法移除任何物理量子比特的子架构——是一个非常困难的问题。基于对最优性标准的松弛，我们引入了一种松弛化的考虑方式，该方式仍能为实际相关的量子电路保持最优性。最终，这产生了两种计算近最优子架构集合的方法，为高效的量子电路映射解决方案奠定了基础。我们在IBM、Google和Rigetti的最先进量子计算机上展示了这一新方法的优势。

英文摘要：

Compiling a high-level quantum circuit down to a low-level description that can be executed on state-of-the-art quantum computers is a crucial part of the software stack for quantum computing. One step in compiling a quantum circuit to some device is quantum circuit mapping, where the circuit is transformed such that it complies with the architecture's limited qubit connectivity. Because the search space in quantum circuit mapping grows exponentially in the number of qubits, it is desirable to consider as few of the device's physical qubits as possible in the process. Previous work conjectured that it suffices to consider only subarchitectures of a quantum computer composed of as many qubits as used in the circuit. In this work, we refute this conjecture and establish criteria for judging whether considering larger parts of the architecture might yield better solutions to the mapping problem. We show that determining subarchitectures that are of minimal size, i.e., of which no physical qubit can be removed without losing the optimal mapping solution for some quantum circuit, is a very hard problem. Based on a relaxation of the criteria for optimality, we introduce a relaxed consideration that still maintains optimality for practically relevant quantum circuits. Eventually, this results in two methods for computing near-optimal sets of subarchitectures$\unicode{x2014}$providing the basis for efficient quantum circuit mapping solutions. We demonstrate the benefits of this novel method for state-of-the-art quantum computers by IBM, Google and Rigetti.

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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