Noisy, intermediate-scale quantum (NISQ) computers are expected to execute quantum circuits of up to a few hundred qubits. The circuits have to conform to NISQ architectural constraints regarding qubit allocation and the execution of multi-qubit gates. Quantum circuit compilation (QCC) takes a nonconforming circuit and outputs a compatible circuit. Can classical optimisation methods be used for QCC? Compilation is a known combinatorial problem shown to be solvable by two types of operations: (1) qubit allocation, and (2) gate scheduling. We show informally that the two operations form a discrete ring. The search landscape of QCC is a two dimensional discrete torus where vertices represent configurations of how circuit qubits are allocated to NISQ registers. Torus edges are weighted by the cost of scheduling circuit gates. The novelty of our approach uses the fact that a circuit’s gate list is circular: compilation can start from any gate as long as all the gates will be processed, and the compiled circuit has the correct gate order. Our work bridges a theoretical and practical gap between classical circuit design automation and the emerging field of quantum circuit optimisation.

嘈杂的中型量子（NISQ）计算机有望执行高达几百个量子比特的量子电路。这些电路必须符合有关量子比特分配和多量子比特门执行的NISQ体系结构约束。量子电路编译（QCC）采用不合格电路并输出兼容电路。QCC可以使用经典的优化方法吗？编译是一个已知的组合问题，可以通过两种操作来解决：（1）量子位分配和（2）门调度。我们非正式地表明这两个操作形成一个离散的环。QCC的搜索范围是二维离散圆环，其中顶点表示电路量子位如何分配给NISQ寄存器的配置。环形边缘由调度电路门的成本加权。我们的方法的新颖性在于电路的门列表是循环的：只要可以处理所有门，编译就可以从任何门开始，并且编译后的电路具有正确的门顺序。我们的工作弥合了经典电路设计自动化与新兴的量子电路优化领域之间的理论和实践差距。