Efficiently mapping quantum circuits onto hardware is integral for the quantum compilation process, wherein a circuit is modified in accordance with a quantum processor’s connectivity. Many techniques currently exist for solving this problem, wherein SWAP-gate overhead is usually prioritized as a cost metric. We reconstitute quantum circuit mapping using tools from quantum information theory, showing that a lower bound, which we dub the lightcone bound, emerges for a circuit executed on hardware. We also develop an initial placement algorithm based on graph similarity search, aiding us in optimally placing circuit qubits onto a device. 600 realistic benchmarks using the IBM Qiskit compiler and a brute-force method are then tested against the lightcone bound, with results unambiguously verifying the veracity of the bound, while permitting trustworthy estimations of minimal overhead in near-term realizations of quantum algorithms. This work constitutes the first use of quantum circuit uncomplexity to practically-relevant quantum computing.

将量子电路有效地映射到硬件上是量子编译过程不可或缺的一部分，其中电路根据量子处理器的连接性进行修改。目前有许多技术可以解决这个问题，其中 SWAP-gate 开销通常被优先作为成本指标。我们使用量子信息论中的工具重建了量子电路映射，表明在硬件上执行的电路出现了一个下界，我们称之为光锥界。我们还开发了一种基于图相似性搜索的初始放置算法，帮助我们以最佳方式将电路量子比特放置在设备上。然后使用 IBM Qiskit 编译器和蛮力方法对 600 个现实基准测试进行了光锥边界测试，结果明确验证了边界的真实性，同时允许在量子算法的近期实现中对最小开销进行可信估计。这项工作首次将量子电路的不复杂性用于实际相关的量子计算。