In the past few years, several quantum computers realized by the noisy intermediate-scale quantum (NISQ) technology have been released. However, there exists a significant limitation to using such computers, i.e., the connectivity constraint between physical qubits. To perform a 2-qubit quantum operation on such NISQ computers, its two logical qubits have to be mapped to a pair of physical qubits that satisfy the connectivity constraint. This mapping procedure requires additional operations to be introduced into the original quantum circuit, reducing its fidelity. Therefore, it is of great significance to design an algorithm that is able to complete the mapping task with minimal additional operations. In this article, we propose an efficient algorithm to solve this problem. Our algorithm consists of two core components, an expansion-from-center scheme to determine the initial mapping and a SWAP-based heuristic search algorithm to update the mapping. We introduce the maximum consecutive positive effect of a SWAP operation as the heuristic cost function, allowing our search algorithm to look ahead dynamically. Our algorithm is evaluated on IBM Q 20. The experimental results show that our algorithm can complete the mapping task in a very short time even for large-scale benchmarks with hundreds of thousands of operations, and outperforms the state-of-the-art in terms of the number of additional operations for most benchmarks considered.

中文翻译：

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NISQ 计算机量子位映射问题的动态前瞻启发式算法

在过去的几年中，已经发布了几款通过嘈杂的中尺度量子（NISQ）技术实现的量子计算机。然而，使用这样的计算机存在很大的限制，即物理量子位之间的连接约束。要在此类 NISQ 计算机上执行 2 量子位量子操作，必须将其两个逻辑量子位映射到满足连接约束的一对物理量子位。这种映射过程需要在原始量子电路中引入额外的操作，从而降低其保真度。因此，设计一种能够以最少的附加操作完成映射任务的算法具有重要意义。在本文中，我们提出了一种有效的算法来解决这个问题。我们的算法由两个核心组件组成，确定初始映射的中心扩展方案和更新映射的基于 SWAP 的启发式搜索算法。我们引入了 SWAP 操作的最大连续积极影响作为启发式成本函数，允许我们的搜索算法动态地向前看。我们的算法在 IBM Q 20 上进行了评估。 实验结果表明，即使对于具有数十万次操作的大规模基准测试，我们的算法也可以在很短的时间内完成映射任务，并且在考虑的大多数基准的附加操作数量。允许我们的搜索算法动态地向前看。我们的算法在 IBM Q 20 上进行了评估。 实验结果表明，即使对于具有数十万次操作的大规模基准测试，我们的算法也可以在很短的时间内完成映射任务，并且在考虑的大多数基准的附加操作数量。允许我们的搜索算法动态地向前看。我们的算法在 IBM Q 20 上进行了评估。 实验结果表明，即使对于具有数十万次操作的大规模基准测试，我们的算法也可以在很短的时间内完成映射任务，并且在考虑的大多数基准的附加操作数量。