Quantum algorithm design usually assumes access to a perfect quantum computer with ideal properties like full connectivity, noise-freedom, and arbitrarily long coherence time. In noisy intermediate-scale quantum (NISQ) devices, however, the number of qubits is highly limited and quantum operation error and qubit coherence are not negligible. Besides, the connectivity of physical qubits in a quantum processing unit (QPU) is also strictly constrained. Thereby, additional operations like SWAP gates have to be inserted to satisfy this constraint while preserving the functionality of the original circuit. This process is known as quantum circuit transformation. Adding additional gates will increase both the size and depth of a quantum circuit and, therefore, cause further decay of the performance of a quantum circuit. Thus, it is crucial to minimize the number of added gates. In this article, we propose an efficient method to solve this problem. We first choose by using simulated annealing an initial mapping which fits well with the input circuit and then, with the help of a heuristic cost function, stepwise apply the best-selected SWAP gates until all quantum gates in the circuit can be executed. Our algorithm runs in time polynomial in all parameters, including the size and the qubit number of the input circuit, and the qubit number in the QPU. Its space complexity is quadratic to the number of edges in the QPU. The experimental results on extensive realistic circuits confirm that the proposed method is efficient and the number of added gates of our algorithm is, on average, only 57% of that of state-of-the-art algorithms on IBM Q20 (Tokyo), the most recent IBM quantum device.

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基于模拟退火和启发式搜索的量子电路变换

量子算法设计通常假设可以使用具有理想特性的完美量子计算机，例如完全连接、无噪声和任意长的相干时间。然而，在嘈杂的中尺度量子 (NISQ) 设备中，量子位的数量非常有限，量子操作误差和量子位相干性不可忽略。此外，量子处理单元（QPU）中物理量子位的连通性也受到严格限制。因此，必须插入额外的操作，如 SWAP 门，以满足此约束，同时保留原始电路的功能。这个过程被称为量子电路变换。添加额外的门会增加量子电路的尺寸和深度，因此会导致量子电路性能的进一步衰减。因此，尽量减少添加的门的数量至关重要。在本文中，我们提出了一种有效的方法来解决这个问题。我们首先通过使用模拟退火选择一个与输入电路非常匹配的初始映射，然后在启发式成本函数的帮助下，逐步应用最佳选择的 SWAP 门，直到可以执行电路中的所有量子门。我们的算法在所有参数中以时间多项式运行，包括输入电路的大小和量子比特数，以及 QPU 中的量子比特数。它的空间复杂度与 QPU 中的边数成二次方。在大量现实电路上的实验结果证实，所提出的方法是有效的，我们算法的添加门数平均仅为 IBM Q20（东京）上最先进算法的 57%，