Before quantum error correction (QEC) is achieved, quantum computers focus on noisy intermediate-scale quantum (NISQ) applications. Compared to the well-known quantum algorithms requiring QEC, like Shor's or Grover's algorithm, NISQ applications have different structures and properties to exploit in compilation. A key step in compilation is mapping the qubits in the program to physical qubits on a given quantum computer, which has been shown to be an NP-hard problem. In this paper, we present OLSQ-GA, an optimal qubit mapper with a key feature of simultaneous SWAP gate absorption during qubit mapping, which we show to be a very effective optimization technique for NISQ applications. For the class of quantum approximate optimization algorithm (QAOA), an important NISQ application, OLSQ-GA reduces depth by up to 50.0% and SWAP count by 100% compared to other state-of-the-art methods, which translates to 55.9% fidelity improvement. The solution optimality of OLSQ-GA is achieved by the exact SMT formulation. For better scalability, we augment our approach with additional constraints in the form of initial mapping or alternating matching, which speeds up OLSQ-GA by up to 272X with no or little loss of optimality.

中文翻译：

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具有同步门吸收的最佳量子位映射

在实现量子纠错 (QEC) 之前，量子计算机专注于嘈杂的中级量子 (NISQ) 应用。与众所周知的需要 QEC 的量子算法（如 Shor 或 Grover 算法）相比，NISQ 应用程序在编译中具有不同的结构和属性可供利用。编译的一个关键步骤是将程序中的量子位映射到给定量子计算机上的物理量子位，这已被证明是一个 NP 难问题。在本文中，我们提出了 OLSQ-GA，这是一种最佳量子位映射器，在量子位映射期间具有同时 SWAP 门吸收的关键特征，我们证明这是一种非常有效的 NISQ 应用优化技术。对于重要的 NISQ 应用量子近似优化算法 (QAOA) 类，OLSQ-GA 将深度减少了 50。与其他最先进的方法相比，0% 和 SWAP 计数为 100%，这意味着保真度提高了 55.9%。OLSQ-GA 的最优解是通过精确的 SMT 公式实现的。为了获得更好的可扩展性，我们通过初始映射或交替匹配形式的附加约束来增强我们的方法，这将 OLSQ-GA 速度提高了 272 倍，而没有或几乎没有优化损失。