Quantum walks are a promising framework for developing quantum algorithms and quantum simulations. They represent an important test case for the application of quantum computers. Here we present different forms of discrete-time quantum walks (DTQWs) and show their equivalence for physical realizations. Using an appropriate digital mapping of the position space on which a walker evolves to the multiqubit states of a quantum processor, we present different configurations of quantum circuits for the implementation of DTQWs in one-dimensional position space. We provide example circuits for a five-qubit processor and address scalability to higher dimensions as well as larger quantum processors.

中文翻译：

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用于在近期量子硬件上实现等效形式的一维离散时间量子行走的量子电路

量子行走是开发量子算法和量子模拟的有前途的框架。它们代表了量子计算机应用的重要测试用例。在这里，我们展示了不同形式的离散时间量子行走 (DTQW)，并展示了它们在物理实现上的等效性。使用步行者进化到量子处理器的多量子位状态的位置空间的适当数字映射，我们提出了用于在一维位置空间中实现 DTQW 的量子电路的不同配置。我们为五量子位处理器提供示例电路，并解决更高维度和更大量子处理器的可扩展性。