Huerta Alderete C, Singh Shivani, Nguyen Nhung H, Zhu Daiwei, Balu Radhakrishnan, Monroe Christopher, Chandrashekar C M, Linke Norbert M
Joint Quantum Institute, Department of Physics, University of Maryland, College Park, MD, 20742, USA.
Instituto Nacional de Astrofísica, Óptica y Electrónica, Calle Luis Enrique Erro No. 1, 72840, Sta. Ma. Tonantzintla, PUE, Mexico.
Nat Commun. 2020 Jul 24;11(1):3720. doi: 10.1038/s41467-020-17519-4.
The quantum walk formalism is a widely used and highly successful framework for modeling quantum systems, such as simulations of the Dirac equation, different dynamics in both the low and high energy regime, and for developing a wide range of quantum algorithms. Here we present the circuit-based implementation of a discrete-time quantum walk in position space on a five-qubit trapped-ion quantum processor. We encode the space of walker positions in particular multi-qubit states and program the system to operate with different quantum walk parameters, experimentally realizing a Dirac cellular automaton with tunable mass parameter. The quantum walk circuits and position state mapping scale favorably to a larger model and physical systems, allowing the implementation of any algorithm based on discrete-time quantum walks algorithm and the dynamics associated with the discretized version of the Dirac equation.
量子行走形式体系是一种广泛使用且非常成功的用于对量子系统进行建模的框架，比如用于模拟狄拉克方程、低能和高能区域的不同动力学，以及用于开发各种量子算法。在此，我们展示了在一个五量子比特囚禁离子量子处理器上基于电路实现的位置空间离散时间量子行走。我们将行走者位置空间编码到特定的多量子比特状态中，并对系统进行编程以使用不同的量子行走参数运行，通过实验实现了具有可调质量参数的狄拉克元胞自动机。量子行走电路和位置状态映射能够很好地扩展到更大的模型和物理系统，从而允许基于离散时间量子行走算法以及与狄拉克方程离散化版本相关的动力学来实现任何算法。
