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arXiv · 2002.02537

Quantum walks and Dirac cellular automata on a programmable trapped-ion quantum computer

C. Huerta Alderete·Shivani Singh·Nhung H. Nguyen·Daiwei Zhu·Radhakrishnan Balu·Christopher Monroe·C. M. Chandrashekar·Norbert M. Linke
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Abstract

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.

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C. Huerta Alderete, Shivani Singh, Nhung H. Nguyen, Daiwei Zhu, Radhakrishnan Balu, Christopher Monroe, C. M. Chandrashekar, Norbert M. Linke. 2020-02-06. Quantum walks and Dirac cellular automata on a programmable trapped-ion quantum computer. https://doi.org/10.1038/s41467-020-17519-4

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