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 and Norbert M. Linke
Additional contact information
C. Huerta Alderete: Department of Physics, University of Maryland
Shivani Singh: C. I. T. Campus
Nhung H. Nguyen: Department of Physics, University of Maryland
Daiwei Zhu: Department of Physics, University of Maryland
Radhakrishnan Balu: Computational and Information Sciences Directorate
Christopher Monroe: Department of Physics, University of Maryland
C. M. Chandrashekar: C. I. T. Campus
Norbert M. Linke: Department of Physics, University of Maryland

Nature Communications, 2020, vol. 11, issue 1, 1-7

Abstract: 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.

Date: 2020
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DOI: 10.1038/s41467-020-17519-4

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