TY - JOUR T1 - Quantum walks and Dirac cellular automata on a programmable trapped-ion quantum computer Y1 - 2020 A1 - C. Huerta Alderete A1 - Shivani Singh A1 - Nhung H. Nguyen A1 - Daiwei Zhu A1 - Radhakrishnan Balu A1 - Christopher Monroe A1 - C. M. Chandrashekar A1 - Norbert M. Linke AB -

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.

UR - https://arxiv.org/abs/2002.02537 ER -