|Title||Quantum walks and Dirac cellular automata on a programmable trapped-ion quantum computer|
|Publication Type||Journal Article|
|Year of Publication||2020|
|Authors||C. Alderete, H, Singh, S, Nguyen, NH, Zhu, D, Balu, R, Monroe, C, Chandrashekar, CM, Linke, NM|
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.