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

• Published in: Nature communications 2020-07, Vol.11 (1), p.3720-3720, Article 3720
• Main Authors: Huerta Alderete, C., Singh, Shivani, Nguyen, Nhung H., Zhu, Daiwei, Balu, Radhakrishnan, Monroe, Christopher, Chandrashekar, C. M., Linke, Norbert M.
• Format: Article
• Language: English
• Subjects: 639/766; 639/766/483/3926; Algorithms; Bias; Cellular automata; Circuits; Computer simulation; Computers; Dirac equation; Hilbert space; Humanities and Social Sciences; Mapping; Mathematical models; Microprocessors; multidisciplinary; Parameters; Quantum computers; Quantum computing; Qubits (quantum computing); Science; Science (multidisciplinary)
• ISSN: 2041-1723; 2041-1723
• 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. Implementations of quantum walks on ion trap quantum computers have been so far limited to the analogue simulation approach. Here, the authors implement a quantum-circuit-based discrete quantum walk in one-dimensional position space, realizing a Dirac cellular automaton with tunable mass parameter.