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.

1 aAlderete, Huerta1 aSingh, Shivani1 aNguyen, Nhung, H.1 aZhu, Daiwei1 aBalu, Radhakrishnan1 aMonroe, Christopher1 aChandrashekar, C., M.1 aLinke, Norbert, M. uhttps://arxiv.org/abs/2002.0253701306nas a2200169 4500008004100000245011300041210006900154260001400223520072000237100001900957700002600976700002401002700002401026700002301050700002601073856003701099 2020 eng d00aUniversal one-dimensional discrete-time quantum walks and their implementation on near term quantum hardware0 aUniversal onedimensional discretetime quantum walks and their im c1/30/20203 aQuantum walks are a promising framework for developing quantum algorithms and quantum simulations. Quantum walks represent an important test case for the application of quantum computers. Here we present different forms of discrete-time quantum walks and show their equivalence for physical realizations. Using an appropriate digital mapping of the position space on which a walker evolves onto the multi-qubit states in a quantum processor, we present different configurations of quantum circuits for the implementation of discrete-time quantum walks in one-dimensional position space. With example circuits for a five qubit machine we address scalability to higher dimensions and larger quantum processors.

1 aSingh, Shivani1 aAlderete, Cinthia, H.1 aBalu, Radhakrishnan1 aMonroe, Christopher1 aLinke, Norbert, M.1 aChandrashekar, C., M. uhttps://arxiv.org/abs/2001.11197