01551nas a2200193 4500008004100000245009300041210006900134260001300203520092900216100002101145700001901166700002201185700001601207700002401223700002401247700002601271700002301297856003701320 2020 eng d00aQuantum walks and Dirac cellular automata on a programmable trapped-ion quantum computer0 aQuantum walks and Dirac cellular automata on a programmable trap c2/6/20203 a
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/2002.02537