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/2002.0253701306nas 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 a

Quantum 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/2001.1119701552nas a2200169 4500008004100000245007500041210006900116520100400185100001901189700002301208700002201231700002401253700002401277700002001301700002401321856003701345 2018 eng d00aDemonstration of Bayesian quantum game on an ion trap quantum computer0 aDemonstration of Bayesian quantum game on an ion trap quantum co3 a

We demonstrate a Bayesian quantum game on an ion trap quantum computer with five qubits. The players share an entangled pair of qubits and perform rotations on their qubit as the strategy choice. Two five-qubit circuits are sufficient to run all 16 possible strategy choice sets in a game with four possible strategies. The data are then parsed into player types randomly in order to combine them classically into a Bayesian framework. We exhaustively compute the possible strategies of the game so that the experimental data can be used to solve for the Nash equilibria of the game directly. Then we compare the payoff at the Nash equilibria and location of phase-change-like transitions obtained from the experimental data to the theory, and study how it changes as a function of the amount of entanglement.

1 aSolmeyer, Neal1 aLinke, Norbert, M.1 aFiggatt, Caroline1 aLandsman, Kevin, A.1 aBalu, Radhakrishnan1 aSiopsis, George1 aMonroe, Christopher uhttps://arxiv.org/abs/1802.08116