TY - JOUR T1 - Quantum walks and Dirac cellular automata on a programmable trapped-ion quantum computer Y1 - 2020 A1 - C. Huerta Alderete A1 - Shivani Singh A1 - Nhung H. Nguyen A1 - Daiwei Zhu A1 - Radhakrishnan Balu A1 - Christopher Monroe A1 - C. M. Chandrashekar A1 - Norbert M. Linke AB -

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.

UR - https://arxiv.org/abs/2002.02537 ER - TY - JOUR T1 - Universal one-dimensional discrete-time quantum walks and their implementation on near term quantum hardware Y1 - 2020 A1 - Shivani Singh A1 - Cinthia H. Alderete A1 - Radhakrishnan Balu A1 - Christopher Monroe A1 - Norbert M. Linke A1 - C. M. Chandrashekar AB -

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.

UR - https://arxiv.org/abs/2001.11197 ER - TY - JOUR T1 - Demonstration of Bayesian quantum game on an ion trap quantum computer Y1 - 2018 A1 - Neal Solmeyer A1 - Norbert M. Linke A1 - Caroline Figgatt A1 - Kevin A. Landsman A1 - Radhakrishnan Balu A1 - George Siopsis A1 - Christopher Monroe AB -

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.

UR - https://arxiv.org/abs/1802.08116 ER -