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Adiabatic quantum computing is implemented on specialized hardware using the heuristics of the quantum annealing algorithm. To solve a problem using quantum annealing, the problem requires formatting as a discrete quadratic function without constraints. The problem of finding Nash equilibrium in two-player, non-cooperative games is a two-fold quadratic optimization problem with constraints. This problem was formatted as a single, constrained quadratic optimization in 1964 by Mangasarian and Stone. Here, we show that adding penalty terms to the quadratic function formulation of Nash equilibrium gives a quadratic unconstrained binary optimization (QUBO) formulation of this problem that can be executed on quantum annealers. Three examples are discussed to highlight the success of the formulation, and an overall, time-to-solution (hardware + software processing) speed up by seven to ten times is reported on quantum annealers developed by D-Wave System. [ABSTRACT FROM AUTHOR]

The production and manipulation of quantum correlation protocols will play a central role where the quantum nature of the correlation can be used as a resource to yield properties unachievable within a classical framework is a very active and important area of research. In this work, we provide a description of a measure of correlation strength between quantum systems, especially for multipartite quantum systems. [ABSTRACT FROM AUTHOR]

Quadratic unconstrained binary optimization (QUBO) is the mathematical formalism for phrasing and solving a class of optimization problems that are combinatorial in nature. Due to their natural equivalence with the two-dimensional Ising model for ferromagnetism in statistical mechanics, problems from the QUBO class can be solved on quantum annealing hardware. In this paper, we report a QUBO formatting of the problem of optimal control of time-dependent traffic signals on an artificial grid-structured road network so as to ease the flow of traffic, and the use of D-Wave Systems' quantum annealer to solve it. Since current-generation D-Wave annealers have a limited number of qubits and limited inter-qubit connectivity, we adopt a hybrid (classical/quantum) approach to this problem. As traffic flow is a continuous and evolving phenomenon, we address this time-dependent problem by adopting a workflow to generate and solve multiple problem instances periodically. [ABSTRACT FROM AUTHOR]

We review both theoretical and experimental developments in the area of quantum games since the inception of the subject circa 1999. We will also offer a narrative on the controversy that surrounded the subject in its early days, and how this controversy has affected the development of the subject. [ABSTRACT FROM AUTHOR]