Quantum Nash Equilibria and Quantum Computing

Abstract

In this paper we review our earlier work on quantum computing and the Nash Equilibrium, in particular, tracing the history of the discovery of new Nash Equilibria and then reviewing the ways in which quantum computing may be expected to generate new classes of Nash equilibria. We then extend this work through a substantive analysis of examples provided by Meyer, Flitney, Iqbal and Weigert and Cheon and Tsutsui with respect to quantized games, quantum game strategies and the extension of Nash Equilibrium to solvable games in Hilbert space. Finally, we review earlier work by Sato, Taiji and Ikegami on non-linear computation and computational classes by way of reference to coherence, decoherence and quantum computating systems.Comment: 18 Pages, 6th International Conference on Complex Systems. Available from http://necsi.org/events/iccs6/papers/12dc335ba096f7ee3cf094c55489.pd

Quantum generative adversarial networks

“…Training GANs is equivalent to finding the Nash equilibrium of a two-player game. This problem is known to be in the complexity class PPAD which is not expected to be contained in BQP [45,46]. Advanced heuristics have been developed to improve the training of classical GANs [5].…”