Related papers: The quantum-to-classical graph homomorphism game
This paper unifies the concepts of evolutionary games and quantum strategies. First, we state the formulation and properties of classical evolutionary strategies, with focus on the destinations of evolution in 2-player 2-strategy games. We…
Quantum game theory is a multidisciplinary field which combines quantum mechanics with game theory by introducing non-classical resources such as entanglement, quantum operations and quantum measurement. By transferring two-player-two…
In the time since a merger of quantum mechanics and game theory was proposed formally in 1999, the two distinct perspectives apparent in this merger of applying quantum mechanics to game theory, referred to henceforth as the theory of…
Quantum walks on graphs are ubiquitous in quantum computing finding a myriad of applications. Likewise, random walks on graphs are a fundamental building block for a large number of algorithms with diverse applications. While the…
A theory is universal contextual if its prediction cannot be reproduced by an ontological model satisfying both preparation and measurement noncontextuality assumptions. In this report, we first generalize the logical proofs of quantum…
Non-local games are studied in quantum information because they provide a simple way for proving the difference between the classical world and the quantum world. A non-local game is a cooperative game played by 2 or more players against a…
We propose a family of non-locality unique games for 2 parties based on a square lattice on an arbitrary surface. We show that, due to structural similarities with error correction codes of Kitaev for fault tolerant quantum computation, the…
The network coloring game has been proposed in the literature of social sciences as a model for conflict-resolution circumstances. The players of the game are the vertices of a graph with $n$ vertices and maximum degree $\Delta$. The game…
The game in which acts of participants don't have an adequate description in terms of Boolean logic and classical theory of probabilities is considered. The model of the game interaction is constructed on the basis of a non-distributive…
Nonlocal games yield an unusual perspective on entangled quantum states. The defining property of such games is that a set of players in joint possession of an entangled state can win the game with higher probability than is allowed by…
The last two decades have witnessed a rapid development of quantum information processing, a new paradigm which studies the power and limit of "quantum advantages" in various information processing tasks. Problems such as when quantum…
We investigate a variation of the graph coloring game, as studied in [2]. In the original coloring game, two players, Alice and Bob, alternate coloring vertices on a graph with legal colors from a fixed color set, where a color {\alpha} is…
Variational quantum algorithms (VQAs) offer a promising near-term approach to finding optimal quantum strategies for playing non-local games. These games test quantum correlations beyond classical limits and enable entanglement…
A quantum algorithm for an oracle problem can be understood as a quantum strategy for a player in a two-player zero-sum game in which the other player is constrained to play classically. I formalize this correspondence and give examples of…
Many computational problems are unchanged under some symmetry operation. In classical machine learning, this can be reflected with the layer structure of the neural network. In quantum machine learning, the ansatz can be tuned to correspond…
The eternal graph colouring problem, recently introduced by Klostermeyer and Mendoza, is a version of the graph colouring game, where two players take turns properly colouring a graph. In this note, we study the eternal game chromatic…
We construct a quantum searching model of a signed edge driven by a quantum walk. The time evolution operator of this quantum walk provides a weighted adjacency matrix induced by the assignment of sign to each edge. This sign can be…
We consider game theory from the perspective of quantum algorithms. Strategies in classical game theory are either pure (deterministic) or mixed (probabilistic). We introduce these basic ideas in the context of a simple example, closely…
We extend the concept of a classical two-person static game to the quantum domain, by giving an Hilbert structure to the space of classical strategies and studying the Battle of the Sexes game. We show that the introduction of entangled…
The "noncommutative graphs" which arise in quantum error correction are a special case of the quantum relations introduced in [N. Weaver, Quantum relations, Mem. Amer. Math. Soc. 215 (2012), v-vi, 81-140]. We use this perspective to…