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arXiv:quant-ph/0504010

Quantum Games and Programmable Quantum Systems

Edward W. Piotrowski, Jan Sładkowski

Published Apr 2, 2005• 3 citations
arXivHTMLPDF

Abstract

Attention to the very physical aspects of information characterizes the current research in quantum computation, quantum cryptography and quantum communication. In most of the cases quantum description of the system provides advantages over the classical approach. Game theory, the study of decision making in conflict situation has already been extended to the quantum domain. We would like to review the latest development in quantum game theory that is relevant to information processing. We will begin by illustrating the general idea of a quantum game and methods of gaining an advantage over "classical opponent". Then we review the most important game theoretical aspects of quantum information processing. On grounds of the discussed material, we reason about possible future development of quantum game theory and its impact on information processing and the emerging information society. The idea of quantum artificial intelligence is explained.

DOI
10.48550/arxiv.quant-ph/0504010

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Attention to the very physical aspects of information characterizes the current research in quantum computation, quantum cryptography and quantum communication. In most of the cases quantum description of the system provides advantages over the classical approach. Game theory, the study of decision making in conflict situation has already been extended to the quantum domain. We would like to review the latest development in quantum game theory that is relevant to information processing. We will begin by illustrating the general idea of a quantum game and methods of gaining an advantage over "classical opponent". Then we review the most important game theoretical aspects of quantum information processing. On grounds of the discussed material, we reason about possible future development of quantum game theory and its impact on information processing and the emerging information society. The idea of quantum artificial intelligence is explained.
The theoretical, experimental and technological areas covering the use of quantum mechanics for communication and computation.Quantum information processing includes investigations in quantum information theory, quantum communication, quantum computation, quantum algorithms and their complexity, and quantum control.The science of quantum information processing is a highly interdisciplinary field.In the context of mathematics it is stimulating research in pure mathematics (e.g.coding theory, *algebras, quantum topology) as well as requiring and providing many opportunities for applied mathematics.The science of quantum information processing emerged from the recognition that usable notions of information need to be physically implementable.In the 1960s and 1970s researchers such as R. Landauer, C. Bennett, C. Helstrom and A. Holevo realized that the laws of physics give rise to fundamental constraints on the ability to implement and manipulate information.Landauer repeatedly stated that "information is physical", providing impetus to the idea that it should be possible to found theories of information on the laws of physics.This is in contrast to the introspective approach which led to the basic definitions of computer science and information theory as formulated by A. Church, A. Turing, C. Shannon and others in the first half of the 20th century.Early work in studying the physical foundations of information focused on the effects of energy limitations and the need for dissipating heat in computation and communication.Beginning with S. Wiesner's work on applications of quantum mechanics to cryptography in the late 1960s, it was realized that there may be intrinsic advantages to using quantum physics in information processing.Quantum cryptography and quantum communication in general were soon established as interesting and non-trivial extensions of classical communication based on bits.That quantum mechanics may be used to improve the efficiency of algorithms was first realized when attempts at simulating quantum mechanical systems resulted in exponentially complex algorithms compared to the physical resources associated with the system simulated.In the 1980s, P. Benioff and R. Feynman introduced the idea of a quantum computer for efficiently implementing quantum physics simulations.Models of quantum computers were developed by D. Deutsch, leading to the formulation of artificial problems that could be solved more efficiently by quantum than by classical computers.The advantages of quantum computers became widely recognized when P.
Game theory is a well established field with applications in many areas including the social sciences, biology, and computer science [6]. Recently, however, researchers in quantum computation have begun to study the implications of games set in the quantum domain (i.e. game theoretical situations where either one or more players have quantum computational power or where the implementation of strategies uses some form of quantum information). Such a setting allows for entanglement and superpositions of strategies and evaluation of payoffs using quantum measurement. This approach to game theory, according to some scholars in the field, could help us understand certain physical systems, improve economic markets, and develop quantum algorithms. I have conducted an investigation into quantum game theory. I have constructed simulation tools using Maple that, along with research into related work, have helped gain some insight into this new field. The important solutions in classical game theory are usually Nash equilibria. What do they look like in the quantum realm? In what
Quantum game theory (QGT) extends traditional game theory by using quantum mechanics to create new models for strategic decision-making. Traditional game theory provides effective tools for analyzing rational human interaction; yet it suffers from three main restrictions because it cannot properly handle uncertain situations, contradictory behavior, and complex relationships among agents. QGT addresses these challenges through its implementation of quantum phenomena, which enable strategic options that go beyond traditional mixed strategies. The extended system introduces fresh equilibrium solutions that allow easier resolution of standard problems. The chapter presents an organized structure to display QGT, which shows its value for strategic decision-making systems. The chapter shows fundamental concepts that link classical theories with quantum theories through its demonstration of how quantum strategies have developed from their original state to their present form, which expands traditional game models. The research investigates optimization methods, cybersecurity measures, economic systems, and artificial intelligence applications. The study identifies implementation obstacles and future research needs. The advanced QGT decision-making systems provide outstanding solutions that allow intelligent systems to interact with their environments and solve complex environmental problems.
Quantum game theory is an exciting new topic that combines the physical behaviour of information in quantum mechanical systems with game theory, the mathematical description of conflict and competition situations, to shed new light on the fields of quantum control and quantum information. This thesis presents quantizations of some classic game-theoretic problems, new results in existing quantization schemes for two player, two strategy non-zero sum games, and in quantum versions of Parrondo's games, where the \ncombination of two losing games can result in a winning game. In addition, quantum cellular automata and quantum walks are discussed, with a history-dependent quantum walk being presented.