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Dirasat: Engineering Sciences

Game-Theoretic Reversibility and m-Valued Quantum Computation

Anas N. Rabadi

Published Sep 14, 2010• 0 citations
OpenAlex

Abstract

This paper introduces the new concept of Reversible Game Theory (RGT) and its Multiple-Valued Quantum Computation (MVQC). Game Theory (GT) involves the study of competition and cooperation, without regard to the particular entities (agents) involved, and issues of rationality associated with such phenomena. Reversibility property in GT can be important in situations where: (1) an outside observer needs to know reversely the paths that lead to specific payoffs on a game’s extensive form, and (2) modeling the (maximin) dynamics using low-power consuming circuits as reversibility is a main requirement for low-power circuit design of future technologies such as in Quantum Computing (QC). Quantum Decision Trees (QDTs) are also presented as a quantum representation for applying MVQC to games’ dynamics.

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This paper introduces the new concept of Reversible Game Theory (RGT) and its Multiple-Valued Quantum Computation (MVQC). Game Theory (GT) involves the study of competition and cooperation, without regard to the particular entities (agents) involved, and issues of rationality associated with such phenomena. Reversibility property in GT can be important in situations where: (1) an outside observer needs to know reversely the paths that lead to specific payoffs on a game’s extensive form, and (2) modeling the (maximin) dynamics using low-power consuming circuits as reversibility is a main requirement for low-power circuit design of future technologies such as in Quantum Computing (QC). Quantum Decision Trees (QDTs) are also presented as a quantum representation for applying MVQC to games’ dynamics.
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.
This paper introduces the m-valued Swap-based quantum computations (QC) of ECA. The fundamental m-valued quantum representations of: (1) m-valued orthonormal computational basis states quantum decision trees (QDTs) and (2) m-valued orthonormal composite basis states QDTs are also introduced as quantum modeling for the representations and operations of the QECA dynamics. The new m-valued quantum representations and their associated operations can play an important role in the automated design of future QECA circuits that consume minimal power in the quantum domain.
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
Research on reversible circuits has gained significance due to its application in quantum computations and many further areas such as the design of encoders. At the same time, the use of multiple-valued logic gained importance since this reduces the number of required entities in physical systems (e.g. in a future quantum computer). While most research is still conducted in the Boolean domain, there exist only few approaches which realize reversible circuits for multiple-valued logic. Moreover, most of the previously proposed solutions for synthesis of multiple-valued reversible circuits are not scalable and consider ternary (i.e. 3-valued circuits) only. Instead of overcoming these issues by developing new synthesis approaches for multiple-valued reversible circuits from scratch, we propose to utilize the recent accomplishments in the design of Boolean reversible circuits and to generalize them for multiple-valued logic. To this end, we discuss how to generalize Quantum Multiple-valued Decision Diagram based (QMDD-based) synthesis - a synthesis approach for Boolean reversible circuits which has been proven to be scalable and which has been used in several recently developed design flows. The discussions eventually show how to bridge the development gap between Boolean and multiple-valued logic for reversible circuits.
Many-valued quantum circuit synthesis of many-valued reversible expansions and fast transforms is introduced in this paper. Since the reduction of power consumption is a major requirement for the circuit design in future technologies, such as in quantum computing, the main features of several future technologies will include reversibility. Consequently, the new quantum circuits can play an important task in the design of future circuits that consume minimal power. In addition, the new quantum circuit methodology is general and can be used to realize any multiple-valued function in the quantum space. It is also shown that the structural generality advantage that results from the new design methodology is opposed with the increased quantum structural complexity disadvantage which may be considered in any further cost-benefit design analysis.