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arXiv:cs/0507003 · International Journal of Theoretical Physics

The Role of Quantum Interference in Quantum Computing

Anwar Y. Shiekh

Published Aug 5, 2006• 16 citations
arXivHTMLPDF
DOI
10.1007/s10773-005-9025-8

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THE GENERAL QUANTUM INTERFERENCE PRINCIPLE AND THE DUALITY QUANTUM COMPUTER

Yang Liu

Here we review the general quantum interference principle and the duality quantum computer which was proposed recently.The general quantum interference principle is the concretization of Dirac's statement about single photon interference and the generalization into multi-photon quantum systems.It applies not only to compact quantum system such as an atom,but also to loose quantum system such as a few independent photons.Using the general quantum interference principle,many debated issues can be explained,for instance the interference in a quantum system of two independent photons.From the view point of general quantum interference principle,two photon or multi-photon interferences,are just the interference of the two photon system with the two photon system itself,the interference of multi-photon system with itself.The general quantum interference principle can be expressed in terms of a general Feynman path-integral of a multi-constituents system and be calculated quantitatively.Based on this principle,we proposed a new type of computer,the duality computer or duality quantum computer.In principle,the duality computer is superior to classical computer and the quantum computer in the sense that it can do more than them.In a duality computer,the wave function of the computer is split into many parts,and each part is processed independently through a series of quantum gates,and then the different parts are recombined to get the final results.In addition to quantum parallelism,there is also duality parallelism in which different gate operations can be performed on different parts of the wave function simultaneously in a duality computer.The mathematical theory of duality computer has been established,and this has paved the way for further research.Studies have shown that a n bits duality computer with d-slits can be simulated by a quantum computer with n+log2d qubits.This relationship makes duality computing in an ordinary quantum computer possible,and also spares the seemingly insurmountable obstacle of building a moving quantum computer which a duality computer at all is.The duality computing in an ordinary quantum computer is called duality computing mode of a quantum computer.This relationship also helps us in understanding the general quantum interference principle.Because the underlying physics of an ordinary quantum computer is just quantum mechanics,the general quantum interference principle is also compatible with the usual quantum mechanics.However this principle exhibits itself only in a multipartite quantum system,thus it is difficult to understand it in simple single particle quantum systems.Duality computer is a new type of computer,and there are many unresolved issues and opportunity as well.In a duality computer,the gate operations need not be unitary and could be any operation that we may think of.The type of gates allowed in duality computing is called duality gate or generalized quantum gate.Generalized quantum gates have attracted the attention of mathematicians and some mathematical results have been obtained on the properties of the generalized quantum gates.Besides the mathematical properties of duality computing,duality computing may offer a bridge between quantum computing and classical computing so that classical algorithms may be transformed into quantum algorithms.Because the nonunitarity of generalized quantum gates,it may play important role in the study of open quantum systems.

Progress in physics•Jan 1, 2008•0 citations
In 1981 Richard Feynman proposed the idea that a computer built of quantum mechanical elements obeying quantum mechanical laws can perform efficient simulations of quantum systems. Quantum computing works on the laws of quantum mechanical properties such as superposition, entanglement, and interference. Unlike in classical computing, in quantum computers a register can exist in all possible states at once due to its superposition properties. It is only when a quantum system is measured that we observe one of the possible states. Such a system is advantageous since, when measured, each state can appear with a certain probability encoded in the state prior to the measurement. Quantum computing works by increasing the probability of the desired state to a sufficiently high value so that the desired state can be obtained with high confidence with a minimal number of measurements. In this regard, quantum interference, which results from quantum superposition, plays a big role since it allows probability amplitudes corresponding to a given state to interfere and cancel each other. This property of quantum interference biases the measurement to a set of states that we desire as the outcome of quantum algorithms. Similarly, quantum entanglement allows one to create a strong correlation between quantum objects, especially qubits, to the advantage of quantum algorithms, as you will see throughout this chapter.
Quantum interference effects play a fundamental role in social decision-making, offering a novel perspective beyond classical decision theories. This study explores the theoretical foundations of quantum decision-making, emphasizing the role of quantum probability in explaining cognitive biases, preference reversals, and decision anomalies. The research presents a quantum probability-based decision model and contrasts it with classical probability models. Through theoretical modeling and experimental design, we demonstrate how quantum interference alters decision probabilities and impacts group decision dynamics. The study further examines the applications of quantum decision theory in game theory, policy-making, financial markets, and artificial intelligence. Our findings suggest that quantum probability provides a more comprehensive and realistic framework for understanding human decision-making processes. Future research should focus on empirical validation, interdisciplinary integration, and the application of quantum computing to social decision modeling.
Here we review the general quantum interference principle and the duality quantum computer which was proposed recently.The general quantum interference principle is the concretization of Dirac's statement about single photon interference and the generalization into multi-photon quantum systems.It applies not only to compact quantum system such as an atom,but also to loose quantum system such as a few independent photons.Using the general quantum interference principle,many debated issues can be explained,for instance the interference in a quantum system of two independent photons.From the view point of general quantum interference principle,two photon or multi-photon interferences,are just the interference of the two photon system with the two photon system itself,the interference of multi-photon system with itself.The general quantum interference principle can be expressed in terms of a general Feynman path-integral of a multi-constituents system and be calculated quantitatively.Based on this principle,we proposed a new type of computer,the duality computer or duality quantum computer.In principle,the duality computer is superior to classical computer and the quantum computer in the sense that it can do more than them.In a duality computer,the wave function of the computer is split into many parts,and each part is processed independently through a series of quantum gates,and then the different parts are recombined to get the final results.In addition to quantum parallelism,there is also duality parallelism in which different gate operations can be performed on different parts of the wave function simultaneously in a duality computer.The mathematical theory of duality computer has been established,and this has paved the way for further research.Studies have shown that a n bits duality computer with d-slits can be simulated by a quantum computer with n+log2d qubits.This relationship makes duality computing in an ordinary quantum computer possible,and also spares the seemingly insurmountable obstacle of building a moving quantum computer which a duality computer at all is.The duality computing in an ordinary quantum computer is called duality computing mode of a quantum computer.This relationship also helps us in understanding the general quantum interference principle.Because the underlying physics of an ordinary quantum computer is just quantum mechanics,the general quantum interference principle is also compatible with the usual quantum mechanics.However this principle exhibits itself only in a multipartite quantum system,thus it is difficult to understand it in simple single particle quantum systems.Duality computer is a new type of computer,and there are many unresolved issues and opportunity as well.In a duality computer,the gate operations need not be unitary and could be any operation that we may think of.The type of gates allowed in duality computing is called duality gate or generalized quantum gate.Generalized quantum gates have attracted the attention of mathematicians and some mathematical results have been obtained on the properties of the generalized quantum gates.Besides the mathematical properties of duality computing,duality computing may offer a bridge between quantum computing and classical computing so that classical algorithms may be transformed into quantum algorithms.Because the nonunitarity of generalized quantum gates,it may play important role in the study of open quantum systems.