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arXiv:quant-ph/0512120 · Communications in Theoretical Physics

General Quantum Interference Principle and Duality Computer

Long Gui-Lu

Published May 1, 2006• 264 citations
arXivHTMLPDF

Abstract

In this article, we propose a general principle of quantum interference for quantum system, and based on this we propose a new type of computing machine, the duality computer, that may outperform in principle both classical computer and the quantum computer. According to the general principle of quantum interference, the very essence of quantum interference is the interference of the sub-waves of the quantum system itself. A quantum system considered here can be any quantum system: a single microscopic particle, a composite quantum system such as an atom or a molecule, or a loose collection of a few quantum objects such as two independent photons. In the duality computer, the wave of the duality computer is split into several sub-waves and they pass through different routes, where different computing gate operations are performed. These sub-waves are then re-combined to interfere to give the computational results. The quantum computer, however, has only used the particle nature of quantum object. In a duality computer, it may be possible to find a marked item from an unsorted database using only a single query, and all NP-complete problems may have polynomial algorithms. Two proof-of-the-principle designs of the duality computer are presented: the giant molecule scheme and the nonlinear quantum optics scheme. We also propose thought experiment to check the related fundamental issues, the measurement efficiency of a partial wave function.

DOI
10.1088/0253-6102/45/5/013

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In this article, we propose a general principle of quantum interference for quantum system, and based on this we propose a new type of computing machine, the duality computer, that may outperform in principle both classical computer and the quantum computer. According to the general principle of quantum interference, the very essence of quantum interference is the interference of the sub-waves of the quantum system itself. A quantum system considered here can be any quantum system: a single microscopic particle, a composite quantum system such as an atom or a molecule, or a loose collection of a few quantum objects such as two independent photons. In the duality computer, the wave of the duality computer is split into several sub-waves and they pass through different routes, where different computing gate operations are performed. These sub-waves are then re-combined to interfere to give the computational results. The quantum computer, however, has only used the particle nature of quantum object. In a duality computer, it may be possible to find a marked item from an unsorted database using only a single query, and all NP-complete problems may have polynomial algorithms. Two proof-of-the-principle designs of the duality computer are presented: the giant molecule scheme and the nonlinear quantum optics scheme. We also propose thought experiment to check the related fundamental issues, the measurement efficiency of a partial wave function.
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.
Abstract The double-slit experiment is a classic experiment that presents the clearest manifestation of wave-particle duality, one of the fundamental principles of quantum mechanics. The double-slit experiment still remains the phenomenon that demonstrates wave-particle duality at the most fundamental level. This phenomenon quantitatively and conceptually demonstrates that microscopic objects can behave like both waves and particles at the same time. This article provides an in-depth analysis of the physical nature of dualism, the mechanism of formation of the interference pattern, and the impact of the act of observation on the dynamics of quantum systems. The need for a new perspective on this topic is due to the fact that the current uncertainty in the interpretation of quantum reality has not yet been completely eliminated, and the boundaries between classical and quantum behavior in microscopic objects are still being explored. The results presented here restructure the deep mechanisms of the interference picture, more clearly frame the relationship between observation and wavefunction collapse, and provide a quantum. Since the article attempts to provide a complete answer to the mechanism of the formation of wave-particle duality, extensive space is given to sections such as historical development, theoretical models, modern research, etc. New approaches to this phenomenon have been developed using modern research and string theory. As a result, a new mathematical expression has been proposed that explains the reasons for the initial emergence of wave-particle duality, and is also important for string theory. The article explains the measurement problem with a more effective physical structure and ontological model.
We present an architecture to investigate wave-particle duality in NNN-path interferometers on a universal quantum computer involving as low as 2log2N2{log}_{2}N2log2​N qubits and develop a measurement scheme that allows the efficient extraction of quantifiers of interference visibility and which-path information. We implement our algorithms for interferometers with up to N=16N=16N=16 paths in proof-of-principle experiments on a noisy intermediate-scale quantum (NISQ) device using down to O(log2N)O({log}_{2}N)O(log2​N) gates and despite increasing noise consistently observe a complementary behavior between interference visibility and which-path information. Our results are in accordance with our current understanding of wave-particle duality and allow its investigation for interferometers with an exponentially growing number of paths on future quantum devices beyond the NISQ era.
Quantum computing exploits quantum mechanical properties to perform computations. It enables quantum parallelism and provides much more powerful data processing capabilities than classical computers. With a quantum computer, one can exponentially accelerate quantum system simulation and accelerate some important classical algorithms. Traditional quantum algorithms use unitary evolution to process information. A quantum computing process is the product of a series of unitary operators. In 1994, Shor invented a quantum prime factorization algorithm that exponentially accelerates the factorization of an integer. In 1996, Grover proposed a quantum search algorithm that accelerates the search of an unsorted database using square-root steps. Afterwards, the development of quantum algorithms slowed down, leading to a subsequent query by Shor in 2003 regarding why no more significant quantum algorithms have been found. Since 2009, many important new quantum algorithms have been proposed, such as a quantum algorithm for solving linear equations with the capability of exponential acceleration, a quantum algorithm for sparse Hamiltonian simulation using linear combinations of unitary operators, and a novel algorithm for Hamiltonian simulation, which provides exponential improvements in precision. In this paper, we first describe the basic principles of quantum computation. We then describe the Shor algorithm and Grover/Long search algorithm. These quantum algorithms are the general quantum algorithms that use unitary operations in their computational processes. Next, we introduce the basic principles of duality quantum computing, which was proposed in 2002. In contrast to traditional quantum computing, duality quantum computing allows the use of linear combinations of unitary operators in the computation process, meaning the multiplication, division, addition, and subtraction of unitary operators are all possible in duality quantum computing. Thus, duality quantum computing provides more flexibility for constructing quantum algorithms and the techniques used in classical algorithm design can be directly used to construct quantum algorithms. We then review recent work regarding newer quantum algorithms that enable the linear combination of unitary operators, which are actually duality quantum algorithms. Additionally, a duality quantum simulation algorithm for open quantum systems is introduced. This algorithm not only reduces computational complexity, but also improves accuracy exponentially. Finally, a summary and the future prospects of quantum algorithms are provided.
Young’s double-slit experiment played a crucial role in establishing the wave nature of light. In this chapter, the shocking result that incident electrons yield a similar interference pattern as that formed by light waves is described. It is shown that the only way the experimental results could be explained is via a wave function description of electrons. It is also shown that, in the same experiment, the interference fringes disappear if the which-path information becomes available. This is the essence of wave–particle duality. The first of the Einstein–Bohr debates on wave-particle duality and Bohr’s principle of complementarity in the double-slit experiment is also discussed. Also presented are the counterintuitive notions of delayed choice and quantum eraser effects showing how the availability or erasure of information generated in the future can affect how the data in the present can be interpreted.