Quantum Interference Computation

Anwar Y. Shiekh

Anwar Y. Shiekh

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.

XUYou-Yang

Long Gui-Lu

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.

Robert B. Griffiths