Quantum mechanical systems exhibit particle wave duality property. This duality property has been exploited for information processing. A duality quantum computer is a quantum computer on the move and passing through a multi‐slits. It offers quantum wave divider and quantum wave combiner operations in addition to those allowed in an ordinary quantum computer. It has been shown that all linear bounded operators can be realized in a duality quantum computer, and a duality quantum computer with n qubits and d‐slits can be realized in an ordinary quantum computer with n qubits and a qudit in the so‐called duality quantum computing mode. The quantum particle‐wave duality can be used in providing secure communication. In this paper, we will review duality quantum computing and duality quantum key distribution.
Quantum mechanical systems exhibit particle wave duality property. This duality property has been exploited for information processing. A duality quantum computer is a quantum computer on the move and passing through a multi‐slits. It offers quantum wave divider and quantum wave combiner operations in addition to those allowed in an ordinary quantum computer. It has been shown that all linear bounded operators can be realized in a duality quantum computer, and a duality quantum computer with n qubits and d‐slits can be realized in an ordinary quantum computer with n qubits and a qudit in the so‐called duality quantum computing mode. The quantum particle‐wave duality can be used in providing secure communication. In this paper, we will review duality quantum computing and duality quantum key distribution.
In this paper, we firstly briefly review the duality quantum computer. Distinctly, the generalized quantum gates, the basic evolution operators in a duality quantum computer are no longer unitary, and they can be expressed in terms of linear combinations of unitary operators. All linear bounded operators can be realized in a duality quantum computer, and unitary operators are just the extreme points of the set of generalized quantum gates. A d-slits duality quantum computer can be realized in an ordinary quantum computer with an additional qudit using the duality quantum computing mode. Duality quantum computer provides flexibility and clear physical picture in designing quantum algorithms, serving as a useful bridge between quantum and classical algorithms. In this review, we will show that duality quantum computer can simulate quantum systems more efficiently than ordinary quantum computers by providing descriptions of the recent efficient quantum simulation algorithms of Childs et al [Quantum Information & Computation, 12(11-12): 901-924 (2012)] for the fast simulation of quantum systems with a sparse Hamiltonian, and the quantum simulation algorithm by Berry et al [Phys. Rev. Lett. 114, 090502 (2015)], which provides exponential improvement in precision for simulating systems with a sparse Hamiltonian.
Quantum mechanics possesses peculiar properties that is hard to comprehend with mundane experience. Exploiting the quantum properties of quantum systems, quantum computer can provide more computing power than classical computer. Duality quantum computer, or duality computer for short, is a new type of quantum computer that exploits the particle wave duality of quantum mechanics. In a duality computer, the computing gates, or generalized quantum gates, need not be unitary. Thus duality computer provides a novel paradigm for quantum computing, and may bring new computing power. In addition, it provides flexibility in computing gates design that is familiar to computer scientists. Here we review the basic concepts of duality quantum computing and give some examples.
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.
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.
Duality quantum computing (DQC) offers the use of linear combination of unitaries (LCU), or generalized quantum gates, in designing quantum algorithms. DQC contains wave divider and wave combiner operations. The wave function of a quantum computer is split into several subwaves after the wave division operation. Then different unitary operations are performed on different subwaves in parallel. A quantum wave combiner combines the subwaves into a final wave function, so that a linear combination of the unitaries are performed on the final state. In this paper, we study of the properties of duality quantum computer with projections on subwaves. In subwave-projection DQC (SWP-DQC), we can realize the linear combinations of non-unitaries, and this not only gives further flexibility for designing quantum algorithms, but also offers additional speedup in the expected time complexity. Specifically, SWP-DQC offers an O(M) acceleration over DQC with only final-wave-projection in the mean time complexity, where M is the number of projections. As an application, we show that the ground state preparation algorithm recently proposed by Ge, Tura, and Cirac is actually an DQC algorithm, and we further optimized the algorithm using SWP-DQC, which can save up to log2N qubits compared DQC without subwave projection, where N is the dimension of the system's Hilbert Space.