General Quantum Interference Principle and Duality Computer

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.     

Duality Computing in Quantum Computers

In this letter, we propose a duality computing mode, which resembles particle-wave duality property when a quantum system such as a quantum computer passes through a double-slit. In this mode, computing operations are not necessarily unitary. The duality mode provides a natural link between classical computing and quantum computing. In addition, the duality mode provides a new tool for quantum algorithm design.     

广义量子干涉原理及对偶量子计算机

我们综述最近提出的广义量子干涉原理及其在量子计算中的应用。广义量子干涉原理是对狄拉克单光子干涉原理的具体化和多光子推广,不但对像原子这样的紧致的量子力学体系适用,而且适用于几个独立的光子这样的松散量子体系。利用广义量子干涉原理,许多引起争议的问题都可以得到合理的解释,例如两个以上的单光子的干涉等问题。从广义量子干涉原理来看双光子或者多光子的干涉就是双光子和双光子自身的干涉,多光子和多光子自身的干涉。广义量子干涉原理可以利用多组分量子力学体系的广义Feynman积分表示,可以定量地计算。基于这个原理我们提出了一种新的计算机,波粒二象计算机,又称为对偶计算机。在原理上对偶计算机超越了经典的计算机和现有的量子计算机。在对偶计算机中,计算机的波函数被分成若干个子波并使其通过不同的路径,在这些路径上进行不同的量子计算门操作,而后这些子波重新合并产生干涉从而给出计算结果。除了量子计算机具有的量子平行性外,对偶计算机还具有对偶平行性。形象地说,对偶计算机是一台通过多狭缝的运动着的量子计算机,在不同的狭缝进行不同的量子操作,实现对偶平行性。目前已经建立起严格的对偶量子计算机的数学理论,为今后的进一步发展打下了基础。本文着重从物理的角度去综述广义量子干涉原理和对偶计算机。现在的研究已经证明,一台d狭缝的n比特的对偶计算机等同与一个n比特+一个d比特(qudit)的普通量子计算机,证明了对偶计算机具有比量子计算机更强大的能力。这样,我们可以使用一台具有n+log2d个比特的普通量子计算机去模拟一个d狭缝的n比特对偶计算机,省去了研制运动量子计算机的巨大的技术上的障碍。我们把这种量子计算机的运行模式称为对偶计算模式,或简称为对偶模式。利用这一联系反过来可以帮助我们理解广义量子干涉原理,因为在量子计算机中一切计算都是普通的量子力学所允许的量子操作,因此广义量子干涉原理就是普通的量子力学体系所允许的原理,而这个原理只是是在多体量子力学体系中才会表现出来。对偶计算机是一种新式的计算机,里面有许多问题期待研究和发展,同时也充满了机会。在对偶计算机中,除了幺正操作外,还可以允许非幺正操作,几乎包括我们可以想到的任何操作,我们称之为对偶门操作或者广义量子门操作。目前这已经引起了数学家的注意,并给出了广义量子门操作的一些数学性质。此外,利用量子计算机和对偶计算机的联系,可以将许多经典计算机的算法移植到量子计算机中,经过改造成为量子算法。由于对偶计算机中的演化是非幺正的,对偶量子计算机将可能在开放量子力学的体系的研究中起到重要的作用。     

Duality Computing in Quantum Computers

In this letter, we propose a duality computing mode, which resembles particle-wave duality property when a quantum system such as a quantum computer passes through a double-slit. In this mode, computing operations are not necessarily unitary. The duality mode provides a natural link between classical computing and quantum computing. In addition, the duality mode provides a new tool for quantum algorithm design.     

Quantum entanglement in the NMR implementation of the Deutsch-Jozsa algorithm

A scheme to execute an n-bit Deutsch-Jozsa (DJ) algorithm using n qubits has been implemented for up to three qubits on an NMR quantum computer. For the one- and the two-bit Deutsch problem, the qubits do not get entangled, and the NMR implementation is achieved without using spin-spin interactions. It is for the three-bit case, that the manipulation of entangled states becomes essential. The interactions through scalar J-couplings in NMR spin systems have been exploited to implement entangling transformations required for the three bit DJ algorithm.     

Allowable Generalized Quantum Gates

In this paper, we give the most general duality gates, or generalized quantum gates in duality quantum computers. Here we show by explicit construction that a n-bit duality quantum computer with d slits can be simulated perfectly with an ordinary quantum computer with n qubits and one auxiliary qudit. Using this model, we give the most general form of duality gates which is of the form ∑i=0^d-1piUi,and the pi ＇s are complex numbers with module less or equal to 1 and constrained by｜∑iPi｜≤1.     

Mathematical Theory of Generalized Duality Quantum Computers Acting on Vector-States

Following the idea of duality quantum computation, a generalized duality quantum computer (GDQC) acting on vector-states is defined as a tuple consisting of a generalized quantum wave divider (GQWD) and a finite number of unitary operators as well as a generalized quantum wave combiner (GQWC). It is proved that the GQWD and GQWC of a GDQC are an isometry and a co-isometry, respectively, and mutually dual. It is also proved that every GDQC gives a contraction, called a generalized duality quantum gate (GDQG). A classification of GDQCs is given and the properties of GDQGs are discussed. Some applications are obtained, including two orthogonal duality quantum computer algorithms for unsorted database search and an understanding of the Mach-Zehnder interferometer.     

Punctured Haag Duality in Locally Covariant Quantum Field Theories

We investigate a new property of nets of local algebras over 4-dimensional globally hyperbolic spacetimes, called punctured Haag duality. This property consists in the usual Haag duality for the restriction of the net to the causal complement of a point p of the spacetime. Punctured Haag duality implies Haag duality and local definiteness. Our main result is that, if we deal with a locally covariant quantum field theory in the sense of Brunetti, Fredenhagen and Verch, then also the converse holds. The free Klein-Gordon field provides an example in which this property is verified.     

Duality Quantum Computers and Quantum Operations

We present a mathematical theory for a new type of quantum computer called a duality quantum computer that is similar to one that has recently been proposed. We discuss the nonunitarity of certain circuits of a duality quantum computer. We then discuss the relevance of this work to quantum operations and their convexity theory. This discussion is based upon isomorphism theorems for completely positive maps.     

Quantum wave processing

In recent years, the concept of quantum computing has arisen as a methodology by which very rapid computations can be achieved. In general, the ‘speed’ of these computations is compared to that of (classical) digital computers, which use sequential algorithms. However, in most quantum computing approaches, the qubits themselves are treated as analog objects. One then needs to ask whether this computational speed-up of the computation is a result of the quantum mechanics, or whether it is due to the nature of the analog structures that are being ‘generated’ for quantum computation? In this paper, we will make two points: (1) quantum computation utilizes analog, parallel computation which often offers no speed advantage over classical computers which are implemented using analog, parallel computation; (2) once this is realized, then there is little advantage in projecting the quantum computation onto the pseudo-binary construct of a qubit. Rather, it becomes more effective to seek the equivalent wave processing that is inherent in the analog, parallel processing. We will examine some wave processing systems which may be useful for quantum computation.     

Quantum computing by optical control of electron spins

We review the progress and main challenges in implementing large-scale quantum computing by optical control of electron spins in quantum dots (QDs). Relevant systems include self-assembled QDs of III–V or II–VI compound semiconductors (such as InGaAs and CdSe), monolayer fluctuation QDs in compound semiconductor quantum wells, and impurity centres in solids, such as P-donors in silicon and nitrogen-vacancy centres in diamond. The decoherence of the electron spin qubits is discussed and various schemes for countering the decoherence problem are reviewed. We put forward designs of local nodes consisting of a few qubits which can be individually addressed and controlled. Remotely separated local nodes are connected by photonic structures (microcavities and waveguides) to form a large-scale distributed quantum system or a quantum network. The operation of the quantum network consists of optical control of a single electron spin, coupling of two spins in a local nodes, optically controlled quantum interfacing between stationary spin qubits in QDs and flying photon qubits in waveguides, rapid initialization of spin qubits and qubit-specific single-shot non-demolition quantum measurement. The rapid qubit initialization may be realized by selectively enhancing certain entropy dumping channels via phonon or photon baths. The single-shot quantum measurement may be in situ implemented through the integrated photonic network. The relevance of quantum non-demolition measurement to large-scale quantum computation is discussed. To illustrate the feasibility and demand, the resources are estimated for the benchmark problem of factorizing 15 with Shor's algorithm.     

Efficient Quantum Algorithms for Simulating Sparse Hamiltonians

We present an efficient quantum algorithm for simulating the evolution of a quantum state for a sparse Hamiltonian H over a given time t in terms of a procedure for computing the matrix entries of H. In particular, when H acts on n qubits, has at most a constant number of nonzero entries in each row/column, and ||H|| is bounded by a constant, we may select any positive integer k such that the simulation requires O((log^* n)t ^1+1/2k ) accesses to matrix entries of H. We also show that the temporal scaling cannot be significantly improved beyond this, because sublinear time scaling is not possible.     

Quantum States as Virtual Singletons: Converting Duality into Symmetry

In a predicative framework from basic logic, defined for a model of quantum parallelism by sequents, we characterize a class of first order domains, called virtual singletons, which allows a generalization of the notion of duality, termed symmetry. Although consistent with the classical notion of duality, symmetry creates an environment where negation has fixed points, for which the direction of logical consequence is irrelevant. Symmetry can model Bell states. So, despite not having sense in a traditional logical setting, symmetry can hide the peculiar advantage of quantum mechanics for the treatment of information.     

Quantum Chains of Hopf Algebras with Quantum Double Cosymmetry

Given a finite dimensional C ^*-Hopf algebra H and its dual Ĥ we construct the infinite crossed product and study its superselection sectors in the framework of algebraic quantum field theory. is the observable algebra of a generalized quantum spin chain with H-order and Ĥ-disorder symmetries, where by a duality transformation the role of order and disorder may also appear interchanged. If is a group algebra then becomes an ordinary G-spin model. We classify all DHR-sectors of – relative to some Haag dual vacuum representation – and prove that their symmetry is described by the Drinfeld double . To achieve this we construct localized coactions and use a certain compressibility property to prove that they are universal amplimorphisms on . In this way the double can be recovered from the observable algebra as a universal cosymmetry. Received: 4 September 1995\,/\,Accepted: 3 December 1996     

Use of small-scale quantum computers in cryptography with many-qubit entangled states

We propose a new cryptographic protocol. It is suggested to encode information in ordinary binary form into many-qubit entangled states with the help of a quantum computer. A state of qubits (realized, e.g., with photons) is transmitted through a quantum channel to the addressee, who applies a quantum computer tuned to realize the inverse unitary-transformation decoding of the message. Different ways of eavesdropping are considered, and an estimate of the time needed for determining the secret unitary transformation is given. It is shown that using even small quantum computers can serve as a basis for very efficient cryptographic protocols. For a suggested cryptographic protocol, the time scale on which communication can be considered secure is exponential in the number of qubits in the entangled states and in the number of gates used to construct the quantum network.     

基于超导量子比特网络的Grover搜索算法实现方案

首先,提出了一个改进超导电路结构,此结构能实现任意两个量子比特的相互作用而非近邻作用,长程作用是实现量子计算所必需的,此结构能用目前的技术制作。其次,基于此结构提出了Grover搜索算法实现的物理方案。由于能实现任意两量子比特之间的控制相位门,所以多比特Grover搜索算法也能实现,以满足各种量子计算的需要。此方案是一个基于电流控制的超导电荷比特网络结构的可扩展及易实现的Grover搜索算法实现方案。     

Quantum Cyclic Controlled Teleportation of Unknown States with Arbitrary Number of Qubits by Using Seven-qubit Entangled Channel

A novel theoretical scheme is proposed to implement quantum cyclic controlled teleportation (QCYCT) of three unknown states by utilizing a seven-qubit entangled state as the quantum channel, where Alice can transmit an unknown m-qubit state to Bob, Bob can transmit an unknown n-qubit state to Candy and Candy can transmit an unknown t-qubit state to Alice under the control of the supervisor David. Only controlled-not (CNOT) operations, Bell-state measurements, a single-qubit measurement and appropriate unitary operations are needed in this scheme, which can be realized in experiment easily. The desired state of each communicator can be recovered deterministically by using auxiliary particles. The direction of the cyclic controlled teleportation can also be altered throughout changing the selection of the particle pairs to be measured of each communicator. Compared with the previous QCYCT schemes, the proposed scheme possesses higher intrinsic efficiency in most cases and can transfer as many qubits as the communicators desire.

     

Prime Factorization in the Duality Computer

We give algorithms to factorize large integers in the duality computer.We provide three duality algorithms for factorization based on a naive factorization method,the Shor algorithm in quantum computing,and the Fermat's method in classical computing.All these algorithms may be polynomial in the input size.     

基于超导量子比特网络的Grover搜索算法实现方案(英文)

提出一个改进超导电路结构,此结构能实现量子计算所必需的任意两量子比特之间的长程作用,此结构能用目前技术制作.其次,基于此结构提出Grover搜索算法实现的物理方案.由于能实现任意两量子比特之间的控制相位门,所以多比特Grover搜索算法也能实现,从而满足各种量子计算的需要.此方案是一个基于电流控制的超导电荷比特网络结构的Grover搜索算法实现方案.     

Quantum Multi-valued Byzantine Agreement Based on d-dimensional Entangled States

Byzantine agreement has always been an important research topic of distributed computing and has been widely applied to blockchain technology in recent years. We propose a quantum protocol for solving multi-valued detectable Byzantine agreement problem in this paper. Each general is firstly distributed a list that no one else knows based on d-dimensional entangled states. Then the n generals can reach an agreement in which t (where t < n/3) of them are disloyal by using these lists. Finally, it is proved that the list distribution process is secure, and the proposed protocol satisfies the definition of the multi-valued detectable Byzantine agreement.