Quantum Computation with Abelian Anyons

A universal quantum computer can be constructed using abelian anyons. Two qubit quantum logic gates such as controlled-NOT operations are performed using topological effects. Single-anyon operations such as hopping from site to site on a lattice suffice to perform all quantum logic operations. Anyonic quantum computation might be realized using quasiparticles of the fractional quantum Hall effect. PACS: 03.65-Lx     

Quantum Computing with Trapped Ion Hyperfine Qubits

We discuss the basic aspects of quantum information processing with trapped ions, including the principles of ion trapping, preparation and detection of hyperfine qubits, single-qubit operations and multi-qubit entanglement protocols. Recent experimental advances and future research directions are outlined. PACS: 03.67.Lx, 32.80.Pj, 32.80.Qk, 42.50.Vk     

COMPLIANCE VERIFICATION OF AGENT INTERACTION: A LOGIC-BASED SOFTWARE TOOL

In open societies of agents, where agents are autonomous and heterogeneous, it is not realistic to assume that agents will always act so as to comply with interaction protocols. Thus, the need arises for a formalism to specify constraints on agent interaction, and for a tool able to observe and check for agent compliance with interaction protocols. In this paper we present a JAVA-PROLOG software component built on logic programming technology, which can be used to verify compliance of agent interaction to protocols, and that has been integrated with the PROSOCS platform.     

Linking Classical and Quantum Key Agreement: Is There a Classical Analog to Bound Entanglement?

Abstract. After carrying out a protocol for quantum key agreement over a noisy quantum channel, the parties Alice and Bob must process the raw key in order to end up with identical keys about which the adversary has virtually no information. In principle, both classical and quantum protocols can be used for this processing. It is a natural question which type of protocol is more powerful. We show that the limits of tolerable noise are identical for classical and quantum protocols in many cases. More specifically, we prove that a quantum state between two parties is entangled if and only if the classical random variables resulting from optimal measurements provide some mutual classical information between the parties. In addition, we present evidence which strongly suggests that the potentials of classical and of quantum protocols are equal in every situation. An important consequence, in the purely classical regime, of such a correspondence would be the existence of a classical counterpart of so-called bound entanglement, namely ``bound information' that cannot be used for generating a secret key by any protocol. This stands in contrast to what was previously believed.     

Estimation of Quantum Channels with Finite Resources

We examine the problem of determining the parameters that describe a quantum channel. It is assumed that the users of the channel have at best only partial knowledge of it and make use of a finite amount of resources to estimate it. We discuss simple protocols for the estimation of the parameters of several classes of channels that are studied in the current literature. A quantitative measures of the quality of the estimation schemes can be given on the basis of the standard deviation or of the fidelity. Protocols that employ entangled particles are also discussed. The use of entangled particles as a nonclassical resource enhances the estimation quality of some classes of quantum channel. Further, the methods presented here can be extended to higher dimensional quantum systems. PACS: 03.67.Hk     

Exogenous Probabilistic Computation Tree Logic

We define a logic EpCTL for reasoning about the evolution of probabilistic systems. System states correspond to probability distributions over classical states and the system evolution is modelled by probabilistic Kripke structures that capture both stochastic and non–deterministic transitions. The proposed logic is a temporal enrichment of Exogenous Probabilistic Propositional Logic (EPPL). The model-checking problem for EpCTL is analysed and the logic is compared with PCTL; the semantics of the former is defined in terms of probability distributions over sets of propositional symbols, whereas the latter is designed for reasoning about distributions over paths of possible behaviour. The intended application of the logic is as a specification formalism for properties of communication protocols, and security protocols in particular; to demonstrate this, we specify relevant security properties for a classical contract signing protocol and for the so–called quantum one–time pad.     

Towards Scalable Linear-Optical Quantum Computers

Scalable quantum computation with linear optics was considered to be impossible due to the lack of efficient two-qubit logic gates, despite the ease of implementation of one-qubit gates. Two-qubit gates necessarily need a non-linear interaction between the two photons, and the efficiency of this non-linear interaction is typically very small in bulk materials. However, it has recently been shown that this barrier can be circumvented with effective non-linearities produced by projective measurements, and with this work linear-optical quantum computing becomes a new avenue towards scalable quantum computation. We review several issues concerning the principles and requirements of this scheme. PACS: 03.67.Lx, 03.67.Pp, 42.50.Dv, 42.65.Lm     

Quantum synchronization of chaotic oscillator behaviors among coupled BEC–optomechanical systems

We consider and theoretically analyze a Bose-Einstein condensate (BEC) trapped inside an optomechanical system consisting of single-mode optical cavity with a moving end mirror. The BEC is formally analogous to a mirror driven by radiation pressure with strong nonlinear coupling. Such a nonlinear enhancement can make the oscillator display chaotic behavior. By establishing proper oscillator couplings, we find that this chaotic motion can be synchronized with other oscillators, even an oscillator network. We also discuss the scheme feasibility by analyzing recent experiment parameters. Our results provide a promising platform for the quantum signal transmission and quantum logic control, and they are of potential applications in quantum information processing and quantum networks.     

Ion Trap Quantum Computing with Ca+ Ions

The scheme of an ion trap quantum computer is described and the implementation of quantum gate operations with trapped Ca⁺ ions is discussed. Quantum information processing with Ca⁺ ions is exemplified with several recent experiments investigating entanglement of ions. PACS: 03.67.Lx, 03.67.Mn, 32.80.Pj     

Controlled gates for multi-level quantum computation

Multi-level (ML) quantum logic can potentially reduce the number of inputs/outputs or quantum cells in a quantum circuit which is a limitation in current quantum technology. In this paper we propose theorems about ML-quantum and reversible logic circuits. New efficient implementations for some basic controlled ML-quantum logic gates, such as three-qudit controlled NOT, Cycle, and Self Shift gates are proposed. We also propose lemmas about r-level quantum arrays and the number of required gates for an arbitrary n-qudit ML gate. An equivalent definition of quantum cost (QC) of binary quantum gates for ML-quantum gates is introduced and QC of controlled quantum gates is calculated.     

Physical synthesis of quantum circuits using templates

Similar to traditional CMOS circuits, quantum circuit design flow is divided into two main processes: logic synthesis and physical design. Addressing the limitations imposed on optimization of the quantum circuit metrics because of no information sharing between logic synthesis and physical design processes, the concept of “physical synthesis” was introduced for quantum circuit flow, and a few techniques were proposed for it. Following that concept, in this paper a new approach for physical synthesis inspired by template matching idea in quantum logic synthesis is proposed to improve the latency of quantum circuits. Experiments show that by using template matching as a physical synthesis approach, the latency of quantum circuits can be improved by more than 23.55 % on average.     

Protocols of quantum key agreement solely using Bell states and Bell measurement

Two protocols of quantum key agreement (QKA) that solely use Bell state and Bell measurement are proposed. The first protocol of QKA proposed here is designed for two-party QKA, whereas the second protocol is designed for multi-party QKA. The proposed protocols are also generalized to implement QKA using a set of multi-partite entangled states (e.g., 4-qubit cluster state and \(\Omega \) state). Security of these protocols arises from the monogamy of entanglement. This is in contrast to the existing protocols of QKA where security arises from the use of non-orthogonal state (non-commutativity principle). Further, it is shown that all the quantum systems that are useful for implementation of quantum dialogue and most of the protocols of secure direct quantum communication can be modified to implement protocols of QKA.     

Six Synthesis Methods for Reversible Logic

The (2 ^w )! reversible transformations on w wires, i.e. reversible logic circuits with w inputs and w outputs, together with the action of cascading, form a group, isomorphic to the symmetric group S ₂ ^w . Therefore, we investigate the group S _n as well as one of its subgroups isomorphic to S _n/2 × S _n/2. We then consider the left cosets, the right cosets, and the double cosets generated by the subgroup. Each element of a coset can function as the representative of the coset. The coset can then be considered as the set of all group elements that differ from the representative by merely multiplying (either to the left or to the right or to both sides) by an arbitrary element of the subgroup. Different choices of the coset space and different choices of the coset representatives lead to six different syntheses for implementing an arbitrary reversible logic operation into hardware. Evaluation of all six methods, by means of three different cost functions (gate cost, switch cost, and quantum cost), leads to a best choice.     

Quantum tasks using six qubit cluster states

The usefulness of the recent experimentally realized six photon cluster state by C. Y. Lu et al. (Nature 3:91, 2007) is investigated for quantum communication protocols like quantum teleportation and quantum information splitting (QIS) and dense coding. We show that the present state can be used for the teleportation of an arbitrary two qubit state deterministically. Later, we devise two distinct protocols for the QIS of an arbitrary two qubit state among two parties. We construct sixteen orthogonal measurement basis on the cluster state, which will lock an arbitrary two qubit state among two parties. The capability of the state for dense coding is investigated and it is shown that one can send five classical bits by sending only three qubits using this state as a shared entangled resource. We finally show that this state can also be utilised in the remote state preparation of an arbitrary two qubit state.     

The effect of quantum noise on two different deterministic remote state preparation of an arbitrary three-particle state protocols

Multi-particle quantum state deterministic remote preparation is a fundamental and important technical branch in quantum communication. Since quantum noise is unavoidable in realistic quantum communication, it is important to analyze the effect of noise on multi-particle quantum communication protocols. In this paper, we study the effects of noise, such as amplitude damping, phase damping, bit-flip and depolarizing noises, on two deterministic remote preparation of an arbitrary three-particle state protocols, which are based on two different entangled channels, namely \(\chi \) state and Brown state. The detailed mathematical analysis shows that the output states of two deterministic remote state preparation (DRSP) protocols are the same in the same noisy environment. That is to say, in the same noisy environment, the effects of noise on two DRSP protocols are the same. This conclusion proves that these two DRSP protocols will produce the same arbitrary three-particle states in the same noise channel environment, and so that these protocols are inherently convergent and can be substituted for each other in certain circumstances. In addition, this paper also takes three-particle states \(a\left| {000} \right\rangle + b{\mathrm{e}^{ic}}\left| {111} \right\rangle \) as an example and studies the relationship between the fidelity, the target state and the size of the noise factor. The results show that if the target state can be selected, an appropriate target state can effectively resist on the bit-flip noise. If the target state cannot be selected, as the increase in the size of noise factor, the fidelities of the two DRSP schemes in the amplitude damping noise and phase damping noise are always larger than those in the bit-flip noise and depolarizing noise. This conclusion indicates that two protocols have better resistance on amplitude damping and phase damping noise than the bit-flip and depolarizing noises. These findings and analyses will provide valid help in deterministic remote preparation of an arbitrary three-particle state in a noisy environment.     

Mathematical models of quantum computation

In this paper, we introduce two mathematical models of realistic quantum computation. First, we develop a theory of bulk quantum computation such as NMR (Nuclear Magnetic Resonance) quantum computation. For this purpose, we define bulk quantum Turing machine (BQTM for short) as a model of bulk quantum computation. Then, we define complexity classes EBQP, BBQP and ZBQP as counterparts of the quantum complexity classes EQP, BQP and ZQP, respectively, and show that EBQP=EQP, BBQP=BQP and ZBQP=ZQP. This implies that BQTMs are polynomially related to ordinary QTMs as long as they are used to solve decision problems. We also show that these two types of QTMs are also polynomially related when they solve a function problem which has a unique solution. Furthermore, we show that BQTMs can solve certain instances of NP-complete problems efficiently. On the other hand, in the theory of quantum computation, only feed-forward quantum circuits are investigated, because a quantum circuit represents a sequence of applications of time evolution operators. But, if a quantum computer is a physical device where the gates are interactions controlled by a current computer such as laser pulses on trapped ions, NMR and most implementation proposals, it is natural to describe quantum circuits as ones that have feedback loops if we want to visualize the total amount of the necessary hardware. For this purpose, we introduce a quantum recurrent circuit model, which is a quantum circuit with feedback loops. LetC be a quantum recurrent circuit which solves the satisfiability problem for a blackbox Boolean function includingn variables with probability at least 1/2. And lets be the size ofC (i.e. the number of the gates inC) andt be the number of iterations that is needed forC to solve the satisfiability problem. Then, we show that, for those quantum recurrent circuits, the minimum value ofmax(s, t) isO(n ²2 ^n/3). Tetsuro Nishino, D.Sc.: He is presently an Associate Professor in the Department of Information and Communication Engineering, The University of Electro-Communications. He received the B.S., M.S. and D.Sc degrees in mathematics from Waseda University, in 1982, 1984 and 1991 respectively. From 1984 to 1987, he joined Tokyo Research Laboratory, IBM Japan. From 1987 to 1992, he was a Research Associate of Tokyo Denki University, and from 1992 to 1994, he was an Associate Professor of Japan Advanced Institute of Science and Technology, Hokuriku. His main interests are circuit complexity theory, computational learning theory and quantum complexity theory.     

Foundations of declarative testing in arbitrary logic programming

Declarative testing is very important in logic program developments, as without testing no one can guarantee that every program is definitely correct, no matter how elegant and high-level the programming languages used. Unfortunately, the activity of declarative testing for logic programs (or even the ordinary testing for conventional programs) has received little attention. There is little formal theory of testing, and attempts to develop a methodology of testing are rare. In this paper, we provide a theoretical foundation for declarative testing in arbitrary first order logic programming using recursion theories. In particular, we present a theoretical analysis of three kinds of declarative testing method: I/O testing, I/Y testing, and X/Y testing for logic programs.     

On figures of merit in reversible and quantum logic designs

Five figures of merit including number of gates, quantum cost, number of constant inputs, number of garbage outputs, and delay are used casually in the literature to compare the performance of different reversible or quantum logic circuits. In this paper we propose new definitions and enhancements, and identify similarities between these figures of merit. We evaluate these measures to show their strength and weakness. Instead of the number of gates, we introduce the weighted number of gates, where a weighting factor is assigned to each quantum or reversible gate, based on its type, size and technology. We compare the quantum cost with weighted number of gates of a circuit and show three major differences between these measures. It is proved that it is not possible to define a universal reversible logic gate without adding constant inputs. We prove that there is an optimum value for number of constant inputs to obtain a circuit with minimum quantum cost. Some reversible logic benchmarks have been synthesized using Toffoli and Fredkin gates to obtain their optimum values of number of constant inputs. We show that the garbage outputs can also be used to decrease the quantum cost of the circuit. A new definition of delay in quantum and reversible logic circuits is proposed for music line style representation. We also propose a procedure to calculate the delay of a circuit, based on the quantum cost and the depth of the circuit. The results of this research show that to achieve a fair comparison among designs, figures of merit should be considered more thoroughly.      

一种分析Timed-Release公钥协议的扩展逻辑

在Coffey和Saidha提出的CS逻辑(CS逻辑将时间与逻辑结构相结合，可用于形式化分析Timed-release公钥协议的时间相关性秘密的安全性)的基础上，提出了CS逻辑的扩展逻辑，它更好地反映了Timed-release公钥协议的特性，并对一个协议实例进行了有效的形式化分析．     

Controllability and Universal Three-qubit Quantum Computation with Trapped Electron States

We show how to control and perform universal three-qubit quantum computation with trapped electron quantum states. The three qubits are the electron spin, and the first two quantum states of the cyclotron and axial harmonic oscillators. We explicitly show how universal three-qubit gates can be performed. As an example of a quantum algorithm, we outline the implementation of the three-qubit Deutsch-Jozsa algorithm in this system.