基于相位匹配的量子行走搜索算法及电路实现

量子行走是经典随机行走在量子力学框架下的对应, 理论上可以用来解决一类无序数据库的搜索问题. 因为携带信息的量子态的扩散速度与经典相比有二次方式的增长, 所以量子行走优于经典随机行走, 量子行走的特性值得加以利用. 量子行走作为一种新发现的物理现象的数学描述, 引发了一种新的思维方式, 孕育了一种新的理论计算模型. 最新研究表明, 量子行走本身也是一种通用计算模型, 可被视为设计量子算法的高级工具, 因此受到部分计算机理论科学领域学者的关注和研究. 对于多数问题求解方案的量子算法的设计, 理论上可以只在量子行走模型下进行考虑. 基于Grover算法的相位匹配条件, 本文提出了一个新的基于量子行走的搜索算法. 理论演算表明: 一般情况下本算法的时间复杂度与Grover算法相同, 但是当搜索的目标数目多于总数的1/3时, 本算法搜索成功的概率要大于Grover算法. 本文不但利用Grover算法中相位匹配条件构造了一个新的量子行走搜索算法, 而且在本研究室原有的量子电路设计研究成果的基础上给出了该算法的量子电路表述.     

Time operators for quantum walks

Letters in Mathematical Physics - We study time operators for discrete-time quantum systems. Quantum walks are typical examples. We construct time operators for one-dimensional homogeneous quantum...     

Quantum field theory of binary alternatives

We describe a framework for quantum field theory that is based on quantized binary alternatives. We discuss the relation of the dynamics of quantum fields and the time evolution of the Heisenberg operators defined by the creation and annihilation operators of the alternatives. An explicit expression for the vacuum vector of the quantum fields is derived. Finally we discuss eigenstates of the momentum operators.     

A Non-Associative Quantum Mechanics

A non-associative quantum mechanics is proposed in which the product of three and more operators can be non-associative one. The multiplication rules of the octonions define the multiplication rules of the corresponding operators with quantum corrections. The self-consistency of the operator algebra is proved for the product of three operators. Some properties of the non-associative quantum mechanics are considered. It is proposed that some generalization of the non-associative algebra of quantum operators can be helpful for understanding of the algebra of field operators with a strong interaction.     

The Representation Theory of Decoherence Functionals in History Quantum Theories

In the first part of this paper the general perspective of history quantum theoriesis reviewed. History quantum theories provide a conceptual and mathematicalframework for formulating quantum theories without a globally definedHamiltonian time evolution and for introducing the concept of space-time eventinto quantum theory. On a mathematical level a history quantum theory ischaracterized by the space of histories, which represent the space-time events, andby the space of decoherence functionals, which represent the quantum mechanicalstates in the history approach. The second part of this paper is devoted to thestudy of the structure of the space of decoherence functionals for some physicallyreasonable spaces of histories in some detail. The temporal reformulation ofstandard Hamiltonian quantum theories suggests to consider the case that thespace of histories is given by (i) the lattice of projection operators on someHilbert space or, slightly more generally, (ii) the set of projection operators insome von Neumann algebra. In the case (i) the conditions are identified underwhich decoherence functionals can be represented by, respectively, trace classoperators, bounded operators, or families of trace class operators on the tensorproduct of the underlying Hilbert space by itself. Moreover, we discuss thenaturally arising representations of decoherence functionals as sesquilinear forms.The paper ends with a discussion of the consequences of the results for thegeneral axiomatic framework of history theories.     

Black holes and the nature of quantum gravity

Hawking and Wald have recently argued that the process of quantum black hole evaporation requires the violation of the fundamental physical law which asserts that the time evolution of quantum states is governed by unitary operators. I show this violation can be avoided by a change in the global boundary conditions. It is remotely possible that astronomical observation could establish whether or not the universe has these boundary conditions in which quantum mechanical time evolution is governed by unitary operators.     

哈密顿算符是SU(1,1)和SU(2)算子含时线性组合量子系统的时间演变及厄密不变量

研究了哈密顿算符是SU(1,1)和SU(2)算子线性组合且系数显含时间量子系统的时间演化,我们发现适当选取厄密不变量,不仅可得到统一的量子态时间演化封闭解,而且可得到时间演化幺正算符。用时间演化算符我们讨论了含时双光子压缩态和SU(1,1)相干态以及SU(2)压缩态的压缩性质。     

Constructing Exactly Solvable Pseudo-hermitian Many-Particle Quantum Systems by Isospectral Deformation

A class of non-Dirac-hermitian many-particle quantum systems admitting entirely real spectra and unitary time-evolution is presented. These quantum models are isospectral with Dirac-hermitian systems and are exactly solvable. The general method involves a realization of the basic canonical commutation relations defining the quantum system in terms of operators those are hermitian with respect to a pre-determined positive definite metric in the Hilbert space. Appropriate combinations of these operators result in a large number of pseudo-hermitian quantum systems admitting entirely real spectra and unitary time evolution. Examples of a pseudo-hermitian rational Calogero model and XXZ spin-chain are considered.     

Exact phase space localized projectors from energy eigenstates

In investigations of the emergence of classicality from quantum theory, a useful step is the construction of quantum operators corresponding to the classical notion that the system resides in a region of phase space. The simplest such constructions are approximate projection operators. Here, we show how to construct exact projection operators which are localized on regions of phase. We elucidate the properties of such operators and explore their time evolution. For the harmonic oscillator we find sets of phase space localized histories which are exactly decoherent for any initial state and have probability 1 for classical evolution.     

Absence of wave operators for one-dimensional quantum walks

Letters in Mathematical Physics - We show that there exist pairs of two time evolution operators which do not have wave operators in a context of one-dimensional discrete time quantum walks. As a...     

Holevo-Ordering and the Continuous-Time Limit for Open Floquet Dynamics

We consider an atomic beam reservoir as a source of quantum noise. The atoms are modelled as two-state systems and interact one-at-a-time with the system. The Floquet operators are described in terms of the Fermionic creation, annihilation and number operators associated with the two-state atom. In the limit where the time between interactions goes to zero and the interaction is suitably scaled, we show that we may obtain a causal (that is, adapted) quantum stochastic differential equation of Hudson—Parthasarathy type, driven by creation, annihilation and conservation processes. The effect of the Floquet operators in the continuous limit is exactly captured by the Holevo ordered form for the stochastic evolution     

Tense Operators on Basic Algebras

The concept of tense operators on a basic algebra is introduced. Since basic algebras can serve as an axiomatization of a many-valued quantum logic (see e.g. Chajda et al. in Algebra Univer. 60(1):63–90, 2009), these tense operators are considered to quantify time dimension, i.e. one expresses the quantification “it is always going to be the case that” and the other expresses “it has always been the case that”. We set up the axiomatization and basic properties of tense operators on basic algebras and involve a certain construction of these operators for left-monotonous basic algebras. Finally, we relate basic algebras with tense operators with another quantum structures which are the so-called dynamic effect algebras.     

Quantum Theory of Solid State Plasma Dielectric Response

We review the quantum mechanical derivation of the random phase approximation (RPA) for solid state plasmas, starting from the Hamilton equations for canonically paired “second quantized” creation and annhilation field operators of interacting quantum many‐body systems. Discussing variational differentiation, the coupled equations of motion for the quantum field operators are derived. The concept of Green's functions is reviewed and interpreted, first for retarded Green's functions, and their equations of motion are developed from the equations of motion for the field operators. Thermodynamic Green's functions are discussed, and their periodicity/antiperiodicity properties in imaginary time are carefully examined with discussion of Matsubara Fourier series and representation in terms of a spectral weight function. The analytic continuation from imaginary time to real time is treated. Finally, we define nonequilibrium Green's functions and discuss the linearized timedependent Hartree approximation leading to the random phase approximation. An interesting application to the case of Graphene in a perpendicular magnetic field is discussed in detail, along with applications to normal systems, in terms of attendant phenomenology involving electron‐hole pair excitations and plasmons (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

加强的量子汉明限

通过研究具有相同重量的算子集合的性质,找到了任意维数纯量子稳定子码参数的新的解析上限.与目前所知最优的解析上限——著名的量子汉明限相比,本文提出的码限强于量子汉明限. 关键词： 量子汉明限 量子稳定子码 量子纠错码 量子信息     

Irreducibility of the set of field operators in NC QFT

Irreducibility of the set of quantum field operators has been proved in noncommutative quantum field theory in the general case when time does not commute with spatial variables.     

再谈含时Schrdinger方程的求解方法

介绍了线性耦合含时量子系统厄米不变量算符的构造方法，并运用Ｌｅｗｉｓ－Ｒｉｅｓｅｎｆｅｌｄ量子不变量理论得到了一些含时薛定谔方程的精确解．同时也给出了系统时间演化算符的构造方法     

Quantum Encoding and Entanglement in Terms of Phase Operators Associated with Harmonic Oscillator

Realization of qudit quantum computation has been presented in terms of number operator and phase operators associated with one-dimensional harmonic oscillator and it has been demonstrated that the representations of generalized Pauli group, viewed in harmonic oscillator operators, allow the qudits to be explicitly encoded in such systems. The non-Hermitian quantum phase operators contained in decomposition of the annihilation and creation operators associated with harmonic oscillator have been analysed in terms of semi unitary transformations (SUT) and it has been shown that the non-vanishing analytic index for harmonic oscillator leads to an alternative class of quantum anomalies. Choosing unitary transformation and the Hermitian phase operator free from quantum anomalies, the truncated annihilation and creation operators have been obtained for harmonic oscillator and it has been demonstrated that any attempt of removal of quantum anomalies leads to absence of minimum uncertainty.     

Definition and existence of multichannel scattering states

The field theoretical formulation of quantum mechanics is used to consider the nonrelativistic multichannel scattering theory. With the help of appropriately constructed time dependent creation operators, Hilbert vectors are formed whose limits in time can be defined as multichannel scattering states in the usual sense. The existence of these states is proved under certain assumptions for the potential, by showing the convergence of the above mentioned operators. The commutation relations for the limits of these operators are given.