Showing papers on "Quantum evolution published in 2012"
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TL;DR: In this article, a quantum version of the game of life has been studied and the evolution of complex structures in a quantum world has been investigated, in particular in terms of the diversity of the structures formed in the steady state.
Abstract: W e introduce aq uantum version of the Game of Life and we use it to study the emergence of complexity in a quantum world. We show that the quantum evolution displays signatures of complex behaviour similar to the classical one, however a regime exists, where the quantum Game of Life creates more complexity, in terms of diversity, with respect to the corresponding classical reversible one. Copyright c EPLA, 2012 The Game of Life (GoL) has been proposed by Conway in 1970 as a wonderful mathematical game which can describe the appearance of complexity and the evolution of "life" under some simple rules (1). Since its introduction it has attracted a lot of attention, as despite its simplicity, it can reveal complex patterns with unpredictable evolu- tion: From the very beginning a lot of structures have been identified, from simple blinking patterns to complex evolving figures which have been named "blinkers", "glid- ers" up to "spaceships" due to their appearance and/or dynamics (2). The classical GoL has been the subject of many studies: It has been shown that cellular automata defined by the GoL have the power of a Universal Turing machine, that is, anything that can be computed algo- rithmically can be computed within Conway's GoL (3,4). Statistical analysis and analytical descriptions of the GoL have been performed; many generalisations or modifica- tions of the initial game have been introduced as, for exam- ple, a simplified one-dimensional version of the GoL and a semi-quantum version (5-7). Finally, to allow a statistical- mechanics description of the GoL, stochastic components have been added (8). In this letter, we bridge the field of complex systems with quantum mechanics introducing a purely quantum GoL and we investigate its dynamical properties. We show that it displays interesting features in common with its classical counterpart, in particular regarding the variety of supported dynamics and different behaviour. The system converges to a quasi-stationary configuration in terms of macroscopic variables, and these stable configurations depend on the initial state, e.g., the initial density of "alive" sites for random initial configurations. We show that simple, local rules support complex behaviour and that the diversity of the structures formed in the steady state resembles that of the classical GoL, however a regime exists where quantum dynamics allows more diversity to be created than possibly reached by the classical one. The universe of the original GoL is an infinite two-dimensional orthogonal grid of square cells with coordination number eight, each of them in one of two possible states, alive or dead (1). At each step in time, the pattern present on the grid evolves instantaneously following simple rules: any dead cell with exactly three live neighbours comes to life; any live cell with less than two or more than three live neighbours dies as if by loneliness or overcrowding. As already pointed out in (7), the rules of the GoL are irreversible, thus their generalisation to the quantum case implies rephrasing them to make them compatible with a quantum reversible evolution. The system under study is a collection of two-level quantum systems, with two possible orthogonal states, namely the state "dead" (|0� ) and "alive" (|1� ). Clearly, differently from the classical case, a site can be also in a superpo- sition of the two possible classical states. The dynamics is defined as follows in terms of the GoL language: a site with two or three neighbouring alive sites is active, where active means that it will come to life and eventually die on a typical timescale T (setting the problem timescale, or time between subsequent generations). That is, if maintained active by the surrounding conditions, the site will complete a full rotation, if not, it is "frozen" in its state. Stretching the analogy with Conway's GoL to the limit, we are describing the evolution of a virus culture: each individual undergoes its life cycle if the environment allows it, otherwise it hibernates in its current state and waits for conditions to change such that the site may
40 citations
TL;DR: In this paper, a class of legitimate memory kernels leading to completely trace-preserving dynamical maps is provided, which can be considered as a quantum version of semi-Markov dynamics which is much more general than Markovian dynamics.
Abstract: We provided a class of legitimate memory kernels leading to completely positive trace-preserving dynamical maps. Our construction is based on a simple normalization procedure. Interestingly, when applied to a classical system it gives rise to semi-Markov evolution. Therefore, it may be considered as a quantum version of semi-Markov dynamics which is much more general than Markovian dynamics.
40 citations
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TL;DR: In this article, the authors consider a large class of operationally defined theories that contain "nonlinear boxes" and show that operational verifiability without superluminal signaling implies a split in the equivalence classes of preparation procedures.
Abstract: Nonlinear modifications to the laws of quantum mechanics have been proposed as a possible way to consistently describe information processing in the presence of closed timelike curves. These have recently generated controversy due to possible exotic information-theoretic effects, including breaking quantum cryptography and radically speeding up both classical and quantum computers. The physical interpretation of such theories, however, is still unclear. We consider a large class of operationally-defined theories that contain "nonlinear boxes" and show that operational verifiability without superluminal signaling implies a split in the equivalence classes of preparation procedures. We conclude that any theory satisfying the above requirements is (a) inconsistent unless it contains distinct representations for the two different kinds of preparations and (b) incomplete unless it also contains a rule for uniquely distinguishing them at the operational level. We refer to this as the preparation problem for nonlinear theories. In addition to its foundational implications, this work shows that, in the presence of nonlinear quantum evolution, the security of quantum cryptography and the existence of other exotic effects remain open questions.
19 citations
TL;DR: In this article, a classical Hamiltonian system of a point moving on a sphere of fixed radius is shown to emerge from the constrained evolution of quantum spin, which corresponds to an appropriate coarse graining of the quantum states into equivalence classes.
Abstract: A classical Hamiltonian system of a point moving on a sphere of fixed radius is shown to emerge from the constrained evolution of quantum spin. The constrained quantum evolution corresponds to an appropriate coarse graining of the quantum states into equivalence classes, and forces the equivalence classes to evolve as single units representing the classical states. The coarse-grained quantum spin with the constrained evolution in the limit of the large spin becomes indistinguishable from the classical system.
13 citations
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TL;DR: In this paper, a context driven actualization of potential (CAP) model is proposed to handle potentiality and describe the evolution of entities as an actualisation of potential through a reiterated interaction with the context.
Abstract: Darwinism conceives evolution as a consequence of random variation and natural selection, hence it is based on a materialistic, i.e. matter-based, view of science inspired by classical physics. But matter in itself is considered a very complex notion in modern physics. More specifically, at a microscopic level, matter and energy are no longer retained within their simple form, and quantum mechanical models are proposed wherein potential form is considered in addition to actual form. In this paper we propose an alternative to standard Neodarwinian evolution theory. We suggest that the starting point of evolution theory cannot be limited to actual variation whereupon is selected, but to variation in the potential of entities according to the context. We therefore develop a formalism, referred to as Context driven Actualization of Potential (CAP), which handles potentiality and describes the evolution of entities as an actualization of potential through a reiterated interaction with the context. As in quantum mechanics, lack of knowledge of the entity, its context, or the interaction between context and entity leads to different forms of indeterminism in relation to the state of the entity. This indeterminism generates a non-Kolmogorovian distribution of probabilities that is different from the classical distribution of chance described by Darwinian evolution theory, which stems from a 'actuality focused', i.e. materialistic, view of nature. We also present a quantum evolution game that highlights the main differences arising from our new perspective and shows that it is more fundamental to consider evolution in general, and biological evolution in specific, as a process of actualization of potential induced by context, for which its material reduction is only a special case.
11 citations
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26 Jun 2012
TL;DR: Based on recent theorems about quantum value-indefiniteness, it is conjectured that many issues of Born's quantum mechanics can be overcome by supposing that only a single pure state exists; and that the quantum evolution permutes this state.
Abstract: Based on recent theorems about quantum value-indefiniteness it is conjectured that many issues of "Born's quantum mechanics" can be overcome by supposing that only a single pure state exists; and that the quantum evolution permutes this state.
4 citations
06 Mar 2012
TL;DR: This paper proposes to combine quantum evolution algorithm and neural network joint use in controller tuning problems, and results show that this is a feasible method, and the controller has enhanced response speed and robustness, and can be used for different kinds of objects and processes.
Abstract: At present, neural network and quantum evolution algorithm have been used in controller tuning problems, separately. In the past, quantum evolution algorithm, the result of fusing of quantum computing and evolution computing, is attractive as one way to give us suitable answers for optimization problems. For a long time, PID control schemes are widely used in most of control system. PID optimal parameters have a great influence on the stability and the performance of the control system, so, how to determine or tune them, is still a very important problem. In this paper, we propose to combine quantum evolution algorithm and neural network joint use. Simulation results show that this is a feasible method, and the controller has enhanced response speed and robustness, and can be used for different kinds of objects and processes.
4 citations
TL;DR: In this article, a quantum dynamics on a digraph is called saturated Z-local if the nonzero transition amplitudes specifying the unitary evolution are in exact correspondence with the directed edges (including loops) of the digraph.
Abstract: Adapting a definition of Aaronson and Ambainis [Theory Comput. 1 (2005), 47--79], we call a quantum dynamics on a digraph "saturated Z-local" if the nonzero transition amplitudes specifying the unitary evolution are in exact correspondence with the directed edges (including loops) of the digraph. This idea appears recurrently in a variety of contexts including angular momentum, quantum chaos, and combinatorial matrix theory. Complete characterization of the digraph properties that allow such a process to exist is a long-standing open question that can also be formulated in terms of minimum rank problems. We prove that saturated Z-local dynamics involving complex amplitudes occur on a proper superset of the digraphs that allow restriction to the real numbers or, even further, the rationals. Consequently, among these fields, complex numbers guarantee the largest possible choice of topologies supporting a discrete quantum evolution. A similar construction separates complex numbers from the skew field of quaternions. The result proposes a concrete ground for distinguishing between complex and quaternionic quantum mechanics.
3 citations
TL;DR: In this article, the authors studied the quantum dynamics of coherent states on a circle and in a box at all time scales in semiclassical approximation and gave detailed information about all stages of quantum evolution.
Abstract: We study a peculiar semiclassical limit of the dynamics of quantum states on a circle and in a box (infinitely deep potential well with rigid walls) as the Planck constant tends to zero and time tends to infinity. Our results describe the dynamics of coherent states on the circle and in the box at all time scales in semiclassical approximation. They give detailed information about all stages of quantum evolution in the semiclassical limit. In particular, we rigorously justify the fact that the spatial distribution of a wave packet is most often close to a uniform distribution. This fact was previously known only from numerical experiments. We apply the results obtained to a problem of classical mechanics: deciding whether the recently suggested functional formulation of classical mechanics is preferable to the traditional one. To do this, we study the semiclassical limit of Husimi functions of quantum states. Both formulations of classical mechanics are shown to adequately describe the system when time is not arbitrarily large. But the functional formulation remains valid at larger time scales than the traditional one and, therefore, is preferable from this point of view. We show that, although quantum dynamics in finite volume is commonly believed to be almost periodic, the probability distribution of the position of a quantum particle in a box has a limit distribution at infinite time if we take into account the inaccuracy in measuring the size of the box.
3 citations
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TL;DR: In this paper, the authors studied the non-Markovian character of a quantum evolution of a driven spin-S$ system weakly coupled to a bosonic bath using a measure for divisibility of a dynamical map.
Abstract: Using a recently proposed measure for divisibility of a dynamical map, we study the non-Markovian character of a quantum evolution of a driven spin-$S$ system weakly coupled to a bosonic bath. The complete tomographic knowledge about the dynamics of the open system is obtained by the time-convolutionless master equation in the secular approximation. The derived equation can be applied to a wide range of spin-boson models with the Hermitian or non-Hermitian coupling operator in the system-environment interaction Hamiltonian. Besides the influence of the environmental spectral densities, the tunneling energy of the system Hamiltonian can affect the measure of quantum non-Markovianity. It is found that the non-Markovian feature of a dynamical map of a high-dimension spin system is noticeable in contrast to that of a low-dimension spin system.
2 citations
TL;DR: In this paper, the authors investigated quantum and classical correlations during quantum brachistochrone evolution (QBE) and found some typical properties of the pair of quantum states sampled randomly by use of the Harr measure in this special kind of quantum evolution.
Abstract: Quantum and classical correlations are investigated during quantum brachistochrone evolution (QBE) in this paper. We found some typical properties of the pair of quantum states sampled randomly by use of the Harr measure in this special kind of quantum evolution. This kind of evolution of a three-qubit system between two distinct states cannot be implemented without classical correlations (including bipartite J2 and tripartite J3) and quantum correlations (including bipartite D2 and tripartite D3). We also found that some QBEs between two distinct GHZ states do not follow the typical behaviour, and that this kind of evolution can be implemented without bipartite quantum correlations. Although the probability density function of the time-averaged bipartite classical correlation, time-averaged bipartite quantum correlations and time-averaged genuine tripartite correlations become more and more uniform with the decrease of angles of separation between an initial state and a final state, the features of their most probable values exhibit a different trend.
TL;DR: In this paper, the authors present a complete derivation of the exact evolution of quantum mechanics for the case when the underlying spectrum is continuous, based on the use of Weyl eigendifferentials.
01 Jun 2012
TL;DR: In this paper, a complete expansion with respect to the small parameter " > 0 which makes sense within the infinite-dimensional setting and fits with finite-dimensional formulae is provided. But the expansion is restricted to the case where the observables are given by a time-dependent quadratic Hamiltonian.
Abstract: The Hepp method is the coherent state approach to the mean field dynamics for bosons or to the semiclassical propagation. A key point is the asymptotic evolution of Wick observables under the evolution given by a time-dependent quadratic Hamiltonian. This article provides a complete expansion with respect to the small parameter " > 0 which makes sense within the infinite-dimensional setting and fits with finite-dimensional formulae.
TL;DR: In this article, the classical limit of the quantum evolution with some rough potential, of wave packets concentrated near singular trajectories of the underlying dynamics, was considered and it was shown that under appropriate conditions, even in the case of BV vector fields, the correct classical limit can be selected.
Abstract: We consider the classical limit of the quantum evolution, with some rough potential, of wave packets concentrated near singular trajectories of the underlying dynamics. We prove that under appropriate conditions, even in the case of BV vector fields, the correct classical limit can be selected.
TL;DR: Based on recent theorems about quantum value-indefiniteness, it is conjectured that many issues of Born's quantum mechanics can be overcome by supposing that only a single pure state exists; and that the quantum evolution permutes this state as discussed by the authors.
Abstract: Based on recent theorems about quantum value-indefiniteness it is conjectured that many issues of "Born's quantum mechanics" can be overcome by supposing that only a single pure state exists; and that the quantum evolution permutes this state.
TL;DR: In this paper, a quantum counting circuit was proposed to compute the two-color Ramsey numbers for r-uniform hypergraphs. But it is not yet a quantum algorithm for the computation of the Ramsey numbers.
Abstract: Gaitan and Clark [Phys. Rev. Lett. 108, 010501 (2012)] have recently shown a quantum algorithm for the computation of the Ramsey numbers using adiabatic quantum evolution. We present a quantum algorithm to compute the two-color Ramsey numbers for r-uniform hypergraphs by using the quantum counting circuit.
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TL;DR: In this paper, a noncommutative Fornasini-marchesini system can be realized within a weak Markov process (a model for quantum evolution) for a discrete time parameter.
Abstract: A noncommutative Fornasini-Marchesini system (a multi-variable version of a linear system) can be realized within a weak Markov process (a model for quantum evolution). For a discrete time parameter the resulting structure is worked out systematically and some quantum mechanical interpretations are given. We introduce subprocesses and quotient processes and then the notion of a $\gamma$-extension for processes which leads to a complete classification of all the ways in which processes can be built from subprocesses and quotient processes. We show that within a $\gamma$-extension we have a cascade of noncommutative Fornasini-Marchesini systems. We study observability in this setting and as an application we gain new insights into stationary Markov chains where observability for the system is closely related to asymptotic completeness in a scattering theory for the chain.