Statistical physics on cellular neural network computers

The computational paradigm represented by Cellular Neural/nonlinear Networks (CNN) and the CNN Universal Machine (CNN-UM) as a Cellular Wave Computer, gives new perspectives also for computational statistical physics. Thousands of locally interconnected cells working in parallel, analog signals giving the possibility of generating truly random numbers, continuity in time and the optical sensors included on the chip are just a few important advantages of such computers. Although CNN computers are mainly used and designed for image processing, here we argue that they are also suitable for solving complex problems in computational statistical physics. This study presents two examples of stochastic simulations on CNN: the site-percolation problem and the two-dimensional Ising model. Promising results are obtained using an ACE16K chip with 128×128 cells. In the second part of the work we discuss the possibility of using the CNN architecture in studying problems related to spin-glasses. A CNN with locally variant parameters is used for developing an optimization algorithm on spin-glass type models. Speed of the algorithms and further trends in developing the CNN chips are discussed.     

Stochastic simulations on the cellular wave computers

The computational paradigm represented by Cellular Neural/nonlinear Networks (CNN) and the CNN Universal Machine (CNN-UM) as a Cellular Wave Computer, gives new perspectives for computational physics. Many numerical problems and simulations can be elegantly addressed on this fully parallelized and analogic architecture. Here we study the possibility of performing stochastic simulations on this chip. First a realistic random number generator is implemented on the CNN-UM, and then as an example the two-dimensional Ising model is studied by Monte Carlo type simulations. The results obtained on an experimental version of the CNN-UM with 128 ×128 cells are in good agreement with the results obtained on digital computers. Computational time measurements suggest that the developing trend of the CNN-UM chips — increasing the lattice size and the number of local logic memories — will assure an important advantage for the CNN-UM in the near future.     

Structural Investigation of Solid Methane at High Pressure

High pressure studies of solid methane are performed using both classical simulated annealing and first-principles methods. A series of simulated annealing and geometry optimization reveal a monoclinic P21/b structure with the unit cell containing four methane molecules. The phonon dispersion curves and vibrational density of states indicate that this structure is stable in the pressure range 10-90 GPa. The electronic band structure and density of states show that this structure has not metalized until 90 GPa.     

Optimization through quantum annealing: theory and some applications

Quantum annealing is a promising tool for solving optimization problems, similar in some ways to the traditional (classical) simulated annealing of Kirkpatrick et al. Simulated annealing takes advantage of thermal fluctuations in order to explore the optimization landscape of the problem at hand, whereas quantum annealing employs quantum fluctuations. Intriguingly, quantum annealing has been proved to be more effective than its classical counterpart in many applications. We illustrate the theory and the practical implementation of both classical and quantum annealing – highlighting the crucial differences between these two methods – by means of results recently obtained in experiments, in simple toy-models, and more challenging combinatorial optimization problems (namely, Random Ising model and Travelling Salesman Problem). The techniques used to implement quantum and classical annealing are either deterministic evolutions, for the simplest models, or Monte Carlo approaches, for harder optimization tasks. We discuss the pro and cons of these approaches and their possible connections to the landscape of the problem addressed.     

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.     

Generalized simulated annealing algorithm and its application to the Thomson model

Based on the Tsallis statistics, the generalized simulated annealing algorithm (GSA) is tested and developed. Studies on the Thomson model show that the GSA is more efficient than the classical simulated annealing and the fast simulated annealing. The fluctuation of energy is reduced drastically. The convergence to the global minimum is fast. We believe the GSA algorithm is a powerful method to find the global minimum in more realistic problems, like the equilibrium structure of big clusters.     

Factoring larger integers with fewer qubits via quantum annealing with optimized parameters

RSA cryptography is based on the difficulty of factoring large integers, which is an NP-hard(and hence intractable) problem for a classical computer. However, Shor's algorithm shows that its complexity is polynomial for a quantum computer, although technical difficulties mean that practical quantum computers that can tackle integer factorizations of meaningful size are still a long way away. Recently, Jiang et al. proposed a transformation that maps the integer factorization problem onto the quadratic unconstrained binary optimization(QUBO) model. They tested their algorithm on a D-Wave 2000 Q quantum annealing machine, raising the record for a quantum factorized integer to 376289 with only 94 qubits. In this study, we optimize the problem Hamiltonian to reduce the number of qubits involved in the final Hamiltonian while maintaining the QUBO coefficients in a reasonable range, enabling the improved algorithm to factorize larger integers with fewer qubits. Tests of our improved algorithm using D-Wave's hybrid quantum/classical simulator qbsolv confirmed that performance was improved, and we were able to factorize 1005973, a new record for quantum factorized integers, with only 89 qubits. In addition, our improved algorithm can tolerate more errors than the original one. Factoring 1005973 using Shor's algorithm would require about 41 universal qubits,which current universal quantum computers cannot reach with acceptable accuracy. In theory, the latest IBM Q System OneTM(Jan. 2019) can only factor up to 10-bit integers, while the D-Wave have a thousand-fold advantage on the factoring scale. This shows that quantum annealing machines, such as those by D-Wave, may be close to cracking practical RSA codes, while universal quantum-circuit-based computers may be many years away from attacking RSA.     

The application of improved block-matching method and block search method for the image motion estimation

Image block matching is one of the motion estimation methods for video inter-frame coding and digital image stabilization. The methods used for matching and searching will greatly affect the accuracy and speed of block matching. The block matching method based on the oblique vectors is suggested in this paper where matching parameters contain both horizontal and vertical vectors in the image blocks at the same time. Improved matching information can be obtained after making correlative calculations in the oblique direction. A novel search method of matching block based on the idea of simulated annealing is presented in this paper to improve the searching speed, accuracy and robustness in the fast operation of the block-matching motion estimation. The simulated annealing algorithm can easily escape from the trap of local minima effectively. With the two methods the block matching can be used for motion estimation at the real-time image processing system and high estimation accuracy can be achieved. An image stabilization system based on DSP (Digital Signal Processing) system is developed to verify this algorithm. Results show that both the matching accuracy and the search speed are improved with the methods presented.     

Strange attractor simulated on a quantum computer

We show that dissipative classical dynamics converging to a strange attractor can be simulated on a quantum computer. Such quantum computations allow to investigate efficiently the small scale structure of strange attractors, yielding new information inaccessible to classical computers. This opens new possibilities for quantum simulations of various dissipative processes in nature. Received 10 August 2002 Published online 29 October 2002 RID="a" ID="a"e-mail: dima@irsamc.ups-tlse.fr RID="b" ID="b"UMR 5626 du CNRS     

Hybrid quantum-classical convolutional neural networks

Deep learning has been shown to be able to recognize data patterns better than humans in specific circumstances or contexts. In parallel, quantum computing has demonstrated to be able to output complex wave functions with a few number of gate operations,which could generate distributions that are hard for a classical computer to produce. Here we propose a hybrid quantum-classical convolutional neural network(QCCNN), inspired by convolutional neural networks(CNNs) but adapted to quantum computing to enhance the feature mapping process. QCCNN is friendly to currently noisy intermediate-scale quantum computers, in terms of both number of qubits as well as circuit's depths, while retaining important features of classical CNN, such as nonlinearity and scalability. We also present a framework to automatically compute the gradients of hybrid quantum-classical loss functions which could be directly applied to other hybrid quantum-classical algorithms. We demonstrate the potential of this architecture by applying it to a Tetris dataset, and show that QCCNN can accomplish classification tasks with learning accuracy surpassing that of classical CNN with the same structure.     

PID数字控制器多指标优化模拟设计方法研究

建立PID数字控制器多指标统一优化模拟设计方法;用SIMULINK仿真研究数字PID控制对模拟PID控制的复现能力和PID计算机控制系统的阶跃响应,用MATLAB仿真筛选PID参数的优化组合值;提出并建立了一种新的PID数字控制器多指标优化模拟设计方法,包括:PID初值确定方法、模拟PID优化参数MATLAB筛选方案和软件流程图、模拟PID参数转换数字PID参数的方法、SIMULINK仿真验证设计结果的有效性的方法等;研究表明,该方法可用于1～5ms采样周期的PID数字控制器多指标优化模拟设计,且能独立使用、无需PID经验数据和其它设计/整定方法;提供了4个代表性的实例设计,验证了该方法的有效性。     

Analog computation through high-dimensional physical chaotic neuro-dynamics

Conventional von Neumann computers have difficulty in solving complex and ill-posed real-world problems. However, living organisms often face such problems in real life, and must quickly obtain suitable solutions through physical, dynamical, and collective computations involving vast assemblies of neurons. These highly parallel computations through high-dimensional dynamics (computation through dynamics) are completely different from the numerical computations on von Neumann computers (computation through algorithms). In this paper, we explore a novel computational mechanism with high-dimensional physical chaotic neuro-dynamics. We physically constructed two hardware prototypes using analog chaotic-neuron integrated circuits. These systems combine analog computations with chaotic neuro-dynamics and digital computation through algorithms. We used quadratic assignment problems (QAPs) as benchmarks. The first prototype utilizes an analog chaotic neural network with 800-dimensional dynamics. An external algorithm constructs a solution for a QAP using the internal dynamics of the network. In the second system, 300-dimensional analog chaotic neuro-dynamics drive a tabu-search algorithm. We demonstrate experimentally that both systems efficiently solve QAPs through physical chaotic dynamics. We also qualitatively analyze the underlying mechanism of the highly parallel and collective analog computations by observing global and local dynamics. Furthermore, we introduce spatial and temporal mutual information to quantitatively evaluate the system dynamics. The experimental results confirm the validity and efficiency of the proposed computational paradigm with the physical analog chaotic neuro-dynamics.     

Time dependent local field distribution and metastable states in the SK-spin-glass

Different sets of metastable states can be reached in glassy systems below some transition temperature depending on initial conditions and details of the dynamics. This is investigated for the Sherrington-Kirkpatrick spin glass model with long ranged interactions. In particular, the time dependent local field distribution and energy are calculated for zero temperature. This is done for a system quenched to zero temperature, slow cooling or simulated annealing, a greedy algorithm and repeated tapping. Results are obtained from Monte-Carlo simulations and a Master-Fokker-Planck approach. A comparison with replica symmetry broken theory, evaluated in high orders, shows that the energies obtained via dynamics are higher than the ground state energy of replica theory. Tapping and simulated annealing yield on the other hand results which are very close to the ground state energy. The local field distribution tends to zero for small fields. This is in contrast to the Edwards flat measure hypothesis. The distribution of energies obtained for different tapping strengths does again not follow the canonical form proposed by Edwards.     

Quantum approach to classical statistical mechanics

We present a new approach to study the thermodynamic properties of d-dimensional classical systems by reducing the problem to the computation of ground state properties of a d-dimensional quantum model. This classical-to-quantum mapping allows us to extend the scope of standard optimization methods by unifying them under a general framework. The quantum annealing method is naturally extended to simulate classical systems at finite temperatures. We derive the rates to assure convergence to the optimal thermodynamic state using the adiabatic theorem of quantum mechanics. For simulated and quantum annealing, we obtain the asymptotic rates of T(t) approximately (pN)/(k(B)logt) and gamma(t) approximately (Nt)(-c/N), for the temperature and magnetic field, respectively. Other annealing strategies are also discussed.     

Quantum simulations of classical annealing processes

We describe a quantum algorithm that solves combinatorial optimization problems by quantum simulation of a classical simulated annealing process. Our algorithm exploits quantum walks and the quantum Zeno effect induced by evolution randomization. It requires order 1/sqrt delta steps to find an optimal solution with bounded error probability, where delta is the minimum spectral gap of the stochastic matrices used in the classical annealing process. This is a quadratic improvement over the order 1/delta steps required by the latter.     

Characteristics in optimization of CGH for array generator

A method of simulated annealing in optimization of a computer generated holo-gram(CGH)is presented.The characteristics of energy in annealing curve are analyzed.Thecooling schedule such as giving an initial temperature,the temperature function,the numberof interactions and stopping criterion are discussed.As an example,an optimization of phaserelief kinoform,a CGH with multiple phase levels,is implemented.     

Optimal combinations of imperfect objects

We consider how to make best use of imperfect objects, such as defective analog and digital components. We show that perfect, or near-perfect, devices can be constructed by taking combinations of such defects. Any remaining objects can be recycled efficiently. In addition to its practical applications, our "defect combination problem" provides a novel generalization of classical optimization problems.     

Fast Optimization of Binary Encrypted Hologram Based on Error Correction Method in Optical Security Systems

In practical optical security systems we must consider various circumstances for reading and decrypting encrypted holograms. Binarization of the hologram is best suited for such applications because of the ease of handling encrypted data. However, the decrypted image is greatly degraded by binarization. Therefore, optimization of a binary hologram is essential in using such a technique. In this paper, we propose a fast optimization method of a binary encrypted hologram to obtain a good reconstruction based on the error correction algorithm. In the proposed method, multiple pixels of the binary hologram are simultaneously flipped for the optimization according to the priority for the correction. The time for the optimization is only 3% of that of the simulated annealing method.     

Spin-glass behavior of the polyvinyl pyrrolidone-protected Prussian blue analog K1.14Mn[Fe(CN)6]0.88 nanocubes

Prussian Blue analog K_1.14Mn[Fe(CN)₆]_0.88 nanocubes were synthesized by using polyvinyl pyrrolidone (PVP) as a protective matrix. The PVP-protected MnFe PBA nanocubes with face centered cubic structure are well dispersed with a narrow size distribution of around 50 nm. A spin-glass behavior (including hysteresis, a peak in the zero-field-cooled magnetization and frequency-dependent AC magnetic susceptibility) is observed in the nanoparticles. A possible origin of this spin-glass freezing is discussed. Spin disorder due to the structural defects may be the reason that causes the spin-glass freezing in the MnFe PBA nanoparticles.     

Magnetic properties of compounds in the system CaBaCo4−x−yZnxAlyO7 (x=0,1,2, y=0,1)

The magnetic properties of four compounds in the series CaBaCo_4−x−yZn_xAl_yO₇ (x=0,1,2, y=0,1) were investigated. Using AC-susceptibility and DC-magnetometry, magnetic transitions (T_fs) were found for all four compositions in the range 50-3 K. The data from the AC measurements proved to be frequency dependent: T_f increases with higher frequencies. An energy-loss in the magnetic coupling, indicated as contributions in the imaginary part of the magnetic susceptibility (χ″), was seen for every compound and its maximum appeared just below the maximum χ′. Modelling the data with Arrhenius-, Vogel-Fulcher-, and the power-law made it possible to relate the four compounds to spin-glass materials. The Casimir-du Pré relation was used to extract average relaxation times at T_f. The DC magnetisations clearly show differences between field-cooled and zero-field-cooled measurements. None of the compounds exhibit any metamagnetic properties up to 8 T. A new method is presented to calculate the saturation fields using DC data. Relaxation measurements on three compounds indicate that the systems relax very fast, in contrast to spin-glasses. Aging does not affect the fast relaxations. The compounds are interpreted as disordered anti-ferromagnets with spin-glass features.