Variational Quantum Chemistry Programs in JaqalPaq

We present example quantum chemistry programs written with JaqalPaq, a python meta-programming language used to code in Jaqal (Just Another Quantum Assembly Language). These JaqalPaq algorithms are intended to be run on the Quantum Scientific Computing Open User Testbed (QSCOUT) platform at Sandia National Laboratories. Our exemplars use the variational quantum eigensolver (VQE) quantum algorithm to compute the ground state energies of the H2, HeH+, and LiH molecules. Since the exemplars focus on how to program in JaqalPaq, the calculations of the second-quantized Hamiltonians are performed with the PySCF python package, and the mappings of the fermions to qubits are obtained from the OpenFermion python package. Using the emulator functionality of JaqalPaq, we emulate how these exemplars would be executed on an error-free QSCOUT platform and compare the emulated computation of the bond-dissociation curves for these molecules with their exact forms within the relevant basis.     

Computation of Kullback–Leibler Divergence in Bayesian Networks

Kullback–Leibler divergence KL(p,q) is the standard measure of error when we have a true probability distribution p which is approximate with probability distribution q. Its efficient computation is essential in many tasks, as in approximate computation or as a measure of error when learning a probability. In high dimensional probabilities, as the ones associated with Bayesian networks, a direct computation can be unfeasible. This paper considers the case of efficiently computing the Kullback–Leibler divergence of two probability distributions, each one of them coming from a different Bayesian network, which might have different structures. The paper is based on an auxiliary deletion algorithm to compute the necessary marginal distributions, but using a cache of operations with potentials in order to reuse past computations whenever they are necessary. The algorithms are tested with Bayesian networks from the bnlearn repository. Computer code in Python is provided taking as basis pgmpy, a library for working with probabilistic graphical models.     

Research on exponential regularization approach for nonnegative Tucker3 decomposition

Methods of nonnegative tensor factorization (NTF), such as NTF1, NTF2, etc., are extension of nonnegative matrix factorization (NMF) for multi-way data analysis. As an existing NTF method, nonnegative Tucker3 decomposition (NTD) is researched for three-way decomposition in this paper. Firstly, an approach utilizing matrix exponentials built on Tikhonov-type regularization to enforce sparseness is proposed to extract image features instead of exclusively using Tucker tensor decomposition. Meanwhile, updating algorithms, derived from updating rules of NMF, are allowed to efficiently implement updating of mode matrices and core tensors alternatively for accuracy. Then, experimental cases of alternating least squares (ALS) and conjugate nonnegative constraints, called nonnegative alternating least squares (NALS), are studied to remedy data overfitting in computing procedures. Lastly, the proposed method exhibits more advantageous results than other algorithms of Tucker3 for feature extraction, thanks to computer simulations performed in the context of data analysis.     

Numerical solution of eigenvalue problems for Hamiltonian systems

This paper discusses the numerical solution of eigenvalue problems for Hamiltonian systems of ordinary differential equations. Two new codes are presented which incorporate the algorithms described here; to the best of the author’s knowledge, these are the first codes capable of solving numerically such general eigenvalue problems. One of these implements a new new method of solving a differential equation whose solution is a unitary matrix. Both codes are fully documented and are written inPfort-verifiedFortran 77, and will be available in netlib/aicm/sl11f and netlib/aicm/sl12f.     

On spanning tree problems with multiple objectives

We investigate two versions of multiple objective minimum spanning tree problems defined on a network with vectorial weights. First, we want to minimize the maximum ofQ linear objective functions taken over the set of all spanning trees (max-linear spanning tree problem, ML-ST). Secondly, we look for efficient spanning trees (multi-criteria spanning tree problem, MC-ST).Problem ML-ST is shown to be NP-complete. An exact algorithm which is based on ranking is presented. The procedure can also be used as an approximation scheme. For solving the bicriterion MC-ST, which in the worst case may have an exponential number of efficient trees, a two-phase procedure is presented. Based on the computation of extremal efficient spanning trees we use neighbourhood search to determine a sequence of solutions with the property that the distance between two consecutive solutions is less than a given accuracy.Partially supported by Deutsche Forschungsgemeinschaft and HCº Contract no. ERBCHRXCT 930087.Partially supported by Alexander von Humboldt-Stiftung.     

Local minima of the trust region problem

We consider the minimization of a quadratic formzVz+2zq subject to the two-norm constraint z=. The problem received considerable attention in the literature, notably due to its applications to a class of trust region methods in nonlinear optimization. While the previous studies were concerned with just the global minimum of the problem, we investigate the existence of all local minima. The problem is approached via the dual Lagrangian, and the necessary and sufficient conditions for the existence of all local minima are derived. We also examine the suitability of the conventional numerical techniques used to solve the problem to a class of single-instruction multiple-data computers known as processor arrays (in our case, AMT DAP 610). Simultaneously, we introduce certain hardware-oriented multisection algorithms, showing their efficiency in the case of small to medium size problems.This research was partially supported by the National Physical Laboratories of England under Contract RTP2/155/127.     

Binary neutron stars gravitational wave detection based on wavelet packet analysis and convolutional neural networks

This work investigates the detection of binary neutron stars gravitational wave based on convolutional neural network(CNN).To promote the detection performance and efficiency,we proposed a scheme based on wavelet packet(WP)decomposition and CNN.The WP decomposition is a time-frequency method and can enhance the discriminant features between gravitational wave signal and noise before detection.The CNN conducts the gravitational wave detection by learning a function mapping relation from the data under being processed to the space of detection results.This function-mapping-relation style detection scheme can detection efficiency significantly.In this work,instrument effects are con-sidered,and the noise are computed from a power spectral density(PSD)equivalent to the Advanced LIGO design sensitivity.The quantitative evaluations and comparisons with the state-of-art method matched filtering show the excellent performances for BNS gravitational wave detection.On efficiency,the current experiments show that this WP-CNN-based scheme is more than 960 times faster than the matched filtering.     

Some optimizations on detecting gravitational wave using convolutional neural network

This work investigates the problem of detecting gravitational wave (GW) events based on simulated damped sinusoid signals contaminated with white Gaussian noise. It is treated as a classification problem with one class for the interesting events. The proposed scheme consists of the following two successive steps: decomposing the data using a wavelet packet, representing the GW signal and noise using the derived decomposition coefficients; and determining the existence of any GW event using a convolutional neural network (CNN) with a logistic regression output layer. The characteristic of this work is its comprehensive investigations on CNN structure, detection window width, data resolution, wavelet packet decomposition and detection window overlap scheme. Extensive simulation experiments show excellent performances for reliable detection of signals with a range of GW model parameters and signal-to-noise ratios. While we use a simple waveform model in this study, we expect the method to be particularly valuable when the potential GW shapes are too complex to be characterized with a template bank.     

基于辐射声功率最小化的安静结构设计

本文研究了一种基于模型修改使结构辐射声功率最小的方法，使用了结构动力学、声学和优化理论等学科知识，对结构修改后固有频率变化可以忽略不计时的声辐射优化进行了研究，将设计变量看作外部阻抗，对结构的表面振速进行了重新分布，可以降低结构辐射的声功率。将质量块与动力吸振器进行组合实现声辐射最小化，不但降低了一定频率范围内的平均声功率，还降低了动力吸振器所对应的单频下的声功率；运用遗传算法搜索结构辐射声功率最小时附加质量块或动力吸振器的位置，对附加质量块和有源控制作用下简支钢板的声功率最小化进行了比较研究，阐明了附加外部结构与有源控制实现安静结构的物理机理。最后，对本文提出的基于平板辐射声功率最小化的安静结构设计方法进行了实验验证。     

Five-step phase-shifting algorithms with unknown values of phase shift

The presented work offers new algorithms for phase evaluation in interferometric measurements. Several phase-shifting algorithms with an arbitrary but constant phase-shift between captured intensity frames are proposed. These phase calculation algorithms need to measure five frames of the intensity of the interference field. The algorithms are similarly derived as so called Carré algorithm. The phase evaluation process then does not depend on the linear phase shift errors. Furthermore, the detailed analysis of the algorithms with respect to most important factors, which affect interferometric measurements, is carried out. It is also studied the dependency of the evaluation algorithms on the phase shift values, and the proposed phase calculation algorithms are compared with respect to the resulting phase errors. The influence of most important factors in the measurement and evaluation process was simulated as systematic and random errors using a proposed mathematical model.