A complete restricted Boltzmann machine on an adiabatic quantum computer

2021 ◽  
pp. 2141003
Author(s):  
Lorenzo Rocutto ◽  
Enrico Prati
Keyword(s):  
Complete Graph ◽  
Quantum Computer ◽  
Restricted Boltzmann Machine ◽  
Computational Time ◽  
Quantum Computers ◽  
Boltzmann Machine ◽  
Computational Power ◽  
Trade Off ◽  
Boltzmann Machines ◽  
The Neural Network

Boltzmann Machines constitute a paramount class of neural networks for unsupervised learning and recommendation systems. Their bipartite version, called Restricted Boltzmann Machine (RBM), is the most developed because of its satisfactory trade-off between computability on classical computers and computational power. Though the diffusion of RBMs is quite limited as their training remains hard. Recently, a renewed interest has emerged as Adiabatic Quantum Computers (AQCs), which suggest a potential increase of the training speed with respect to conventional hardware. Due to the limited number of connections among the qubits forming the graph of existing hardware, associating one qubit per node of the neural network implies an incomplete graph. Thanks to embedding techniques, we developed a complete graph connecting nodes constituted by virtual qubits. The complete graph outperforms previous implementations based on incomplete graphs. Despite the fact that the learning rate per epoch is still slower with respect to a classical machine, the advantage is expected by the increase of number of nodes which impacts on the classical computational time but not on the quantum hardware based computation.

scholarly journals An Algorithm of Quantum Restricted Boltzmann Machine Network Based on Quantum Gates and Its Application

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Peilin Zhang ◽  
Sheng Li ◽  
Yu Zhou
Keyword(s):  
Quantum Computer ◽  
Quantum Circuit ◽  
Classification Performance ◽  
Generative Model ◽  
Restricted Boltzmann Machine ◽  
Quantum Gates ◽  
Boltzmann Machine ◽  
Discriminative Models

We present an algorithm of quantum restricted Boltzmann machine network based on quantum gates. The algorithm is used to initialize the procedure that adjusts the qubit and weights. After adjusting, the network forms an unsupervised generative model that gives better classification performance than other discriminative models. In addition, we show how the algorithm can be constructed with quantum circuit for quantum computer.

TYPE-II QUANTUM COMPUTERS

2001 ◽  
Vol 12 (09) ◽  
pp. 1273-1284 ◽  
Author(s):  
JEFFREY YEPEZ
Keyword(s):  
Short Range ◽  
Quantum Computer ◽  
Quantum Mechanical ◽  
Quantum Computers ◽  
Type Ii ◽  
Computational Power ◽  
Classical Communication ◽  
Small Quantum ◽  
Short Time ◽  
Quantum Parallelism

This paper discusses a computing architecture that uses both classical parallelism and quantum parallelism. We consider a large parallel array of small quantum computers, connected together by classical communication channels. This kind of computer is called a type-II quantum computer, to differentiate it from a globally phase-coherent quantum computer, which is the first type of quantum computer that has received nearly exclusive attention in the literature. Although a hybrid, a type-II quantum computer retains the crucial advantage allowed by quantum mechanical superposition that its computational power grows exponentially in the number of phase-coherent qubits per node, only short-range and short time phase-coherence is needed, which significantly reduces the level of engineering facility required to achieve its construction. Therefore, the primary factor limiting its computational power is an economic one and not a technological one, since the volume of its computational medium can in principle scale indefinitely.

scholarly journals Analyzing joint brand purchases by conditional restricted Boltzmann machines

2021 ◽  
Author(s):  
Harald Hruschka
Keyword(s):  
Hidden Variables ◽  
Restricted Boltzmann Machine ◽  
Boltzmann Machine ◽  
Restricted Boltzmann Machines ◽  
Market Basket ◽  
Boltzmann Machines ◽  
Independent Variables ◽  
Product Categories ◽  
Pseudo Likelihood ◽  
Marketing Variables

AbstractWe introduce the conditional restricted Boltzmann machine as method to analyze brand-level market basket data of individual households. The conditional restricted Boltzmann machine includes marketing variables and household attributes as independent variables. To our knowledge this is the first study comparing the conditional restricted Boltzmann machine to homogeneous and heterogeneous multivariate logit models for brand-level market basket data across several product categories. We explain how to estimate the conditional restricted Boltzmann machine starting from a restricted Boltzmann machine without independent variables. The conditional restricted Boltzmann machine turns out to excel all the other investigated models in terms of log pseudo-likelihood for holdout data. We interpret the selected conditional restricted Boltzmann machine based on coefficients linking purchases to hidden variables, interdependences between brand pairs as well as own and cross effects of marketing variables. The conditional restricted Boltzmann machine indicates pairwise relationships between brands that are more varied than those of the multivariate logit model are. Based on the pairwise interdependences inferred from the restricted Boltzmann machine we determine the competitive structure of brands by means of cluster analysis. Using counterfactual simulations, we investigate what three different models (independent logit, heterogeneous multivariate logit, conditional restricted Boltzmann machine) imply with respect to the retailer’s revenue if each brand is put on display. Finally, we mention possibilities for further research, such as applying the conditional restricted Boltzmann machine to other areas in marketing or retailing.

scholarly journals adabmDCA: adaptive Boltzmann machine learning for biological sequences

2021 ◽  
Vol 22 (1) ◽  
Author(s):  
Anna Paola Muntoni ◽  
Andrea Pagnani ◽  
Martin Weigt ◽  
Francesco Zamponi
Keyword(s):  
Machine Learning ◽  
Three Dimensional ◽  
Computational Time ◽  
Model Parameters ◽  
User Requirements ◽  
Boltzmann Machine ◽  
Target Domain ◽  
Contact Map ◽  
Boltzmann Machines

Abstract Background Boltzmann machines are energy-based models that have been shown to provide an accurate statistical description of domains of evolutionary-related protein and RNA families. They are parametrized in terms of local biases accounting for residue conservation, and pairwise terms to model epistatic coevolution between residues. From the model parameters, it is possible to extract an accurate prediction of the three-dimensional contact map of the target domain. More recently, the accuracy of these models has been also assessed in terms of their ability in predicting mutational effects and generating in silico functional sequences. Results Our adaptive implementation of Boltzmann machine learning, , can be generally applied to both protein and RNA families and accomplishes several learning set-ups, depending on the complexity of the input data and on the user requirements. The code is fully available at https://github.com/anna-pa-m/adabmDCA. As an example, we have performed the learning of three Boltzmann machines modeling the Kunitz and Beta-lactamase2 protein domains and TPP-riboswitch RNA domain. Conclusions The models learned by are comparable to those obtained by state-of-the-art techniques for this task, in terms of the quality of the inferred contact map as well as of the synthetically generated sequences. In addition, the code implements both equilibrium and out-of-equilibrium learning, which allows for an accurate and lossless training when the equilibrium one is prohibitive in terms of computational time, and allows for pruning irrelevant parameters using an information-based criterion.

scholarly journals Comparison of quantum and classical methods for labels and patterns in Restricted Boltzmann Machines

2021 ◽  
Vol 2122 (1) ◽  
pp. 012007
Author(s):  
Vivek Dixit ◽  
Yaroslav Koshka ◽  
Tamer Aldwairi ◽  
M.A. Novotny
Keyword(s):  
Classification Accuracy ◽  
Quantum Computer ◽  
Quantum Effect ◽  
Low Energy ◽  
Data Reconstruction ◽  
Boltzmann Machine ◽  
Restricted Boltzmann Machines ◽  
Boltzmann Machines ◽  
Comparable Performance ◽  
D Wave

Abstract Classification and data reconstruction using a restricted Boltzmann machine (RBM) is presented. RBM is an energy-based model which assigns low energy values to the configurations of interest. It is a generative model, once trained it can be used to produce samples from the target distribution. The D-Wave 2000Q is a quantum computer which has been used to exploit its quantum effect for machine learning. Bars-and-stripes (BAS) and cybersecurity (ISCX) datasets were used to train RBMs. The weights and biases of trained RBMs were used to map onto the D-Wave. Classification as well as image reconstruction were performed. Classification accuracy of both datasets indicates comparable performance using D-Wave’s adiabatic annealing and classical Gibb’s sampling.

Replication of Quantum Computing towards an Unconventional Environment using QuIDE

2019 ◽  
Vol 8 (4) ◽  
pp. 9461-9464
Keyword(s):  
Quantum Computer ◽  
Source Code ◽  
Circuit Diagram ◽  
Quantum Computers ◽  
Coordinated Development ◽  
Development Environment ◽  
Integrated Development ◽  
Complexity Of Algorithms ◽  
Performance Results ◽  
Exponential Complexity

Current quantum computer simulation strategies are inefficient in simulation and their realizations are also failed to minimize those impacts of the exponential complexity for simulated quantum computations. We proposed a Quantum computer simulator model in this paper which is a coordinated Development Environment – QuIDE (Quantum Integrated Development Environment) to support the improvement of algorithm for future quantum computers. The development environment provides the circuit diagram of graphical building and flexibility of source code. Analyze the complexity of algorithms shows the performance results of the simulator and used for simulation as well as result of its deployment during simulation

scholarly journals Asset–liability modelling in the quantum era

2021 ◽  
Vol 26 ◽  
Author(s):  
T. Berry ◽  
J. Sharpe
Keyword(s):  
Quantum Mechanics ◽  
Quantum Computer ◽  
Quantum Algorithm ◽  
Capital Requirements ◽  
Quantum Computers ◽  
Investment Management ◽  
Asset Liability Management ◽  
Liability Management ◽  
Insight Into ◽  
Current Practices

Abstract This paper introduces and demonstrates the use of quantum computers for asset–liability management (ALM). A summary of historical and current practices in ALM used by actuaries is given showing how the challenges have previously been met. We give an insight into what ALM may be like in the immediate future demonstrating how quantum computers can be used for ALM. A quantum algorithm for optimising ALM calculations is presented and tested using a quantum computer. We conclude that the discovery of the strange world of quantum mechanics has the potential to create investment management efficiencies. This in turn may lead to lower capital requirements for shareholders and lower premiums and higher insured retirement incomes for policyholders.

scholarly journals A divide-and-conquer algorithm for quantum state preparation

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Israel F. Araujo ◽  
Daniel K. Park ◽  
Francesco Petruccione ◽  
Adenilton J. da Silva
Keyword(s):  
Computational Cost ◽  
Quantum Circuit ◽  
Divide And Conquer ◽  
Computational Time ◽  
Quantum Computers ◽  
Dimensional Vector ◽  
Quantum Devices ◽  
Divide And Conquer Algorithm ◽  
Quantum State Preparation ◽  
Quantum Device

AbstractAdvantages in several fields of research and industry are expected with the rise of quantum computers. However, the computational cost to load classical data in quantum computers can impose restrictions on possible quantum speedups. Known algorithms to create arbitrary quantum states require quantum circuits with depth O(N) to load an N-dimensional vector. Here, we show that it is possible to load an N-dimensional vector with exponential time advantage using a quantum circuit with polylogarithmic depth and entangled information in ancillary qubits. Results show that we can efficiently load data in quantum devices using a divide-and-conquer strategy to exchange computational time for space. We demonstrate a proof of concept on a real quantum device and present two applications for quantum machine learning. We expect that this new loading strategy allows the quantum speedup of tasks that require to load a significant volume of information to quantum devices.

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