d-wave | ScienceGate

Quantum annealers, such as the device built by D-Wave Systems, Inc., offer a way to compute solutions of NP-hard problems that can be expressed in Ising or quadratic unconstrained binary optimization (QUBO) form. Although such solutions are typically of very high quality, problem instances are usually not solved to optimality due to imperfections of the current generations quantum annealers. In this contribution, we aim to understand some of the factors contributing to the hardness of a problem instance, and to use machine learning models to predict the accuracy of the D-Wave 2000Q annealer for solving specific problems. We focus on the maximum clique problem, a classic NP-hard problem with important applications in network analysis, bioinformatics, and computational chemistry. By training a machine learning classification model on basic problem characteristics such as the number of edges in the graph, or annealing parameters, such as the D-Wave’s chain strength, we are able to rank certain features in the order of their contribution to the solution hardness, and present a simple decision tree which allows to predict whether a problem will be solvable to optimality with the D-Wave 2000Q. We extend these results by training a machine learning regression model that predicts the clique size found by D-Wave.

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d-wave superconductor as a model of high-Tcsuperconductors

Physical Review B ◽

10.1103/physrevb.49.1397 ◽

1994 ◽

Vol 49 (2) ◽

pp. 1397-1402 ◽

Cited By ~ 301

Author(s):

Hyekyung Won ◽

Kazumi Maki

Keyword(s):

D Wave

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Theory of strongly phase fluctuating d-wave superconductors and the spin response in underdoped cuprates

Physica C Superconductivity ◽

10.1016/j.physc.2004.03.021 ◽

2004 ◽

Vol 408-410 ◽

pp. 414-415 ◽

Cited By ~ 2

Author(s):

Igor F. Herbut

Keyword(s):

Spin Response ◽

Underdoped Cuprates ◽

D Wave

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Adaptive hyperparameter updating for training restricted Boltzmann machines on quantum annealers

Scientific Reports ◽

10.1038/s41598-021-82197-1 ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Guanglei Xu ◽

William S. Oates

Keyword(s):

Neural Network ◽

Maximum Likelihood ◽

Image Reconstruction ◽

Image Recognition ◽

Shannon Entropy ◽

Reconstruction Error ◽

Likelihood Method ◽

Restricted Boltzmann Machines ◽

Boltzmann Machines ◽

D Wave

AbstractRestricted Boltzmann Machines (RBMs) have been proposed for developing neural networks for a variety of unsupervised machine learning applications such as image recognition, drug discovery, and materials design. The Boltzmann probability distribution is used as a model to identify network parameters by optimizing the likelihood of predicting an output given hidden states trained on available data. Training such networks often requires sampling over a large probability space that must be approximated during gradient based optimization. Quantum annealing has been proposed as a means to search this space more efficiently which has been experimentally investigated on D-Wave hardware. D-Wave implementation requires selection of an effective inverse temperature or hyperparameter ($$\beta $$ β ) within the Boltzmann distribution which can strongly influence optimization. Here, we show how this parameter can be estimated as a hyperparameter applied to D-Wave hardware during neural network training by maximizing the likelihood or minimizing the Shannon entropy. We find both methods improve training RBMs based upon D-Wave hardware experimental validation on an image recognition problem. Neural network image reconstruction errors are evaluated using Bayesian uncertainty analysis which illustrate more than an order magnitude lower image reconstruction error using the maximum likelihood over manually optimizing the hyperparameter. The maximum likelihood method is also shown to out-perform minimizing the Shannon entropy for image reconstruction.

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Benchmarking Quantum Annealing Against “Hard” Instances of the Bipartite Matching Problem

SN Computer Science ◽

10.1007/s42979-021-00483-1 ◽

2021 ◽

Vol 2 (2) ◽

Author(s):

Daniel Vert ◽

Renaud Sirdey ◽

Stéphane Louise

Keyword(s):

Simulated Annealing ◽

Polynomial Time ◽

Optimal Solution ◽

Quantum Computers ◽

Quantum Annealing ◽

Maximum Cardinality ◽

Matching Problem ◽

Bipartite Matching ◽

Wave Device ◽

D Wave

AbstractThis paper experimentally investigates the behavior of analog quantum computers as commercialized by D-Wave when confronted to instances of the maximum cardinality matching problem which is specifically designed to be hard to solve by means of simulated annealing. We benchmark a D-Wave “Washington” (2X) with 1098 operational qubits on various sizes of such instances and observe that for all but the most trivially small of these it fails to obtain an optimal solution. Thus, our results suggest that quantum annealing, at least as implemented in a D-Wave device, falls in the same pitfalls as simulated annealing and hence provides additional evidences suggesting that there exist polynomial-time problems that such a machine cannot solve efficiently to optimality. Additionally, we investigate the extent to which the qubits interconnection topologies explains these latter experimental results. In particular, we provide evidences that the sparsity of these topologies which, as such, lead to QUBO problems of artificially inflated sizes can partly explain the aforementioned disappointing observations. Therefore, this paper hints that denser interconnection topologies are necessary to unleash the potential of the quantum annealing approach.

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