Reinforcement Learning Using Quantum Boltzmann Machines

Crawford, Daniel J.; Levit, Anna; Ghadermarzy, Navid; Oberoi, Jaspreet S.; Ronagh, Pooya

doi:10.48550/arxiv.1612.05695

Cited by 25 publications

(27 citation statements)

References 39 publications

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“…A large number of applications have been modeled in the quadratic case. For example, in combinatorial scientific computing [21][22][23][24], chemistry [25,26], and machine learning [27][28][29] In the following subsections, we give examples that consist of problems modeled as a HOBO with higher-order terms greater than two.…”

Section: Applicationsmentioning

confidence: 99%

Compressed Quadratization of Higher Order Binary Optimization Problems

Mandal¹,

Upadhyay²,

Ushijima‐Mwesigwa³

2020

Preprint

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Recent hardware advances in quantum and quantum-inspired annealers promise substantial speed up for solving NP-hard combinatorial optimization problems compared to general purpose computers. These special purpose hardware are built for solving hard instances of Quadratic Unconstrained Binary Optimization (QUBO) problems. In terms of number of variables and precision these hardware are usually resource constrained and they work either in Ising space {−1, 1} or in Boolean space {0, 1}. Many naturally occurring problem instances are higher order in nature. The known method to reduce the degree of a higher order optimization problem uses Rosenberg's polynomial. The method works in Boolean space by reducing degree of one term by introducing one extra variable. In this work, we prove that in Ising space the degree reduction of one term requires introduction of two variables. Our proposed method of degree reduction works directly in Ising space, as opposed to converting an Ising polynomial to Boolean space and applying previously known Rosenberg's polynomial. For sparse higher order Ising problems, this results in more compact representation of the resultant QUBO problem, which is crucial for utilizing resource constrained QUBO solvers.

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Section: Applicationsmentioning

confidence: 99%

Compressed Quadratization of Higher Order Binary Optimization Problems

Mandal¹,

Upadhyay²,

Ushijima‐Mwesigwa³

2020

Preprint

View full text Add to dashboard Cite

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“…With these new chips having more couplers between the qubits, we will be able to embed shapes with more elements and hopefully determine smoother geometries. We will continue to focus on laying the foundation for solving practically relevant problems by means of quantum computing, quantum simulation, and quantum optimization [16,17,[28][29][30][31][32][33].…”

Section: Future Workmentioning

confidence: 99%

Quantum-assisted finite-element design optimization

van Vreumingen,

Neukart,

Von Dollen

et al. 2019

Preprint

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Quantum annealing devices such as the ones produced by D-Wave systems are typically used for solving optimization and sampling tasks [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15], and in both academia and industry the characterization of their usefulness is subject to active research. Any problem that can naturally be described as a weighted, undirected graph may be a particularly interesting candidate [16,17], since such a problem may be formulated a as quadratic unconstrained binary optimization (QUBO) instance, which is solvable on D-Wave's Chimera graph architecture. In this paper, we introduce a quantum-assisted finite-element method for design optimization. We show that we can minimize a shape-specific quantity, in our case a ray approximation of sound pressure at a specific position around an object, by manipulating the shape of this object. Our algorithm belongs to the class of quantum-assisted algorithms, as the optimization task runs iteratively on a D-Wave 2000Q quantum processing unit (QPU), whereby the evaluation and interpretation of the results happens classically. Our first and foremost aim is to explain how to represent and solve parts of these problems with the help of a QPU, and not to prove supremacy over existing classical finite-element algorithms for design optimization.

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“…While D-Wave machines were designed to be solvers and not samplers, the operating principle of AQC suggests that those machines could be efficiently used to sample from Boltzmann distributions. In fact, Boltzmann sampling using a D-wave machine has already been investigated in the existing literature [4], [5], [6], where the authors aim to train Boltzmann Machines. Yet, the implemented protocol allowing to perform such sampling is usually difficult to reproduce.…”

Section: Introductionmentioning

confidence: 99%

On the challenges of using D-Wave computers to sample Boltzmann Random Variables

Pochart¹,

Jacquot²,

Mikael³

2021

Preprint

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Sampling random variables following a Boltzmann distribution is an NP-hard problem involved in various applications such as training of Boltzmann machines, a specific kind of neural network. Several attempts have been made to use a D-Wave quantum computer to sample such a distribution, as this could lead to significant speedup in these applications. Yet, at present, several challenges remain to efficiently perform such sampling. We detail the various obstacles and explain the remaining difficulties in solving the sampling problem on a D-wave machine.

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Reinforcement Learning Using Quantum Boltzmann Machines

Cited by 25 publications

References 39 publications

Compressed Quadratization of Higher Order Binary Optimization Problems

Compressed Quadratization of Higher Order Binary Optimization Problems

Quantum-assisted finite-element design optimization

On the challenges of using D-Wave computers to sample Boltzmann Random Variables

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