Quantum Annealing versus Digital Computing

Jünger, Michael; Lobe, Elisabeth; Mutzel, Petra; Reinelt, Gerhard; Rendl, Franz; Rinaldi, Giovanni; Stollenwerk, Tobias

doi:10.1145/3459606

Cited by 26 publications

(16 citation statements)

References 43 publications

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“…Due to this specific structure, so far, materials science related applications of this technology are still rare. Instead, actual research focuses mainly on the benchmarking and performance tests of quantum annealing compared to classical approaches [12][13][14] . Some first applications in the field of biology and traffic research in the sense of optimization problems have been developed recently.…”

Section: Introductionmentioning

confidence: 99%

Quantum annealing for microstructure equilibration with long-range elastic interactions

Sandt

Bouar

Spatschek

2023

Preprint

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We demonstrate the use and benefits of quantum annealing approaches for the determination of equilibrated microstructures in shape memory alloys and other materials with long-range elastic interaction between coherent grains and their different martensite variants and phases. After a one dimensional illustration of the general approach, which requires to formulate the energy of the system in terms of an Ising Hamiltonian, we use distant dependent elastic interactions between grains to predict the variant selection for different transformation eigenstrains. The results and performance of the computations are compared to classical algorithms, demonstrating that the new approach can lead to a significant acceleration of the simulations. Beyond a discretization using simple cuboidal elements, also a direct representation of arbitrary microstructures is possible, allowing fast simulations with currently up to several thousand grains.

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Section: Introductionmentioning

confidence: 99%

Quantum annealing for microstructure equilibration with long-range elastic interactions

Sandt

Bouar

Spatschek

2023

Preprint

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“…Although several physical effects prevent the ideal realization of the underlying adiabatic theorem, and optimal solutions can thus only be found with some probability, the experimental results appear to be promising for certain applications [25]. However, the advantage over classical computation is still under discussion [13].…”

Section: Introductionmentioning

confidence: 99%

Optimal Sufficient Requirements on the Embedded Ising Problem in Polynomial Time

Lobe¹,

Kaibel²

2023

Preprint

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One of the central applications for quantum annealers is to find the solutions of Ising problems. Suitable Ising problems, however, need to be formulated such that they, on the one hand, respect the specific restrictions of the hardware and, on the other hand, represent the original problems which shall actually be solved. We evaluate sufficient requirements on such an embedded Ising problem analytically and transform them into a linear optimization problem. With an objective function aiming to minimize the maximal absolute problem parameter, the precision issues of the annealers are addressed. Due to the redundancy of several constraints, we can show that the formally exponentially large optimization problem can be reduced and finally solved in polynomial time for the standard embedding setting where the embedded vertices induce trees. This allows to formulate provably equivalent embedded Ising problems in a practical setup.

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“…There have also been various articles on exact solution. See Barahona et al (4) for an early, Rendl et al (37) for a more recent, and Jünger et al (25) for an up-to-date overview. In the last years, more focus has been put on the development of methods that are best suited for dense instances, see for example (22; 23; 31) for state-of-the-art methods.…”

Section: Introductionmentioning

confidence: 99%

Faster exact solution of sparse MaxCut and QUBO problems

Rehfeldt¹,

Koch²,

Shinano³

2022

Preprint

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The maximum-cut problem is one of the fundamental problems in combinatorial optimization. With the advent of quantum computers, both the maximum-cut and the equivalent quadratic unconstrained binary optimization problem have experienced much interest in recent years.This article aims to advance the state of the art in the exact solution of both problems-by using mathematical programming techniques on digital computers. The main focus lies on sparse problem instances, although also dense ones can be solved. We enhance several algorithmic components such as reduction techniques and cutting-plane separation algorithms, and combine them in an exact branch-and-cut solver. Furthermore, we provide a parallel implementation. The new solver is shown to significantly outperform existing state-of-the-art software for sparse MaxCut and QUBO instances. Furthermore, we improve the best known bounds for several instances from the 7th DIMACS Challenge and the QPLIB, and solve some of them (for the first time) to optimality.

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Quantum Annealing versus Digital Computing

Cited by 26 publications

References 43 publications

Quantum annealing for microstructure equilibration with long-range elastic interactions

Quantum annealing for microstructure equilibration with long-range elastic interactions

Optimal Sufficient Requirements on the Embedded Ising Problem in Polynomial Time

Faster exact solution of sparse MaxCut and QUBO problems

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