Quantum Annealing versus Digital Computing

2021 ◽  
Vol 26 ◽  
pp. 1-30
Author(s):  
Michael Jünger ◽  
Elisabeth Lobe ◽  
Petra Mutzel ◽  
Gerhard Reinelt ◽  
Franz Rendl ◽  
...  
Keyword(s):  
Ising Models ◽  
Branch And Cut ◽  
Processing Unit ◽  
Quantum Annealing ◽  
Maximum Cut ◽  
Quadratic Unconstrained Binary Optimization ◽  
Cut Problems ◽  
Programming Algorithms ◽  
D Wave

Quantum annealing is getting increasing attention in combinatorial optimization. The quantum processing unit by D-Wave is constructed to approximately solve Ising models on so-called Chimera graphs. Ising models are equivalent to quadratic unconstrained binary optimization (QUBO) problems and maximum cut problems on the associated graphs. We have tailored branch-and-cut as well as semidefinite programming algorithms for solving Ising models for Chimera graphs to provable optimality and use the strength of these approaches for comparing our solution values to those obtained on the current quantum annealing machine, D-Wave 2000Q. This allows for the assessment of the quality of solutions produced by the D-Wave hardware. In addition, we also evaluate the performance of a heuristic by Selby. It has been a matter of discussion in the literature how well the D-Wave hardware performs at its native task, and our experiments shed some more light on this issue. In particular, we examine how reliably the D-Wave computer can deliver true optimum solutions and present some surprising results.

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

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.

scholarly journals Quantum annealing algorithms for track pattern recognition

2020 ◽  
Vol 245 ◽  
pp. 10006
Author(s):  
Masahiko Saito ◽  
Paolo Calafiura ◽  
Heather Gray ◽  
Wim Lavrijsen ◽  
Lucy Linder ◽  
...  
Keyword(s):  
Pattern Recognition ◽  
Simulated Annealing ◽  
Hadron Collider ◽  
Recognition Algorithm ◽  
Quantum Annealing ◽  
Discovery Potential ◽  
Energy Frontier ◽  
Track Pattern ◽  
Annealing Algorithms ◽  
D Wave

The High-Luminosity Large Hadron Collider (HL-LHC) starts from 2027 to extend the physics discovery potential at the energy frontier. The HL-LHC produces experimental data with a much higher luminosity, requiring a large amount of computing resources mainly due to the complexity of a track pattern recognition algorithm. Quantum annealing might be a solution for an efficient track pattern recognition in the HL-LHC environment. We demonstrated to perform the track pattern recognition by using the D-Wave annealing machine and the Fujitsu Digital Annealer. The tracking efficiency and purity for the D-Wave quantum annealer are comparable with those for a classical simulated annealing at a low pileup condition, while a drop in performance is found at a high pileup condition, corresponding to the HL-LHC pileup environment. The tracking efficiency and purity for the Fujitsu Digital Annealer are nearly the same as the classical simulated annealing.

scholarly journals Temperatures and periods of drying delay and quality of corn seeds harvested on the ears

2019 ◽  
Vol 41 (3) ◽  
pp. 336-343
Author(s):  
Everson Reis Carvalho ◽  
Victor Moss Francischini ◽  
Suemar Alexandre Gonçalves Avelar ◽  
Júlia Camargos da Costa
Keyword(s):  
Processing Unit ◽  
High Moisture Content ◽  
High Moisture ◽  
Seed Processing ◽  
Randomized Design ◽  
Delay Times ◽  
Physiological Quality ◽  
Completely Randomized Design ◽  
Corn Hybrid

Abstract: Seeds harvested on the ears have high moisture content. On that account, this study aimed at evaluating the loss of physiological quality of corn seeds harvested on the ears, as a function of different drying-delay times. Hybrid corn ears were harvested at 31% moisture and then had their drying postponed for 0, 12, 24 and 36 h, while subjected to temperatures of 30, 40, 50 and 60 °C. The physiological quality was evaluated after 0, 4, 8 and 12 months of storage. A completely randomized design was employed, in a 4 x 4 x 4 factorial scheme, with four replications. In addition, a study was performed in a seed-processing unit, reporting the average waiting time before drying and the temperatures of all loads of a corn hybrid received at the facility. The physiological quality was not affected by temperatures below 40 °C, considering 36 h of waiting before drying. At 50 ºC during the drying delay, the germination was impaired 36 h afterward, and the vigor was compromised after 24 h, with the damage effects intensifying as the storage advanced. At the temperature of 60 ºC, the deficits in germination and vigor occurred within the first hours of drying delay.

scholarly journals Solving the Traveling Salesman Problem on the D-Wave Quantum Computer

2021 ◽  
Vol 9 ◽  
Author(s):  
Siddharth Jain
Keyword(s):  
Combinatorial Optimization ◽  
Traveling Salesman Problem ◽  
Quantum Computer ◽  
Traveling Salesman ◽  
Hard Problem ◽  
Problem Size ◽  
Quadratic Unconstrained Binary Optimization ◽  
Np Hard Problem ◽  
The Traveling Salesman Problem ◽  
D Wave

The traveling salesman problem is a well-known NP-hard problem in combinatorial optimization. This paper shows how to solve it on an Ising Hamiltonian based quantum annealer by casting it as a quadratic unconstrained binary optimization (QUBO) problem. Results of practical experiments are also presented using D-Wave’s 5,000 qubit Advantage 1.1 quantum annealer and the performance is compared to a classical solver. It is found the quantum annealer can only handle a problem size of 8 or less nodes and its performance is subpar compared to the classical solver both in terms of time and accuracy.

scholarly journals A QUBO Formulation of Minimum Multicut Problem Instances in Trees for D-Wave Quantum Annealers

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
William Cruz-Santos ◽  
Salvador E. Venegas-Andraca ◽  
Marco Lanzagorta
Keyword(s):  
Optimization Problems ◽  
Theoretical Computer Science ◽  
Scaling Analysis ◽  
Quantum Annealing ◽  
Theoretical Computer ◽  
Combinatorial Optimization Problems ◽  
Hard Problems ◽  
Problem Instances ◽  
Annealing Algorithms ◽  
D Wave

AbstractQuantum annealing algorithms were introduced to solve combinatorial optimization problems by taking advantage of quantum fluctuations to escape local minima in complex energy landscapes typical of NP − hard problems. In this work, we propose using quantum annealing for the theory of cuts, a field of paramount importance in theoretical computer science. We have proposed a method to formulate the Minimum Multicut Problem into the QUBO representation, and the technical difficulties faced when embedding and submitting a problem to the quantum annealer processor. We show two constructions of the quadratic unconstrained binary optimization functions for the Minimum Multicut Problem and we review several tradeoffs between the two mappings and provide numerical scaling analysis results from several classical approaches. Furthermore, we discuss some of the expected challenges and tradeoffs in the implementation of our mapping in the current generation of D-Wave machines.

scholarly journals Smoothing Algorithm for Planar and Surface Mesh Based on Element Geometric Deformation

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Shuli Sun ◽  
Minglei Zhang ◽  
Zhihong Gou
Keyword(s):  
Weighted Average ◽  
Processing Unit ◽  
Smoothing Algorithm ◽  
Surface Mesh ◽  
Polygonal Mesh ◽  
Second Stage ◽  
Geometric Deformation ◽  
Error Metric ◽  
The Individual

Smoothing is one of the basic procedures for improvement of mesh quality. In this paper, a novel and efficient smoothing approach for planar and surface mesh based on element geometric deformation is developed. The presented approach involves two main stages. The first stage is geometric deformation of all the individual elements through a specially designed two-step stretching-shrinking operation (SSO), which is performed by moving the vertices of each element according to a certain rule in order to get better shape of the element. The second stage is to determine the position of each node of the mesh by a weighted average strategy according to quality changes of its adjacent elements. The suggested SSO-based smoothing algorithm works efficiently for triangular mesh and can be naturally expanded to quadrilateral mesh, arbitrary polygonal mesh, and mixed mesh. Combined with quadratic error metric (QEM), this approach may be also applied to improve the quality of surface mesh. The proposed method is simple to program and inherently very suitable for parallelization, especially on graphic processing unit (GPU). Results of numerical experiments demonstrate the effectiveness and potential of this method.

D-Wave and predecessors: From simulated to quantum annealing

2014 ◽  
Vol 12 (03) ◽  
pp. 1430002 ◽  
Author(s):  
Eliahu Cohen ◽  
Boaz Tamir
Keyword(s):  
Genetic Algorithm ◽  
Image Processing ◽  
Large Scale ◽  
Quantum Computer ◽  
Research Area ◽  
Hill Climbing ◽  
Quantum Annealing ◽  
Challenging Research ◽  
Computer Based ◽  
D Wave

On May 2011, D-Wave Systems Inc. announced "D-Wave One", as "the world's first commercially available quantum computer". No wonder this adiabatic quantum computer based on 128-qubit chip-set provoked an immediate controversy. Over the last 40 years, quantum computation has been a very promising yet challenging research area, facing major difficulties producing a large scale quantum computer. Today, after Google has purchased "D-Wave Two" containing 512 qubits, criticism has only increased. In this work, we examine the theory underlying the D-Wave, seeking to shed some light on this intriguing quantum computer. Starting from classical algorithms such as Metropolis algorithm, genetic algorithm (GA), hill climbing and simulated annealing, we continue to adiabatic computation and quantum annealing towards better understanding of the D-Wave mechanism. Finally, we outline some applications within the fields of information and image processing. In addition, we suggest a few related theoretical ideas and hypotheses.

On maximum leaf trees and connections to connected maximum cut problems

2018 ◽  
Vol 129 ◽  
pp. 31-34 ◽  
Author(s):  
Rajiv Gandhi ◽  
Mohammad Taghi Hajiaghayi ◽  
Guy Kortsarz ◽  
Manish Purohit ◽  
Kanthi Sarpatwar
Keyword(s):  
Maximum Cut ◽  
Cut Problems
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