QUBO formulations for the graph isomorphism problem and related problems

Calude, Cristian S.; Dinneen, Michael J.; Hua, Richard

doi:10.1016/j.tcs.2017.04.016

Cited by 46 publications

(58 citation statements)

References 7 publications

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“…Motivated by the limited number of physical qubits in current hardware, we present an improved version of the QUBO formulation given in [14] and empirically compare their performance. Our experimental results indicate that the improved version is much more suitable for current hardware not only in terms of better embedding, but also has a higher probability of obtaining the correct answer when run on a quantum annealer.…”

Section: Graph Isomorphism Problemmentioning

confidence: 99%

“…For the sake of completeness, we will first introduce the QUBO formulation for the Graph Isomorphism Problem developed in [14]. Note that we assume that the two input graphs G 1 and G 2 have the same order and size.…”

Section: Qubo Formulation For the Graph Isomorphism Problem And Impromentioning

confidence: 99%

“…Note that we assume that the two input graphs G 1 and G 2 have the same order and size. Now suppose G 1 = (V 1 , E 2 ) and G 2 = (V 2 , E 2 ) are two graphs both of order n and size m. The objective function of [14] requires a total of n 2 logical qubits, one variable x i,j for each integer pair i and j where 0 ≤ i < n and 0 ≤ j < n . If x i,j = 1 then the vertex mapping maps v i in G 1 to v j in G 2 .…”

Section: Qubo Formulation For the Graph Isomorphism Problem And Impromentioning

confidence: 99%

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Improved QUBO Formulation of the Graph Isomorphism Problem

Hua

Dinneen

2019

SN COMPUT. SCI.

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In this paper, we provide a practically efficient QUBO formulation for the Graph Isomorphism Problem that is suitable for quantum annealers such as those produced by D-Wave. After proving the correctness of our new method, based on exploiting vertex degree classes, we did some experimental work on a D-Wave 2X computer. We observe that for all "hard" graphs of 6 vertices, we save around 50-95% of the number of required physical qubits over the standard QUBO formulation that was given earlier by Calude et al. (Theor Comput Sci 701:54-69, 2017). We also provide some theoretical analysis showing that, for two random graphs with the same degree sequence, our new method substantially improves in qubit savings as the number of vertices increases beyond 6.

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Section: Graph Isomorphism Problemmentioning

confidence: 99%

Section: Qubo Formulation For the Graph Isomorphism Problem And Impromentioning

confidence: 99%

Section: Qubo Formulation For the Graph Isomorphism Problem And Impromentioning

confidence: 99%

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Improved QUBO Formulation of the Graph Isomorphism Problem

Hua

Dinneen

2019

SN COMPUT. SCI.

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“…Ising and QUBO Objective Function For a problem to be solved by D-Wave, it must be mapped onto an Ising or QUBO objective function, which are defined respectively, as follows [Calude, 2017]:…”

Section: Optimization Modelsmentioning

confidence: 99%

“…In the Ising function, h i and J i,j are the same parameters that appear in H Ising , and in the QUBO function, Q is an upper-triangular N × N matrix of real coefficients which serve as weights. [Calude, 2017] Note that both equations take binary inputs (i.e. s ∈ {−1, 1} and x ∈ {0, 1}) which can be converted easily by the formula s = 2x − 1.…”

Section: Optimization Modelsmentioning

confidence: 99%

Portfolio Asset Identification Using Graph Algorithms on a Quantum Annealer

2018

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The Road to Quantum Computational Supremacy

Calude

2020

Springer Proceedings in Mathematics &Amp; Statistics

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We present an idiosyncratic view of the race for quantum computational supremacy. Google's approach and IBM challenge are examined. An unexpected side-effect of the race is the significant progress in designing fast classical algorithms. Quantum supremacy, if achieved, won't make classical computing obsolete.A hyper-fast quantum computer is the digital equivalent of a nuclear bomb; whoever possesses one will be able to shred any encryption and break any code in existence. 3 [44] 1 Fairy tales or more cautionary tales?Following the development of Shor's quantum algorithm [64] in 1994 and Grover's quantum algorithm [40] two years later, quantum computing was seen as a bright beacon in computer science, which led to a surge of theoretical and experimental results. The field captured the interest and imagination of the large public and media, and not surprisingly, unfounded claims about the power of quantum computing and its applications proliferated.A certain degree of pessimism began to infiltrate when experimental groups floundered while attempting to control more than a handful of qubits. Recently, a broad wave of ambitious industry-led research programmes in quantum computing-driven by D-Wave Systems, 4 the tech giants Google, IBM, Microsoft, Intel and startups like Rigetti Computing and Quantum Circuits Incorporated-has emerged 5 and bold claims about a future revolutionised by quantum computing are resurfacing.

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QUBO formulations for the graph isomorphism problem and related problems

Cited by 46 publications

References 7 publications

Improved QUBO Formulation of the Graph Isomorphism Problem

Improved QUBO Formulation of the Graph Isomorphism Problem

Portfolio Asset Identification Using Graph Algorithms on a Quantum Annealer

The Road to Quantum Computational Supremacy

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