2012
DOI: 10.1103/physreva.86.042310
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Solving the graph-isomorphism problem with a quantum annealer

Abstract: We propose a novel method using a quantum annealer -an analog quantum computer based on the principles of quantum adiabatic evolution -to solve the Graph Isomorphism problem, in which one has to determine whether two graphs are isomorphic (i.e., can be transformed into each other simply by a relabeling of the vertices). We demonstrate the capabilities of the method by analyzing several types of graph families, focusing on graphs with particularly high symmetry called strongly regular graphs (SRG's). We also sh… Show more

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Cited by 34 publications
(45 citation statements)
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“…Because CAM recall using orthogonal memories is expected to be well behaved, we use that case to test the fundamental performance of the D-Wave processor to recall stored memories. The remaining parameters are chosen from the following sets respectively, n ∈ {8, 12,16,20,24,28 For each parameter combination (n, m, θ), 100 problem instances are randomly generated as specified in Section 3.1 and utilizing one of the learning rules to encode the memories into a weight matrix. Each selected problem instance is then programmed and executed N = 1000 times on the D-Wave QPU to calculate the average recall accuracy c.…”
Section: Methodsmentioning
confidence: 99%
See 1 more Smart Citation
“…Because CAM recall using orthogonal memories is expected to be well behaved, we use that case to test the fundamental performance of the D-Wave processor to recall stored memories. The remaining parameters are chosen from the following sets respectively, n ∈ {8, 12,16,20,24,28 For each parameter combination (n, m, θ), 100 problem instances are randomly generated as specified in Section 3.1 and utilizing one of the learning rules to encode the memories into a weight matrix. Each selected problem instance is then programmed and executed N = 1000 times on the D-Wave QPU to calculate the average recall accuracy c.…”
Section: Methodsmentioning
confidence: 99%
“…This finite-temperature, open system model is expected to more accurately describe the dynamics underlying the QPU [8]. Nevertheless, several experimental tests of the D-Wave QPU have been carried out including applications of machine learning, binary classification, protein folding, graph analysis, and network analysis [9][10][11][12][13][14][15][16][17][18]. Demonstrations of enhanced performance using the D-Wave QPU have been found only for a few selected and highly contrived problem instances [19][20][21].…”
Section: Introductionmentioning
confidence: 99%
“…The distinguishing power of the algorithm increases with the number of walker moving along the graph; the technique, however, is not universal and there are non-isomorphic graphs that cannot be distinguished. A different approach, based on the Adiabatic Quantum Computation paradigm (AQC) [14,15], has been recently proposed in [16,17]. In order to distinguish nonisomorphic graphs, for example, Vinci et al look at the values assumed by a set non-isomorphism witnesses during the adiabatic evolution of the couple of graphs under investigation.…”
Section: Introductionmentioning
confidence: 99%
“…[1][2][3][4][5][6][7][8][9] This interest is due in a large part to demonstration of the underlying principles of quantum annealing in condensed matter systems 10 and the more recent development of a programmable annealing device by D-Wave Systems Inc. 11,12 Although the niobium superconducting quantum interference device (SQUIDs) which are the basic building blocks of the D-Wave annealer display limited coherence, it has been used to demonstrate that quantum tunneling is an exploitable resource in a computational setting. 13 Furthermore the development of annealers using aluminum SQUIDs with orders-of-magnitude longer coherence lifetimes 14 may enable further improvements in the computational performance of future quantum annealers.…”
Section: Introductionmentioning
confidence: 99%
“…[1][2][3][4][5][6][7][8][9] This interest is due in a large part to demonstration of the underlying principles of quantum annealing in condensed matter systems 10 and the more recent development of a programmable annealing device by D-Wave Systems Inc.…”
mentioning
confidence: 99%