article

Fast clique minor generation in Chimera qubit connectivity graphs

Authors:

Andrew D. King,

Aidan RoyAuthors Info & Claims

Quantum Information Processing, Volume 15, Issue 1

Pages 495 - 508

https://doi.org/10.1007/s11128-015-1150-6

Published: 01 January 2016 Publication History

Abstract

The current generation of D-Wave quantum annealing processor is designed to minimize the energy of an Ising spin configuration whose pairwise interactions lie on the edges of a Chimera graph $${\mathcal {C}}_{M,N,L}$$CM,N,L. In order to solve an Ising spin problem with arbitrary pairwise interaction structure, the corresponding graph must be minor-embedded into a Chimera graph. We define a combinatorial class of native clique minors in Chimera graphs with vertex images of uniform, near minimal size and provide a polynomial-time algorithm that finds a maximum native clique minor in a given induced subgraph of a Chimera graph. These minors allow improvement over recent work and have immediate practical applications in the field of quantum annealing.

References

[1]

Albash, T., Vinci, W., Mishra, A., Warburton, P.A., Lidar, D.A.: Consistency tests of classical and quantum models for a quantum annealer. Phys. Rev. A 91(4), 042,314 (2015)

[2]

Berkley, A.J., Johnson, M.W., Bunyk, P., Harris, R., Johansson, J., Lanting, T., Ladizinsky, E., Tolkacheva, E., Amin, M.H.S., Rose, G.: A scalable readout system for a superconducting adiabatic quantum optimization system. Supercond. Sci. Technol. 23(10), 105,014 (2010)

[3]

Boixo, S., Smelyanskiy, V.N., Shabani, A., Isakov, S.V., Dykman, M., Denchev, V.S., Amin, M., Smirnov, A., Mohseni, M., Neven, H.: Computational role of collective tunneling in a quantum annealer. arXiv preprint arXiv:1411.4036 (2014)

[4]

Cai, J., Macready, W., Roy, A.: A practical heuristic for finding graph minors. arXiv preprint arXiv:1406.2741 (2014)

[5]

Choi, V.: Minor-embedding in adiabatic quantum computation: I. The parameter setting problem. Quantum Inf. Process. 7(5), 193---209 (2008)

Digital Library

[6]

Choi, V.: Minor-embedding in adiabatic quantum computation: II. Minor-universal graph design. Quantum Inf. Process. 10(3), 343---353 (2011)

Digital Library

[7]

Das, A., Chakrabarti, B.K.: Colloquium: quantum annealing and analog quantum computation. Rev. Mod. Phys. 80, 1061---1081 (2008)

[8]

Dickson, N., et al.: Thermally assisted quantum annealing of a 16-qubit problem. Nature Communications 4(May), 1903 (2013). URL http://www.ncbi.nlm.nih.gov/ /23695697

[9]

Dziarmaga, J.: Dynamics of a quantum phase transition: exact solution of the quantum ising model. Phys. Rev. Lett. 95(24), 245,701 (2005)

[10]

Farhi, E., Goldstone, J., Gutmann, S., Sipser, M.: Quantum computation by adiabatic evolution (2000). URL arXiv:quant-ph/0001106

[11]

Finilla, A.B., Gomez, M.A., Sebenik, C., Doll, D.J.: Quantum annealing: a new method for minimizing multidimensional functions. Chem. Phys. Lett. 219, 343---348 (1994)

[12]

Harris, R., Johansson, J., Berkley, A.J., Johnson, M.W., Lanting, T., Han, S., Bunyk, P., Ladizinsky, E., Oh, T., Perminov, I., Tolkacheva, E., Uchaikin, S., Chapple, E.M., Enderud, C., Rich, C., Thom, M., Wang, J., Wilson, B., Rose, G.: Experimental demonstration of a robust and scalable flux qubit. Phys. Rev. B 81, 134,510 (2010)

[13]

Johnson, M., Amin, M., Gildert, S., Lanting, T., Hamze, F., Dickson, N., Harris, R., Berkley, A., Johansson, J., Bunyk, P., et al.: Quantum annealing with manufactured spins. Nature 473(7346), 194---198 (2011)

[14]

Kadowaki, T., Nishimori, H.: Quantum annealing in the transverse Ising model. Phys. Rev. E 58(5), 5355 (1998)

[15]

Katzgraber, H., Hamze, F., Andrist, R.: Glassy Chimeras could be blind to quantum speedup: designing better benchmarks for quantum annealing machines. Phys. Rev. X 4(2), 021,008 (2014)

[16]

King, A.D., McGeoch, C.C.: Algorithm engineering for a quantum annealing platform. arXiv preprint arXiv:1410.2628 (2014)

[17]

Klymko, C., Sullivan, B.D., Humble, T.S.: Adiabatic quantum programming: minor embedding with hard faults. Quantum Inf. Process. 13(3), 709---729 (2014)

Digital Library

[18]

Perdomo-Ortiz, A., Fluegemann, J., Biswas, R., Smelyanskiy, V.N.: A performance estimator for quantum annealers: gauge selection and parameter setting. arXiv preprint arXiv:1503.01083 (2015)

[19]

Santoro, G.E., Tosatti, E.: Optimization using quantum mechanics: quantum annealing through adiabatic evolution. J. Phys. A Math. Gen. 39(36), R393 (2006)

[20]

Vatter, V., Waton, S.: On points drawn from a circle. Electronic J. Comb. 18(1), P223 (2011)

[21]

Venturelli, D., Mandrà, S., Knysh, S., O'Gorman, B., Biswas, R., Smelyanskiy, V.: Quantum optimization of fully-connected spin glasses. arXiv preprint arXiv:1406.7553 (2014)

[22]

Young, K., Blume-Kohout, R., Lidar, D.: Adiabatic quantum optimization with the wrong Hamiltonian. Phys. Rev. A 88(6), 062,314 (2013)

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Teramoto KKugaya MKudo STakenaga YYamamoto Y(2024)Approximate Block Diagonalization of Symmetric Matrices Using Quantum AnnealingProceedings of the International Conference on High Performance Computing in Asia-Pacific Region10.1145/3635035.3635044(47-54)Online publication date: 18-Jan-2024
https://dl.acm.org/doi/10.1145/3635035.3635044
Gilbert VLouise S(2024)Quantum Annealers Chain Strengths: A Simple Heuristic to Set Them AllComputational Science – ICCS 202410.1007/978-3-031-63778-0_21(292-306)Online publication date: 2-Jul-2024
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Raymond JStevanovic RBernoudy WBoothby KMcGeoch CBerkley AFarré PPasvolsky JKing A(2023)Hybrid Quantum Annealing for Larger-than-QPU Lattice-structured ProblemsACM Transactions on Quantum Computing10.1145/35793684:3(1-30)Online publication date: 8-Apr-2023
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Fast clique minor generation in Chimera qubit connectivity graphs
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
2. Theory of computation

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cover image Quantum Information Processing

Quantum Information Processing Volume 15, Issue 1

January 2016

591 pages

ISSN:1570-0755

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Copyright © Copyright © 2016 Springer Science+Business Media New York.

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Kluwer Academic Publishers

United States

Publication History

Published: 01 January 2016

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Cited By

Teramoto KKugaya MKudo STakenaga YYamamoto Y(2024)Approximate Block Diagonalization of Symmetric Matrices Using Quantum AnnealingProceedings of the International Conference on High Performance Computing in Asia-Pacific Region10.1145/3635035.3635044(47-54)Online publication date: 18-Jan-2024
https://dl.acm.org/doi/10.1145/3635035.3635044
Gilbert VLouise S(2024)Quantum Annealers Chain Strengths: A Simple Heuristic to Set Them AllComputational Science – ICCS 202410.1007/978-3-031-63778-0_21(292-306)Online publication date: 2-Jul-2024
https://dl.acm.org/doi/10.1007/978-3-031-63778-0_21
Raymond JStevanovic RBernoudy WBoothby KMcGeoch CBerkley AFarré PPasvolsky JKing A(2023)Hybrid Quantum Annealing for Larger-than-QPU Lattice-structured ProblemsACM Transactions on Quantum Computing10.1145/35793684:3(1-30)Online publication date: 8-Apr-2023
https://dl.acm.org/doi/10.1145/3579368
Pinilla JWilton SWolf FShende SCulhane CAlam SJagode H(2022)Positive-phase temperature scaling for quantum-assisted boltzmann machine trainingProceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis10.5555/3571885.3571975(1-12)Online publication date: 13-Nov-2022
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Serra THuang TRaghunathan ABergman D(2022)Template-Based Minor Embedding for Adiabatic Quantum OptimizationINFORMS Journal on Computing10.1287/ijoc.2021.106534:1(427-439)Online publication date: 1-Jan-2022
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Kim MVenturelli DKaewell JJamieson K(2022)Warm-started quantum sphere decoding via reverse annealing for massive IoT connectivityProceedings of the 28th Annual International Conference on Mobile Computing And Networking10.1145/3495243.3560516(1-14)Online publication date: 14-Oct-2022
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Jünger MLobe EMutzel PReinelt GRendl FRinaldi GStollenwerk T(2021)Quantum Annealing versus Digital ComputingACM Journal of Experimental Algorithmics10.1145/345960626(1-30)Online publication date: 9-Jul-2021
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Codognet P(2021)Constraint Solving by Quantum Annealing50th International Conference on Parallel Processing Workshop10.1145/3458744.3473364(1-10)Online publication date: 9-Aug-2021
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Ushijima-Mwesigwa HShaydulin RNegre CMniszewski SAlexeev YSafro I(2021)Multilevel Combinatorial Optimization across Quantum ArchitecturesACM Transactions on Quantum Computing10.1145/34256072:1(1-29)Online publication date: 13-Feb-2021
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Nath RThapliyal HHumble T(2021)A Review of Machine Learning Classification Using Quantum Annealing for Real-World ApplicationsSN Computer Science10.1007/s42979-021-00751-02:5Online publication date: 3-Jul-2021
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