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Melchert O, Katzgraber HG, Novotny MA. Site- and bond-percolation thresholds in K_{n,n}-based lattices: Vulnerability of quantum annealers to random qubit and coupler failures on chimera topologies. Phys Rev E. 2016;93:042128doi: 10.1103/PhysRevE.93.042128.
Melchert, O., Katzgraber, H. G., & Novotny, M. A. (2016). Site- and bond-percolation thresholds in K_{n,n}-based lattices: Vulnerability of quantum annealers to random qubit and coupler failures on chimera topologies. Physical review. E, 93042128. https://doi.org/10.1103/PhysRevE.93.042128
Melchert, O, et al. "Site- and bond-percolation thresholds in K_{n,n}-based lattices: Vulnerability of quantum annealers to random qubit and coupler failures on chimera topologies." Physical review. E vol. 93 (2016): 042128. doi: https://doi.org/10.1103/PhysRevE.93.042128
Melchert O, Katzgraber HG, Novotny MA. Site- and bond-percolation thresholds in K_{n,n}-based lattices: Vulnerability of quantum annealers to random qubit and coupler failures on chimera topologies. Phys Rev E. 2016 Apr;93:042128. doi: 10.1103/PhysRevE.93.042128. Epub 2016 Apr 25. PMID: 27176275.
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Phys Rev E. 2016 Apr;93:042128. doi: 10.1103/PhysRevE.93.042128. Epub 2016 Apr 25.

Site- and bond-percolation thresholds in K_{n,n}-based lattices: Vulnerability of quantum annealers to random qubit and coupler failures on chimera topologies.

Physical review. E

O Melchert, Helmut G Katzgraber, M A Novotny

Affiliations

  1. Department of Physics and Astronomy, Texas A&M University, College Station, Texas 77843-4242, USA.
  2. Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA.
  3. Applied Mathematics Research Centre, Coventry University, Coventry, CV1 5FB, England.
  4. Department of Physics and Astronomy, Mississippi State University, Mississippi State, Mississippi 39762-5167, USA.
  5. HPC2 Center for Computational Sciences, Mississippi State University, Mississippi State, Mississippi 39762-5167, USA.

PMID: 27176275 DOI: 10.1103/PhysRevE.93.042128

Abstract

We estimate the critical thresholds of bond and site percolation on nonplanar, effectively two-dimensional graphs with chimeralike topology. The building blocks of these graphs are complete and symmetric bipartite subgraphs of size 2n, referred to as K_{n,n} graphs. For the numerical simulations we use an efficient union-find-based algorithm and employ a finite-size scaling analysis to obtain the critical properties for both bond and site percolation. We report the respective percolation thresholds for different sizes of the bipartite subgraph and verify that the associated universality class is that of standard two-dimensional percolation. For the canonical chimera graph used in the D-Wave Systems Inc. quantum annealer (n=4), we discuss device failure in terms of network vulnerability, i.e., we determine the critical fraction of qubits and couplers that can be absent due to random failures prior to losing large-scale connectivity throughout the device.

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