Site- and bond-percolation thresholds inKn,n-based lattices: Vulnerability of quantum annealers to random qubit and coupler failures on chimera topologies

O. Melchert, Helmut G. Katzgraber, M. A. Novotny
2016 Physical review. E  
We estimate the critical thresholds of bond and site percolation on nonplanar, effectively two-dimensional graphs with chimera like 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
more » ... ds 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.
doi:10.1103/physreve.93.042128 pmid:27176275 fatcat:6ucl4xp22ng7lctkx7f5mdesry