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We estimate the critical thresholds of bond and site percolation onnonplanar, effectively two-dimensional graphs with chimera like topology. Thebuilding blocks of these graphs are complete and symmetric bipartite subgraphsof size $2n$, referred to as $K_{n,n}$ graphs. For the numerical simulations weuse an efficient union-find based algorithm and employ a finite-size scalinganalysis to obtain the critical properties for both bond and site percolation.We report the respective percolation thresholds for different sizes of thebipartite subgraph and verify that the associated universality class is that ofstandard two-dimensional percolation. For the canonical chimera graph used inthe D-Wave Systems Inc.~quantum annealer ($n = 4$), we discuss device failurein terms of network vulnerability, i.e., we determine the critical fraction ofqubits and couplers that can be absent due to random failures prior to losinglarge-scale connectivity throughout the device.

physical review. e

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