Graph minors. XIII: the disjoint paths problem
Journal of Combinatorial Theory Series B
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
Discrete Applied Mathematics
Short paths in expander graphs
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Minor-embedding in adiabatic quantum computation: I. The parameter setting problem
Quantum Information Processing
Approximation Algorithms for Treewidth
Algorithmica
Minor-embedding in adiabatic quantum computation: II. Minor-universal graph design
Quantum Information Processing
Faster parameterized algorithms for minor containment
Theoretical Computer Science
Quantum adiabatic machine learning
Quantum Information Processing
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Adiabatic quantum programming defines the time-dependent mapping of a quantum algorithm into an underlying hardware or logical fabric. An essential step is embedding problem-specific information into the quantum logical fabric. We present algorithms for embedding arbitrary instances of the adiabatic quantum optimization algorithm into a square lattice of specialized unit cells. These methods extend with fabric growth while scaling linearly in time and quadratically in footprint. We also provide methods for handling hard faults in the logical fabric without invoking approximations to the original problem and illustrate their versatility through numerical studies of embeddability versus fault rates in square lattices of complete bipartite unit cells. The studies show that these algorithms are more resilient to faulty fabrics than naive embedding approaches, a feature which should prove useful in benchmarking the adiabatic quantum optimization algorithm on existing faulty hardware.