Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Graph minors. XIII: the disjoint paths problem
Journal of Combinatorial Theory Series B
A partial k-arboretum of graphs with bounded treewidth
Theoretical Computer Science
Discrete Applied Mathematics
Short paths in expander graphs
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Adiabatic Quantum Computation is Equivalent to Standard Quantum Computation
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Optimal universal graphs with deterministic embedding
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Simulating Quantum Computation by Contracting Tensor Networks
SIAM Journal on Computing
Minor-embedding in adiabatic quantum computation: I. The parameter setting problem
Quantum Information Processing
Adiabatic quantum programming: minor embedding with hard faults
Quantum Information Processing
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In Choi (Quantum Inf Process, 7:193---209, 2008), we introduced the notion of minor-embedding in adiabatic quantum optimization. A minor-embedding of a graph G in a quantum hardware graph U is a subgraph of U such that G can be obtained from it by contracting edges. In this paper, we describe the intertwined adiabatic quantum architecture design problem, which is to construct a hardware graph U that satisfies all known physical constraints and, at the same time, permits an efficient minor-embedding algorithm. We illustrate an optimal complete-graph-minor hardware graph. Given a family $${\mathcal{F}}$$ of graphs, a (host) graph U is called $${\mathcal{F}}$$ -minor-universal if for each graph G in $${\mathcal{F}, U}$$ contains a minor-embedding of G. The problem for designing a $${{\mathcal{F}}}$$ -minor-universal hardware graph U sparse in which $${{\mathcal{F}}}$$ consists of a family of sparse graphs (e.g., bounded degree graphs) is open.