Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Approximation algorithms for NP-complete problems on planar graphs
Journal of the ACM (JACM)
Graph minors. XIII: the disjoint paths problem
Journal of Combinatorial Theory Series B
Discrete Applied Mathematics
Short paths in expander graphs
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
How Powerful is Adiabatic Quantum Computation?
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
The quantum adiabatic optimization algorithm and local minima
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Adiabatic Quantum Computation is Equivalent to Standard Quantum Computation
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
The Complexity of the Local Hamiltonian Problem
SIAM Journal on Computing
Quantum Information & Computation
The complexity of quantum spin systems on a two-dimensional square lattice
Quantum Information & Computation
Minor-embedding in adiabatic quantum computation: II. Minor-universal graph design
Quantum Information Processing
Quantum Information & Computation
Quantum adiabatic machine learning
Quantum Information Processing
Experimental evaluation of an adiabiatic quantum system for combinatorial optimization
Proceedings of the ACM International Conference on Computing Frontiers
Adiabatic quantum programming: minor embedding with hard faults
Quantum Information Processing
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We show that the NP-hard quadratic unconstrained binary optimization (QUBO) problem on a graph G can be solved using an adiabatic quantum computer that implements an Ising spin-1/2 Hamiltonian, by reduction through minor-embedding of G in the quantum hardware graph U. There are two components to this reduction: embedding and parameter setting. The embedding problem is to find a minor-embedding G emb of a graph G in U, which is a subgraph of U such that G can be obtained from G emb by contracting edges. The parameter setting problem is to determine the corresponding parameters, qubit biases and coupler strengths, of the embedded Ising Hamiltonian. In this paper, we focus on the parameter setting problem. As an example, we demonstrate the embedded Ising Hamiltonian for solving the maximum independent set (MIS) problem via adiabatic quantum computation (AQC) using an Ising spin-1/2 system. We close by discussing several related algorithmic problems that need to be investigated in order to facilitate the design of adiabatic algorithms and AQC architectures.