Quantum Information Processing

, Volume 7, Issue 5, pp 193–209 | Cite as

Minor-embedding in adiabatic quantum computation: I. The parameter setting problem

  • Vicky ChoiEmail author


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.


Adiabatic quantum computation Graph minor Quadratic unconstrained binary optimization Ising Hamiltonian 


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© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.D-Wave Systems Inc.BurnabyCanada

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