Minor-Embedding in Adiabatic Quantum Computation: I. The Parameter Setting Problem

Details Minor-Embedding in Adiabatic Quantum Computation: I. The Parameter Setting Problem Minor-Embedding in Adiabatic Quantum Computation: I. The Parameter Setting Problem

2008-04-30

arxiv.org/abs/0804.4884v1

Quantum Information Processing, 7, pp193--209, 2008

Physics

Quantum Physics

17 pages, 5 figures, submitted

Scientific paper

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.

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