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

TL;DR

This paper addresses the parameter setting problem in minor-embedding for adiabatic quantum computation, crucial for solving QUBO problems on quantum hardware, and demonstrates its application to the maximum independent set problem.

Contribution

It focuses on the parameter setting aspect of minor-embedding, providing insights essential for designing adiabatic algorithms and quantum architectures.

Findings

Demonstrated the embedded Ising Hamiltonian for MIS problem

Clarified the parameter setting process in minor-embedding

Discussed related algorithmic problems for AQC design

Abstract

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.