Optimal Sufficient Requirements on the Embedded Ising Problem in Polynomial Time

TL;DR

This paper analytically evaluates and optimizes the requirements for embedding Ising problems into quantum annealers, demonstrating polynomial-time solvability for certain standard embeddings by reducing the problem complexity.

Contribution

It introduces a linear optimization approach to determine sufficient embedding requirements, enabling polynomial-time solutions for specific Ising problem embeddings.

Findings

Optimization problem can be reduced from exponential to polynomial time.

Linear programming formulation addresses precision issues in quantum annealing.

Applicable to standard embedding where vertices induce trees.

Abstract

One of the central applications for quantum annealers is to find the solutions of Ising problems. Suitable Ising problems, however, need to be formulated such that they, on the one hand, respect the specific restrictions of the hardware and, on the other hand, represent the original problems which shall actually be solved. We evaluate sufficient requirements on such an embedded Ising problem analytically and transform them into a linear optimization problem. With an objective function aiming to minimize the maximal absolute problem parameter, the precision issues of the annealers are addressed. Due to the redundancy of several constraints, we can show that the formally exponentially large optimization problem can be reduced and finally solved in polynomial time for the standard embedding setting where the embedded vertices induce trees. This allows to formulate provably equivalent embedded Ising problems in a practical setup.