Linearizing Binary Optimization Problems Using Variable Posets for Ising Machines

TL;DR

This paper introduces a novel linearization method for QUBO problems using variable posets, simplifying energy landscapes and enabling more efficient embedding into Ising machines for better optimization performance.

Contribution

The paper proposes a new linearization technique for QUBO problems using variable posets, improving embedding and solution quality on Ising machines.

Findings

Enhanced minor-embedding of QUBO problems.

Improved performance of Ising machines on linearized problems.

Reduced complexity of QUBO instances through linearization.

Abstract

Ising machines are next-generation computers expected to efficiently sample near-optimal solutions of combinatorial optimization problems. Combinatorial optimization problems are modeled as quadratic unconstrained binary optimization (QUBO) problems to apply an Ising machine. However, current state-of-the-art Ising machines still often fail to output near-optimal solutions due to the complicated energy landscape of QUBO problems. Furthermore, the physical implementation of Ising machines severely restricts the size of QUBO problems to be input as a result of limited hardware graph structures. In this study, we take a new approach to these challenges by injecting auxiliary penalties preserving the optimum, which reduces quadratic terms in QUBO objective functions. The process simultaneously simplifies the energy landscape of QUBO problems, allowing the search for near-optimal solutions, and makes QUBO problems sparser, facilitating encoding into Ising machines with restriction on the hardware graph structure. We propose linearization of QUBO problems using variable posets as an outcome of the approach. By applying the proposed method to synthetic QUBO instances and to multi-dimensional knapsack problems, we empirically validate the effects on enhancing minor-embedding of QUBO problems and the performance of Ising machines.