# Equation Planting: A Tool for Benchmarking Ising Machines

## TL;DR

This paper presents 'equation planting', a novel method for creating benchmark problems for Ising machines by transforming linear systems into Ising models, enabling better evaluation and understanding of these devices.

## Contribution

The paper introduces 'equation planting', a new technique to generate challenging benchmark problems for Ising machines from linear systems, aiding in performance assessment and mechanistic studies.

## Key findings

- Equation planting creates NP-hard-like problems from linear systems.
- The method helps evaluate Ising machines as optimizers and samplers.
- It provides insights into the operation of Ising devices.

## Abstract

We introduce a methodology for generating benchmark problem sets for Ising machines---devices designed to solve discrete optimization problems cast as Ising models. In our approach, linear systems of equations are cast as Ising cost functions. While linear systems are easily solvable, the corresponding optimization problems are known to exhibit some of the salient features of NP-hardness, such as strong exponential scaling of heuristic solvers' runtimes and extensive distances between ground and low-lying excited states. We show how the proposed technique, which we refer to as `equation planting,' can serve as a useful tool for evaluating the utility of Ising solvers functioning either as optimizers or as ground-state samplers. We further argue that equation-planted problems can be used to probe the mechanisms underlying the operation of Ising machines.