# Accuracy and minor embedding in subqubo decomposition with fully connected large problems: a case study about the number partitioning problem

## TL;DR

This paper evaluates the D-Wave 2000Q quantum annealer's ability to solve large, complex Number Partitioning Problems using a hybrid quantum-classical approach, demonstrating successful solution finding through parameter tuning.

## Contribution

It introduces a hybrid quantum-classical workflow for large, complex problems and shows how to optimize quantum annealing parameters for better solutions.

## Key findings

- Successful solution of complex instances with quantum annealer
- Parameter tuning improves solution quality in worst cases
- Scalability analysis of quantum-classical workflow

## Abstract

In this work we investigate the capabilities of a hybrid quantum-classical procedure to explore the solution space using the D-Wave $2000Q^{TM}$ Quantum Annealer device. Here we study the ability of the Quantum hardware to solve the Number Partitioning Problem, a well-known NP-Hard optimization model that poses some challenges typical of those encountered in real-world applications. This represents one of the most complex scenario in terms of qubits connectivity and, by increasing the input problem size, we analyse the scaling properties of the quantum-classical workflow. We find remarkable results in most instances of the model; for the most complex ones, we investigate further the D-Wave Hybrid suite. Specifically, we were able to find the optimal solutions even in the worst cases by fine-tuning the parameters that schedule the annealing time and allowing a pause in the annealing cycle.