Multilevel Combinatorial Optimization Across Quantum Architectures

TL;DR

This paper proposes a multilevel framework for hybrid quantum-classical algorithms to solve large-scale combinatorial optimization problems, demonstrating its effectiveness on quantum hardware with promising results.

Contribution

It introduces a multilevel approach for hybrid quantum-classical algorithms applied to combinatorial optimization, utilizing quantum processors for local search.

Findings

Quantum local search achieves solutions comparable to classical solvers.

The approach scales to larger graphs than current quantum hardware size.

Hybrid algorithms outperform some existing methods in solution quality.

Abstract

Emerging quantum processors provide an opportunity to explore new approaches for solving traditional problems in the post Moore's law supercomputing era. However, the limited number of qubits makes it infeasible to tackle massive real-world datasets directly in the near future, leading to new challenges in utilizing these quantum processors for practical purposes. Hybrid quantum-classical algorithms that leverage both quantum and classical types of devices are considered as one of the main strategies to apply quantum computing to large-scale problems. In this paper, we advocate the use of multilevel frameworks for combinatorial optimization as a promising general paradigm for designing hybrid quantum-classical algorithms. In order to demonstrate this approach, we apply this method to two well-known combinatorial optimization problems, namely, the Graph Partitioning Problem, and the Community Detection Problem. We develop hybrid multilevel solvers with quantum local search on D-Wave's quantum annealer and IBM's gate-model based quantum processor. We carry out experiments on graphs that are orders of magnitudes larger than the current quantum hardware size, and we observe results comparable to state-of-the-art solvers in terms of quality of the solution.