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Evaluation of Quantum and Hybrid Solvers for Combinatorial Optimization

Amedeo Bertuzzi, Davide Ferrari, Antonio Manzalini, Michele Amoretti

TL;DR

The paper addresses energy optimization in cloud data centers by formulating the problem as a Constrained Quadratic Model (CQM) suitable for quantum and hybrid solvers. It benchmarks D-Wave quantum solvers and Leap's hybrid CQM workflow against classical CPLEX on a tree-structured topology, demonstrating that Leap's hybrid CQM can solve larger instances with competitive or better energy outcomes, while pure QPU approaches are constrained by current hardware. The study highlights the practical potential of hybrid quantum-classical approaches for large-scale combinatorial problems and provides guidance on when to favor hybrid workflows over purely classical or quantum methods. It also outlines avenues for future benchmarking across different topologies and problem classes to better delineate the strengths and limits of quantum-accelerated optimization.

Abstract

Academic and industrial sectors have been engaged in a fierce competition to develop quantum technologies, fueled by the explosive advancements in quantum hardware. While universal quantum computers have been shown to support up to hundreds of qubits, the scale of quantum annealers has reached three orders of magnitude (i.e., thousands of qubits). Therefore, quantum algorithms are becoming increasingly popular in a variety of fields, with optimization being one of the most prominent. This work aims to explore the topic of quantum optimization by comprehensively evaluating the technologies provided by D-Wave Systems. To do so, a model for the energy optimization of data centers is proposed as a benchmark. D-Wave quantum and hybrid solvers are compared, in order to identify the most suitable one for the considered application. To highlight its advantageous performance capabilities and associated solving potential, the selected D-Wave hybrid solver is then contrasted with CPLEX, a highly efficient classical solver.

Evaluation of Quantum and Hybrid Solvers for Combinatorial Optimization

TL;DR

The paper addresses energy optimization in cloud data centers by formulating the problem as a Constrained Quadratic Model (CQM) suitable for quantum and hybrid solvers. It benchmarks D-Wave quantum solvers and Leap's hybrid CQM workflow against classical CPLEX on a tree-structured topology, demonstrating that Leap's hybrid CQM can solve larger instances with competitive or better energy outcomes, while pure QPU approaches are constrained by current hardware. The study highlights the practical potential of hybrid quantum-classical approaches for large-scale combinatorial problems and provides guidance on when to favor hybrid workflows over purely classical or quantum methods. It also outlines avenues for future benchmarking across different topologies and problem classes to better delineate the strengths and limits of quantum-accelerated optimization.

Abstract

Academic and industrial sectors have been engaged in a fierce competition to develop quantum technologies, fueled by the explosive advancements in quantum hardware. While universal quantum computers have been shown to support up to hundreds of qubits, the scale of quantum annealers has reached three orders of magnitude (i.e., thousands of qubits). Therefore, quantum algorithms are becoming increasingly popular in a variety of fields, with optimization being one of the most prominent. This work aims to explore the topic of quantum optimization by comprehensively evaluating the technologies provided by D-Wave Systems. To do so, a model for the energy optimization of data centers is proposed as a benchmark. D-Wave quantum and hybrid solvers are compared, in order to identify the most suitable one for the considered application. To highlight its advantageous performance capabilities and associated solving potential, the selected D-Wave hybrid solver is then contrasted with CPLEX, a highly efficient classical solver.
Paper Structure (19 sections, 2 equations, 4 figures, 6 tables)

This paper contains 19 sections, 2 equations, 4 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Preliminary Concepts
  3. Combinatorial Optimization Problems
  4. Adiabatic Quantum Computation
  5. Problem Statement
  6. Topology and ILP Model
  7. D-Wave Solvers
  8. QPU Structure
  9. Quantum Solvers
  10. Hybrid Solvers
  11. Hybrid Workflow Solvers
  12. Leap's Hybrid Solvers
  13. Results
  14. Implementation
  15. Experimental Setup
  16. ...and 4 more sections

Figures (4)

  • Figure 1: Servers and switches connected in a complex tree topology
  • Figure 2: The full quantum methodology: the Solver API (front-end) is directly connected to the QPU (back-end).
  • Figure 3: Example of hybrid workflow solver architecture.
  • Figure 4: Generic flow structure of a Leap's hybrid solver.