Hybrid Meta-Solving for Practical Quantum Computing

TL;DR

The paper addresses the challenge of translating theoretical quantum advantages into practical optimization by introducing Hybrid Meta-Solving, a framework that decomposes problems into Meta-Solver Steps and assembles Solution Paths combining classical and quantum solvers. It formalizes Meta-Solver Concepts (Strategies, Steps, Paths) and implements them in the ProvideQ toolbox to enable semi-automatic input interpretation, solver selection, parallel execution, and backend management, creating a reusable platform for hybrid optimization. Evaluation on vehicle routing problems shows that state-of-the-art classical solvers (e.g., $QUBO$-reformulations and ILP/MILP flows) achieve near-optimal results, while quantum subroutines currently incur substantial overhead and often underperform in this setting, though the framework remains ready to exploit future quantum hardware. Collectively, the work provides a practical blueprint for building a hybrid optimization platform that can adapt to evolving quantum technologies, improve accessibility, and guide practitioners in selecting solution paths under varying trade-offs between quality and speed.

Abstract

The advent of quantum algorithms has initiated a discourse on the potential for quantum speedups for optimization problems. However, several factors still hinder a practical realization of the potential benefits. These include the lack of advanced, error-free quantum hardware, the absence of accessible software stacks for seamless integration and interaction, and the lack of methods that allow us to leverage the theoretical advantages to real-world use cases. This paper works towards the creation of an accessible hybrid software stack for solving optimization problems, aiming to create a fundamental platform that can utilize quantum technologies to enhance the solving process. We introduce a novel approach that we call Hybrid Meta-Solving, which combines classical and quantum optimization techniques to create customizable and extensible hybrid solvers. We decompose mathematical problems into multiple sub-problems that can be solved by classical or quantum solvers, and propose techniques to semi-automatically build the best solver for a given problem. Implemented in our ProvideQ toolbox prototype, Meta-Solving provides interactive workflows for accessing quantum computing capabilities. Our evaluation demonstrates the applicability of Meta-Solving in industrial use cases. It shows that we can reuse state-of-the-art classical algorithms and extend them with quantum computing techniques. Our approach is designed to be at least as efficient as state-of-the-art classical techniques, while having the potential to outperform them if future advances in the quantum domain are made.

Figures (7)

• Figure 1: Meta-Solver Strategy for Vehicle Routing Problems.
• Figure 2: Example process that visualizes how a user applies Meta-Solving.
• Figure 3: Overview of the Orchestration Unit that decomposes an algorithmic problem to execute a Solution Path, calls the associated Meta-Solver Steps, and then composes the results.
• Figure 4: Example Meta-Solver Strategy for Integer Linear Programs.
• Figure 5: User Interface mockup of the ProvideQ Toolbox. It combines the Vehicle Routing example from Figure \ref{['fig:ms_cvrp']} with the workflow from Figure \ref{['fig:process']}

Theorems & Definitions (3)

• Definition 3.1: Meta-Solver Strategy
• Definition 3.2: Meta-Solver Step
• Definition 3.3: Solution Path