Solving the Turbine Balancing Problem using Quantum Annealing

TL;DR

The paper tackles the NP-hard Turbine Balancing Problem in a single plane by formulating it as a Quadratic Unconstrained Binary Optimization (QUBO) with binary variables $x in {0,1}^n$ and objective $x^T Q x$. It benchmarks a classical rule-based heuristic against a D-Wave Quantum Annealer (Advantage_system4.1) on real-world and synthetic data. It shows that quantum hardware can significantly improve the heuristic’s solutions for small-scale instances, motivating the development of a quantum-inspired classical solver based on simulated annealing that achieves industrially acceptable performance across all datasets. Together, the results position QUBO-based turbine balancing as a practical early-quantum benchmark and demonstrate a viable pathway from quantum hardware to high-quality classical heuristics.

Abstract

Quantum computing has the potential for disruptive change in many sectors of industry, especially in materials science and optimization. In this paper, we describe how the Turbine Balancing Problem can be solved with quantum computing, which is the NP-hard optimization problem of analytically balancing rotor blades in a single plane as found in turbine assembly. Small yet relevant instances occur in industry, which makes the problem interesting for early quantum computing benchmarks. We model it as a Quadratic Unconstrained Binary Optimization problem and compare the performance of a classical rule-based heuristic and D-Wave Systems' Quantum Annealer Advantage_system4.1. In this case study, we use real-world as well as synthetic datasets and observe that the quantum hardware significantly improves an actively used heuristic's solution for small-scale problem instances with bare disk imbalance in terms of solution quality. Motivated by this performance gain, we subsequently design a quantum-inspired classical heuristic based on simulated annealing that achieves extremely good results on all given problem instances, essentially solving the optimization problem sufficiently well for all considered datasets, according to industrial requirements.