Open Access

ARTICLE

Comparative Study of CPLEX and D-Wave for Track Finding Resolution

Duy Dao¹, Hervé Kerivin², Philippe Lacomme^2,*, Bogdan Vulpescu³

1 Clermont-Auvergne-INP, Université Clermont-Auvergne, 1 rue de la Chébarde, Aubière, 63178, France[-2pc]
2 LIMOS—UMR CNRS 6158, Clermont-Auvergne-INP, Université Clermont-Auvergne, 1 rue de la Chébarde, Aubière, 63178, France
3 Laboratoire de Physique de Clermont Auvergne, Campus Universitaire des Cézeaux, 4 Avenue Blaise Pascal, Aubière, 63178, France

* Corresponding Author: Philippe Lacomme. Email:

Journal of Quantum Computing 2025, 7, 39-54. https://doi.org/10.32604/jqc.2025.064764

Received 23 February 2025; Accepted 29 April 2025; Issue published 30 May 2025

Abstract

Track finding is a complex optimization problem, originally introduced in particle physics for the reconstruction of the trajectories of particles. A track is typically composed of several consecutive segments, which together form a smooth curve without any bifurcations. In this paper, we investigate various modeling approaches to assess their effectiveness and impact when applied to track finding, using both quantum and classical methods. We present implementations of three classical models using CPLEX, two quantum models on actual D-Wave quantum computers, and one quantum model on a D-Wave simulator. The results show that, while CPLEX provides better results than D-Wave on small instances, D-Wave is able to propose solutions in shorter computation times for large instances, although the gap with the optimal solution tends to increase. To the best of our knowledge, this is the first numerical study comparing a non-quantum approach based on classical algorithms (Simplex and Branch and Bound) used in commercial software with a quantum approach offered by D-Wave. The results do not show the quantum supremacy typically expected, but they do demonstrate that quantum solutions can be competitive with classical approaches, and even more efficient than some classical modeling and solving methods.

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Keywords

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