High-energy physics is facing increasingly computational challenges in real-time event reconstruction for the near-future high-luminosity era. Using the LHCb vertex detector as a use-case, we explore a new algorithm for particle track reconstruction based on the minimisation of an Ising-like Hamiltonian with a linear algebra approach. The use of a classical matrix inversion technique results in tracking performance similar to the current state-of-the-art but with worse scaling complexity in time. To solve this problem, we also present an implementation as quantum algorithm, using the Harrow-Hassadim-Lloyd (HHL) algorithm: this approach can potentially provide an exponential speedup as a function of the number of input hits over its classical counterpart, in spite of limitations due to the well-known HHL Hamiltonian simulation and readout problems. The findings presented in this paper shed light on the potential of leveraging quantum computing for real-time particle track reconstruction in high-energy physics.
@article{arxiv.2308.00619,
title = {A quantum algorithm for track reconstruction in the LHCb vertex detector},
author = {Davide Nicotra and Miriam Lucio Martinez and Jacco Andreas de Vries and Marcel Merk and Kurt Driessens and Ronald Leonard Westra and Domenica Dibenedetto and Daniel Hugo Cámpora Pérez},
journal= {arXiv preprint arXiv:2308.00619},
year = {2025}
}