TrackHHL: A Quantum Computing Algorithm for Track Reconstruction at the LHCb

¹ Department of Advanced Computing Sciences, Maastricht University, Maastricht, The Netherlands
² Gravitational Waves and Fundamental Physics, Maastricht University, Maastricht, The Netherlands
³ Instituto de Fisica Corpuscular, Centro Mixto Universidad de Valencia - CSIC, Valencia, Spain

^* e-mail: xenofon.chiotopoulos@maastrichtuniversity.nl
^** e-mail: Miriam.lucio@ific.uv.es
^*** e-mail: d.nicotra@maastrichtuniversity.nl
^**** e-mail: jacco.devries@maastrichtuniversity.nl
^† e-mail: kurt.driessens@maastrichtuniversity.nl
^‡ e-mail: m.merk@maastrichtuniversity.nl
^§ e-mail: m.winands@maastrichtuniversity.nl

Published online: 7 October 2025

Abstract

In the future high-luminosity LHC era, high-energy physics experiments face unprecedented computational challenges for event reconstruction. Employing the LHCb vertex locator as a case study we investigate a novel approach for charged particle track reconstruction. The algorithm hinges on minimizing an Ising-like Hamiltonian using matrix inversion. Solving this matrix inversion classically achieves reconstruction efficiencies akin to current stateof-the-art algorithms. Exploiting the Harrow-Hassidim-Lloyd (HHL) quantum algorithm for linear systems holds the promise of an exponential speedup in the number of input hits over its classical counterpart, contingent on the conditions of efficient quantum phase estimation (QPE) and effectively reading out the algorithm’s output. This contribution builds on previous work by Nicotra et al. [1] and strives to fulfill these conditions and further streamlines the algorithm’s circuit depth by a factor up to 10⁴. Our version of the HHL algorithm restricts the QPE precision to one bit, largely reducing circuit depth and addressing HHL’s readout issue. Furthermore, this allows for the implementation of a post-processing algorithm that reconstructs event Primary Vertices (PVs). The findings presented here aim to further illuminate the potential of harnessing quantum computing for the future of particle track reconstruction in high-energy physics.