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

TL;DR

This paper explores a quantum algorithm for particle track reconstruction at the LHCb, aiming to significantly speed up the process using HHL quantum linear system solving, with practical circuit optimizations and a focus on future high-energy physics applications.

Contribution

It introduces a streamlined, low-precision HHL quantum algorithm for track reconstruction, reducing circuit depth and addressing readout issues, advancing quantum computing applications in high-energy physics.

Findings

Classical approach achieves current state-of-the-art efficiency.

Quantum HHL algorithm offers potential exponential speedup under certain conditions.

Circuit depth reduced by a factor of up to 10,000 with low-precision QPE.

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 state-of-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 and strives to fulfill these conditions and further streamlines the algorithm's circuit depth by a factor up to $10^4$. 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.