A quantum algorithm for track reconstruction in the LHCb vertex detector

TL;DR

This paper explores a quantum algorithm for particle track reconstruction in high-energy physics, aiming to improve computational efficiency using quantum computing techniques like the HHL algorithm, with potential exponential speedup over classical methods.

Contribution

It introduces a quantum algorithm for track reconstruction based on Hamiltonian minimization, demonstrating potential exponential speedup despite current quantum limitations.

Findings

Classical approach has quadratic scaling in time complexity.

Quantum algorithm shows potential for exponential speedup.

Limitations due to Hamiltonian simulation and readout are discussed.

Abstract

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.