Variational Quantum Algorithms for Particle Track Reconstruction

📝 Abstract

Quantum Computing is a rapidly developing field with the potential to tackle the increasing computational challenges faced in high-energy physics. In this work, we explore the potential and limitations of variational quantum algorithms in solving the particle track reconstruction problem. We present an analysis of two distinct formulations for identifying straight-line tracks in a multilayer detection system, inspired by the LHCb vertex detector. The first approach is formulated as a ground-state energy problem, while the second approach is formulated as a system of linear equations. This work addresses one of the main challenges when dealing with variational quantum algorithms on general problems, namely designing an expressive and efficient quantum ansatz working on tracking events with fixed detector geometry. For this purpose, we employed a quantum architecture search method based on Monte Carlo Tree Search to design the quantum circuits for different problem sizes. We provide experimental results to test our approach on both formulations for different problem sizes in terms of performance and computational cost.

💡 Analysis

Quantum Computing is a rapidly developing field with the potential to tackle the increasing computational challenges faced in high-energy physics. In this work, we explore the potential and limitations of variational quantum algorithms in solving the particle track reconstruction problem. We present an analysis of two distinct formulations for identifying straight-line tracks in a multilayer detection system, inspired by the LHCb vertex detector. The first approach is formulated as a ground-state energy problem, while the second approach is formulated as a system of linear equations. This work addresses one of the main challenges when dealing with variational quantum algorithms on general problems, namely designing an expressive and efficient quantum ansatz working on tracking events with fixed detector geometry. For this purpose, we employed a quantum architecture search method based on Monte Carlo Tree Search to design the quantum circuits for different problem sizes. We provide experimental results to test our approach on both formulations for different problem sizes in terms of performance and computational cost.

📄 Content

Variational Quantum Algorithms for Particle Track Reconstruction Vincenzo Lipardi1 †[0009−0000−3243−7969], Xenofon Chiotopoulos1,2,3 †[0009−0006−5762−6559], Jacco A. de Vries2,3[0000−0003−4712−9816], Domenica Dibenedetto1[0000−0002−2538−3170], Kurt Driessens1[0000−0001−7871−2495], Marcel Merk 2,3[0000−0003−0818−4695], and Mark H.M. Winands1[0000−0002−0125−0824] 1 Department of Advanced Computing Sciences, Maastricht University, The Netherlands 2 Gravitational Waves and Fundamental Physics, Maastricht University, The Netherlands {vincenzo.lipardi, xenofon.chiotopoulos}@maastrichtuniversity.nl 3 Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands Abstract. Quantum Computing is a rapidly developing field with the potential to tackle the increasing computational challenges faced in high- energy physics. In this work, we explore the potential and limitations of variational quantum algorithms in solving the particle track recon- struction problem. We present an analysis of two distinct formulations for identifying straight-line tracks in a multilayer detection system, in- spired by the LHCb vertex detector. The first approach is formulated as a ground-state energy problem, while the second approach is formu- lated as a system of linear equations. This work addresses one of the main challenges when dealing with variational quantum algorithms on general problems, namely designing an expressive and efficient quantum ansatz working on tracking events with fixed detector geometry. For this purpose, we employed a quantum architecture search method based on Monte Carlo Tree Search to design the quantum circuits for different problem sizes. We provide experimental results to test our approach on both formulations for different problem sizes in terms of performance and computational cost. Keywords: Variational Quantum Algorithms · Particle Track Recon- struction · Monte Carlo Tree Search · Quantum Ansatz Search. 1 Introduction In large-scale particle physics experiments, particles are collided at high energies and at high frequencies of 40 MHz, in order to study the fundamental forces of nature. In a single collision event, hundreds of new particles are simultaneously produced and traverse through sensitive detection layers where they deposit † These authors contributed equally to this work. The order of the first two authors has been chosen by flipping a quantum coin. arXiv:2511.11397v1 [quant-ph] 14 Nov 2025 2 Lipardi et al. small amounts of energy, resulting in so-called hits in the detectors. These hits are then reconstructed with fast algorithms into particle trajectories or tracks that are used in subsequent analyses. In the upcoming High Luminosity phase of the Large Hadron Collider (LHC), the number of simultaneous collisions will increase significantly leading to the production of unprecedented data volumes to be processed. The increase in complexity presents a challenge still to be re- solved, since the track reconstruction task scales to the power of 2-3 with the number of hits per layer. Various approaches have been pursued [14], at the time of writing the most per- formant approach is based on GPU parallel track reconstruction of events [12]. There have been attempts to leverage quantum computing to solve the track- ing problem. As tracking can be expressed as a Quadratic Unconstrained Binary Optimization (QUBO) problem many quantum algorithms can be applied. Some popular approaches are; Quantum Graph Neural Networks [11,19,41], quantum annealing [3,35], quantum annealing-inspired algorithms [31] and Variational Quantum Eigensolver (VQE) using a sub-QUBO formulation of the problem and tested it on real hardware [18]. Moreover, the tracking problem has been mapped to a linear system of equations and in [29] the authors prove that it ful- fills all the properties necessary to employ the Harrow–Hassidim–Lloyd (HHL) algorithm, which gives theoretical guarantees for an exponential advantage com- pared to classical techniques in terms of computational complexity. Although experimental results have shown promising results, a more extensive application of the HHL algorithm is still unfeasible on Near Intermediate-Scale Quantum (NISQ) devices [33]. In this article, we employ the hardware-tailored approach of the Variational Quantum Algorithms (VQAs) for the particle tracking problem, that allows con- sideration of the user’s available hardware specifications. We address one of the main limitations of these methods, that is the choice of the quantum circuit ansatz [7], as also highlighted for our specific problem in [18]. VQAs are hybrid quantum-classical algorithms where the problem of interest is encoded into an optimization task over parameterized quantum circuits. The choice of quantum circuit to optimize on, known as ansatz, significantly affects the performance of the algorithm [7]. In this context, it the automatic design of ansatz for VQA emerged as a relevant research direction, known

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