Variational Quantum Algorithms for Particle Track Reconstruction

TL;DR

The paper addresses particle track reconstruction in high-energy physics by formulating two variational quantum algorithm (VQA) approaches: a ground-state energy problem via an Ising-like Hamiltonian $H_{VQE}$ and a linear-system problem via $H_{VQLS}$. It introduces an automated quantum ansatz search using Monte Carlo Tree Search to design hardware-tailored circuits and compares these formulations with noiseless simulations on a VELO-like toy detector, highlighting that VQE generally offers more favorable performance under fixed resources, while VQLS scales to larger problems with greater cost. The work demonstrates the potential and current limitations of VQAs for track reconstruction, showing that problem-specific circuit design and encoding are crucial for performance on NISQ devices and that domain-informed rollout strategies could yield further gains. Overall, it provides a pathway to hardware-aware quantum track reconstruction and motivates further development toward real-data, noise-resilient deployments and improved ansatz-search strategies.

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.

Figures (5)

• Figure 1: A full event example of the LHCb VELO detector. The white dots represent the detector hits and the blue lines are the reconstructed tracks. Credit: D. Nicotra.
• Figure 2: Graph representation of an event with 5 detector layers and 6 particles (Toy Model). The vertical lines represent the detection layers, and the red circles are the hits interconnected with doublets/segments. The full-color segments are part of the found tracks, the grey segments are combinatoric backgrounds. Where $S_i$ and $S_j$ are doublets with their value indicating if they are part of a track nicotra2023quantum.
• Figure 3: The goal in QAS is to define the ordered sequence of quantum gates $V_i(\theta_i)$ composing the variational state $V(\theta)\ket{0}$, which optimizes a given objective function $C$.
• Figure 4: Monte Carlo Tree Search scheme for quantum circuit design, taken from vincenzo. In our QAS framework, the action space is defined by sampling a discrete number of quantum circuit modifications from a continuous set of them.
• Figure 5: Experimental results for the problem with $n=4$ qubits .