The physics background and its relevance are presented in the science case which in turn leads to, and justifies, the ensuing plan for all aspects of the experiment: Our choice of experimental parameters allows (i) field strengths to be probed where the coupling to charges becomes non-perturbative and (ii) a precision to be achieved that permits a detailed comparison of the measured data with calculations. We will reach this hitherto inaccessible regime of quantum physics by analysing high-energy electron-photon and photon-photon interactions in the extreme environment provided by an intense laser focus. This Conceptual Design Report describes LUXE (Laser Und XFEL Experiment), an experimental campaign that aims to combine the high-quality and high-energy electron beam of the European XFEL with a powerful laser to explore the uncharted terrain of quantum electrodynamics characterised by both high energy and high intensity. These results can be used to build a future road map to further develop circuit-based hybrid quantum-classical graph neural networks. Also, we explore parametrized quantum circuits (PQC) with different expressibility and entangling capacities, and compare their training performance in order to quantify the expected benefits. We show that this hybrid model can perform similar to the classical approach. This work explores the possibility of converting a novel graph neural network model, that can optimally take into account the sparse nature of the tracking detector data and their complex geometry, to a hybrid quantum-classical graph neural network that benefits from using variational quantum layers. The HL-LHC will yield many more detector hits, which will pose a combinatorial challenge by using reconstruction algorithms to determine particle trajectories from those hits. The interaction of particles with a detector is referred to as “hit”. This increase in luminosity will significantly increase the number of particles interacting with the detector. The Large Hadron Collider (LHC) at the European Organisation for Nuclear Research (CERN) will be upgraded to further increase the instantaneous rate of particle collisions (luminosity) and become the High Luminosity LHC (HL-LHC). We discuss the conceptual design and technical implementation of ACTS, selected applications and performance of ACTS, and the lessons learned. It provides a set of high-level track reconstruction tools which are agnostic to the details of the detection technologies and magnetic field configuration and tested for strict thread-safety to support multi-threaded event processing. We present here A Common Tracking Software (ACTS) toolkit, which draws on the experience with track reconstruction algorithms in the ATLAS experiment and presents them in an experiment-independent and framework-independent toolkit. At the same time, the intense environment of the High-Luminosity LHC accelerator and other future experiments is expected to put even greater computational stress on track reconstruction software, motivating the development of more performant algorithms. While the tuning of track reconstruction algorithms can depend strongly on details of the detector geometry, the algorithms currently in use by experiments share many common features. The reconstruction of the trajectories of charged particles, or track reconstruction, is a key computational challenge for particle and nuclear physics experiments. Finally, the results from the quantum simulations are discussed and compared with traditional classical track reconstruction algorithms. The reconstruction problem is formulated in terms of a quadratic unconstrained binary optimisation. This paper presents a preliminary study to explore the potential of quantum computers to solve this problem and to reconstruct the positron trajectories from the detector energy deposits. The large number of expected positrons traversing the sensitive detector layers results in an extremely challenging combinatorial problem, which can become computationally very hard for classical computers. LUXE intends to measure the positron production rate in this unprecedented regime by using, among others, a silicon tracking detector. This manifests itself in the creation of physical electron-positron pairs from the QED vacuum. The LUXE experiment (LASER Und XFEL Experiment) is a new experiment in planning at DESY Hamburg, which will study Quantum Electrodynamics (QED) at the strong-field frontier.
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