Volume 1 of the FCC Feasibility Report presents an overview of the physics case, experimental programme, and detector concepts for the Future Circular Collider (FCC). This volume outlines how FCC would address some of the most profound open questions in particle physics, from precision studies of the Higgs and EW bosons and of the top quark, to the exploration of physics beyond the Standard Model. The report reviews the experimental opportunities offered by the staged implementation of FCC, beginning with an electron-positron collider (FCC-ee), operating at several centre-of-mass energies, followed by a hadron collider (FCC-hh). Benchmark examples are given of the expected physics performance, in terms of precision and sensitivity to new phenomena, of each collider stage. Detector requirements and conceptual designs for FCC-ee experiments are discussed, as are the specific demands that the physics programme imposes on the accelerator in the domains of the calibration of the collision energy, and the interface region between the accelerator and the detector. The report also highlights advances in detector, software and computing technologies, as well as the theoretical tools/reconstruction techniques that will enable the precision measurements and discovery potential of the FCC experimental programme. The content and structure of this report are guided by the scope and priorities defined in the mandate of the FCC Feasibility Study. It is therefore not intended to serve as an exhaustive review of the full physics potential of FCC. Several topics, already covered in earlier reports such as the FCC CDR, are not reiterated here or are addressed only briefly, in alignment with the study’s focus. This volume reflects the outcome of a global collaborative effort involving hundreds of scientists and institutions, aided by a dedicated community-building coordination, and provides a targeted assessment of the scientific opportunities and experimental foundations of the FCC programme.

Free energy-based reinforcement learning (FERL) with clamped quantum Boltzmann machines (QBM) was shown to significantly improve the learning efficiency compared to classical Q-learning with the restriction, however, to discrete state-action space environments. In this paper, the FERL approach is extended to multi-dimensional continuous state-action space environments to open the doors for a broader range of real-world applications. First, free energy-based Q-learning is studied for discrete action spaces, but continuous state spaces and the impact of experience replay on sample efficiency is assessed. In a second step, a hybrid actor-critic (A-C) scheme for continuous state-action spaces is developed based on the deep deterministic policy gradient algorithm combining a classical actor network with a QBM-based critic. The results obtained with quantum annealing (QA), both simulated and with D-Wave QA hardware, are discussed, and the performance is compared to classical reinforcement learning methods. The environments used throughout represent existing particle accelerator beam lines at the European Organisation for Nuclear Research. Among others, the hybrid A-C agent is evaluated on the actual electron beam line of the Advanced Wakefield Experiment (AWAKE).

In the past, transverse coherent instabilities have been observed at the Hadron-Electron Ring Accelerator (HERA) proton ring that were instigated by the presence of linear coupling. Linear coupling can also potentially explain some transverse instabilities that were observed in the Large Hadron Collider (LHC) in both run I and run II, however a detailed description of the destabilizing mechanism of linear coupling was not known at the time. A study into the effect of linear coupling on transverse beam stability was carried out, and a new mechanism that could incite transverse instabilities by causing a loss of Landau damping has been found. The study includes time domain simulations with PyHEADTAIL and frequency domain computations based on analytical approaches, and was then verified by measurements with a single proton bunch in the LHC.