Resonant scattering links particle interactions to the formation and decay of unstable excitations. We develop a hybrid quantum-computing framework to study these dynamics through fermion--antifermion collisions. Our formulation of $(1+1)$-dimensional Yukawa theory encodes fermions in qubits and the scalar field in qumodes. We identify the operations needed for a photonic implementation and benchmark the dynamics with tensor-network simulations. Near resonance, we resolve the build-up of a localised scalar excitation and the subsequent partial return of energy to the fermions. Enhanced entanglement accompanies this exchange. Time-dependent correlator measurements reproduce the analytically predicted decay rate to a few percent precision, with energy scans exhibiting a resonance peak consistent with packet-averaged Breit--Wigner behaviour. These results establish a concrete scattering benchmark for hybrid quantum computers and demonstrate how local real-time observables can probe particle-resonance dynamics.
Resonant scattering links particle interactions to the formation and decay of unstable excitations. We develop a hybrid quantum-computing framework to study these dynamics through fermion--antifermion collisions. Our formulation of (1+1)-dimensional Yukawa theory encodes fermions in qubits and the scalar field in qumodes. We identify the operations needed for a photonic implementation and benchmark the dynamics with tensor-network simulations. Near resonance, we resolve the build-up of a localised scalar excitation and the subsequent partial return of energy to the fermions. Enhanced entanglement accompanies this exchange. Time-dependent correlator measurements reproduce the analytically predicted decay rate to a few percent precision, with energy scans exhibiting a resonance peak consistent with packet-averaged Breit--Wigner behaviour. These results establish a concrete scattering benchmark for hybrid quantum computers and demonstrate how local real-time observables can probe particle-resonance dynamics.
Collider experiments play a central role in understanding the subatomic structure of matter, as well as developing and verifying the fundamental theory of elementary particle interactions. However, comprehending scattering processes at a fundamental level in theory remains a significant challenge. The necessary involved time evolution and the with time rapidly increasing bond dimension in Tensor Networks make simulating the scattering process with this classical method challenging. On the other hand, quantum computers hold great promise to efficiently simulate real-time dynamics of lattice field theories. In this work, we take the first step in this direction toward simulating fermionic scattering using a digital-quantum computing approach. Specifically, we propose a method based on Givens rotation to prepare the initial state of the fermionic scattering process, which consists of two fermionic wave packets with opposite momenta. With a time evolution operator based on the underlying Hamiltonian acting on the initial state, the two fermionic wave packets propagate and interact with each other. Using the lattice Thirring model as the test bed and the Qiskit Statevector simulator, we observe an elastic scattering between fermions and antifermions in the strong interaction region. In addition, we clearly observe an entanglement production in the scattering process. We consider our work also as an indispensable step towards a quantum simulation of a scattering process on a real quantum device.
With the aim of studying nonperturbative out-of-equilibrium dynamics of high-energy particle collisions on quantum simulators, we investigate the scattering dynamics of lattice quantum electrodynamics in 1+1 dimensions. Working in the bosonized formulation of the model and in the thermodynamic limit, we use uniform-matrix-product-state tensor networks to construct multiparticle wave-packet states, evolve them in time, and detect outgoing particles post collision. This facilitates the numerical simulation of scattering experiments in both confined and deconfined regimes of the model at different energies, giving rise to rich phenomenology, including inelastic production of quark and meson states, meson disintegration, and dynamical string formation and breaking. We obtain elastic and inelastic scattering cross sections, together with time-resolved momentum and position distributions of the outgoing particles. Furthermore, we propose an analog circuit-QED implementation of the scattering process that is native to the platform, requires minimal ingredients and approximations, and enables practical schemes for particle wave-packet preparation and evolution. This study highlights the role of classical and quantum simulation in enhancing our understanding of scattering processes in quantum field theories in real time.
Scattering processes are a crucial ingredient for the investigation of fundamental interactions. The ever-increasing amount of data produced at particle colliders has fuelled recent progresses in the field of scattering amplitudes computation. To date, on the numerical side, the results achieved are mainly based on Monte-Carlo simulations. In this Thesis the problem is attacked with a different approach: a real-time simulation of the dynamics of a 1+1 dimensional quantum field theory is performed, exploiting the powerful tensor network methods from many-body theory. A matrix product state representation of the asymptotic input states is identified, allowing for the preparation of the initial momentum wave packets. This initial state is then evolved and we aim to compute the S-matrix elements from the knowledge of the final state. We focus on a specific fermionic U(1)-gauge model, developing a set of tools which are relevant for a broader class of 1+1 dimensional quantum field theories with global or local symmetries.
Abstract Simulating real-time evolution in theories of fundamental interactions represents one of the central challenges in contemporary theoretical physics. Cold-atom platforms stand as promising candidates to realize quantum simulations of non-perturbative phenomena in gauge theories, such as vacuum decay and hadron collisions, in prohibitive conditions for direct experiments. In this work, we demonstrate that present-day quantum simulators can imitate linear particle accelerators, giving access to S -matrix measurements of elastic and inelastic meson collisions in low-dimensional abelian gauge theories. Considering for definiteness a (1 + 1)-dimensional Z 2 -lattice gauge theory realizable with Rydberg-atom arrays, we present protocols to observe and measure selected meson–meson scattering processes. We provide a benchmark theoretical study of scattering amplitudes in the regime of large fermion mass, including an exact solution valid for arbitrary coupling strength. This allows us to discuss the occurrence of inelastic scattering channels, featuring the production of new mesons with different internal structures. We present numerical simulations of realistic wavepacket collisions, which reproduce the predicted cross section peaks. This work highlights the potential of quantum simulations to give unprecedented access to real-time scattering dynamics.
A bstract We present a first real-time study of hadronic scattering in a (1+1)-dimensional SU(2) lattice gauge theory with fundamental fermions using tensor-network techniques. Working in the gaugeless Hamiltonian formulation — where the gauge field is exactly integrated out and no truncation of the electric flux is required — we investigate scattering processes across sectors of fixed global baryon number B = 0, 1, 2. These correspond respectively to meson-meson, meson-baryon, and baryon-baryon collisions. At strong coupling, the B = 0 and B = 2 channels exhibit predominantly elastic dynamics closely resembling those of the U(1) Schwinger model. In contrast, the mixed B = 1 sector shows qualitatively new behavior: meson and baryon wavepackets become entangled during the collision, and depending on their initial kinematics, the slower state becomes spatially delocalized while the faster one propagates ballistically. We characterize these processes through local observables, entanglement entropy, and the information-lattice, which together reveal how correlations build up and relax during the interaction. Our results establish a first benchmark for non-Abelian real-time scattering from first principles and open the path toward quantum-simulation studies of baryon-number dynamics and inelastic processes in gauge theories.
Quantum computing may allow unprecedented access to nonequilibrium quantum dynamics, including problems of interest in particle physics, like the real-time development of scattering processes. Although fault-tolerant simulations at scale are still in the future, recent advancements toward early fault-tolerant simulations motivate building increasingly elaborate benchmark problems in order to assess state-of-the-art capabilities and test new algorithms and observables. In this work, we study glueball scattering on a line-of-plaquettes lattice in pure SU(3) lattice gauge theory. We characterize scattering of the lowest-energy glueball states using classical exact diagonalization methods, identifying the continuum resonance structure using real-time simulations and approximate analytic methods, and we propose time-domain observables for extracting properties of the resonance from quantum simulations. We furthermore construct a toy model that shares the spectral features of the lattice gauge theory and demonstrate extraction of the observables. Feasibility on near-term hardware is demonstrated through simulation of a resonant collision of this toy model on Quantinuum System Model H2-2, with a 14-plaquette chain encoded in 28 qubits. The Trotterized circuit after optimization and compression requires ∼25n entangling gates for n Trotter steps.