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arXiv:2307.02522 · Physical Review Letters

High-Energy Collision of Quarks and Mesons in the Schwinger Model: From Tensor Networks to Circuit QED

Ron Belyansky, Seth Whitsitt, Niklas Mueller, Ali Fahimniya, Elizabeth R. Bennewitz, Zohreh Davoudi, Alexey Vyacheslavovich Gorshkov

Published Feb 28, 2024• 51 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.132.091903

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Tensor network methods have demonstrated their suitability for the study of equilibrium properties of lattice gauge theories, even close to the continuum limit. We use them in an out-of-equilibrium scenario, much less explored so far, by simulating the real-time collisions of composite mesons in the lattice Schwinger model. Constructing wave-packets of vector mesons at different incoming momenta, we observe the opening of the inelastic channel in which two heavier mesons are produced and identify the momentum threshold. To detect the products of the collision in the strong coupling regime we propose local quantitites that could be measured in current quantum simulation platforms.
We study real-time meson-meson scattering processes in (1+11+11+1)-dimensional QED by means of tensor networks. We prepare initial meson wave packets with given momentum and position introducing an approximation based on the free fermions model. Then, we compute the dynamics of two initially separated colliding mesons, observing a rich phenomenology as the interaction strength and the initial states are varied in the weak and intermediate coupling regimes. Finally, we consider elastic collisions and measure some scattering amplitudes as well as the entanglement generated by the process. Remarkably, we identify two different regimes for the asymptotic entanglement between the outgoing mesons: it is perturbatively small below a threshold coupling, past which its growth as a function of the coupling abruptly accelerates.
We study real-time meson-meson scattering processes in (1+1)(1+1)(1+1)-dimensional QED by means of Tensor Networks. We prepare initial meson wave packets with given momentum and position, starting from the free fermions model and extending it to the interaction theory. Then, we compute the dynamics of two initially separated colliding mesons, observing a rich phenomenology as the interaction strength and the initial states are varied in the weak and intermediate coupling regimes. Finally, we measure the scattering amplitudes for the process in terms of the initial and final momenta and the entanglement produced by the collision. We remarkably find two different regimes for the asymptotic entanglement between the two mesons: it is perturbatively small for weak couplings, while, in the intermediate regime, it turns out to reach a non-zero value at long times after the scattering.
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.
Simulating the real-time dynamics of particle collisions is a promising application of quantum simulators, because classical methods such as tensor networks struggle to capture the highly entangled states generated in high-energy scattering. Realizing such simulations requires both the preparation of incoming wave packets and the detection of the outgoing scattering products. In this work, we propose protocols that address both challenges on programmable analog and digital quantum simulation platforms. Our state-preparation scheme uses a weakly coupled auxiliary qubit - or, more generally, a customized local quench - to inject a single quasiparticle with well-defined momentum. Because it relies only on conservation of energy, this scheme requires no fine-tuning or prior knowledge about particle eigenstates, making it robust against errors in calibration and implementation. The momenta of scattering products are then extracted, using only local measurements, from the interference pattern that arises when particles are reflected at the system's boundary. We validate our protocols through numerical simulations, first in a simple single-particle model and subsequently in two interacting many-body systems: a Rydberg atom chain and an Ising chain in a mixed field. We demonstrate how high-energy regimes, necessary to access inelastic scattering processes, can be reached through an adiabatic ramp, and how the wave packet shape can be optimized by spatially modulating the Hamiltonian. Finally, we show how the protocol can be generalized to systems with more than one spatial dimension. Our proposal provides a versatile approach to the quantum simulation of scattering phenomena, and is compatible with several quantum simulation platforms that are already experimentally available.
Scattering processes are essential for understanding the structure of matter, yet their real-time dynamics remain challenging to simulate classically. Quantum computers offer a promising path toward efficient simulation of such physical systems. Here, we present a general and scalable framework for simulating meson scattering in lattice gauge theories on digital quantum hardware. Our approach addresses two key challenges: First, we introduce a symmetry-preserving quantum subspace expansion method for constructing high-fidelity meson creation operators across a wide range of coupling and momenta. Second, we design a quantum circuit for meson wave packet preparation using Givens rotations, improving accuracy while reducing circuit depth compared to existing approaches. We demonstrate the method in a ( 1 + 1 )-dimensional Z 2 gauge theory and explore meson scattering dynamics with tensor network simulations. We study both elastic and inelastic scattering and provide a comprehensive characterization of the scattering process in terms of energy transfer, entanglement entropy, and heavier particle production during the dynamics. Our work provides a scalable, nonvariational approach for simulating meson scattering on near-term quantum devices and offers a concrete strategy for probing nonperturbative dynamics in confining gauge theories.