Observation of hadron scattering in a lattice gauge theory on a quantum computer

TL;DR

Real-time scattering dynamics in gauge theories are computationally challenging for classical methods. This work demonstrates a digital quantum simulation of electron-positron and meson-meson scattering in a 1+1D U(1) lattice gauge theory on IBM quantum hardware, encoding matter as domain-wall states within a quantum-link spin model and evolving via a first-order Trotter-Suzuki decomposition. The authors implement a novel marginal Distribution Error Mitigation (mDEM) to extract local observables with reduced bias, achieving good agreement with matrix product state benchmarks up to substantial evolution times and revealing Theta-term–dependent confinement, mass-quench–induced inelastic scattering, and scar-like dynamics. Overall, the study validates the use of near-term quantum devices for first-principles exploration of real-time high-energy physics dynamics and points toward scalable simulations of more complex gauge theories.

Abstract

Scattering experiments are at the heart of high-energy physics (HEP), breaking matter down to its fundamental constituents, probing its formation, and providing deep insight into the inner workings of nature. In the current huge drive to forge quantum computers into complementary venues that are ideally suited to capture snapshots of far-from-equilibrium HEP dynamics, a major goal is to utilize these devices for scattering experiments. A major obstacle in this endeavor has been the hardware overhead required to access the late-time post-collision dynamics while implementing the underlying gauge symmetry. Here, we report on the first quantum simulation of scattering in a lattice gauge theory (LGT), performed on \texttt{IBM}'s \texttt{ibm\_marrakesh} quantum computer. Specifically, we quantum-simulate the collision dynamics of electrons and positrons as well as mesons in a $\mathrm{U}(1)$ LGT representing $1+1$D quantum electrodynamics (QED), uncovering rich post-collision dynamics that we can precisely tune with a topological $Θ$-term and the fermionic mass. By monitoring the time evolution of the scattering processes, we are able to distinguish between two main regimes in the wake of the collision. The first is characterized by the delocalization of particles when the topological $Θ$-term is weak, while the second regime shows localized particles with a clear signature when the $Θ$-term is nontrivial. Furthermore, we show that by quenching to a small mass at the collision point, inelastic scattering occurs with a large production of matter reminiscent of quantum many-body scarring. Our work provides a major step forward in the utility of quantum computers for investigating the real-time quantum dynamics of HEP collisions.

Figures (17)

• Figure 1: Particle scattering on a quantum computer. a An example of qubit representation of particles in a lattice gauge theory, and subsequent Quantum circuit to implement time evolution and particle scattering. Coupling is turned off for the initial time steps at the dashed lines to prepare moving wavepackets toward each other. b Gauss's law in the $\hat{G}_\ell\ket{\Psi}=0$ gauge sector of the spin-1/2 lattice QED model, and their qubit representation. c The quantum circuit implementing the gauge-invariant coupling term in the Hamiltonian, where dynamical gauge fields couples the hopping of matter fields. d The IBM Marrakesh quantum processor employed in this work. The color of the nodes represents the readout error of the corresponding qubits. The color of the links represents the CZ gate error between the connected qubits. (Reported error rates obtained on April 11, 2025).
• Figure 2: Dynamics of electron-positron scattering without and with confinement for electrons and positrons with mass $m = 1.5\kappa$. a,c,e Evolution of the particle occupation number during the scattering of an electron and a positron. a Classical reference obtained with MPS simulations. c Mitigated results obtained on quantum hardware. e Different representation of the same data as in c. Electron occupation number is shown in blue, positron occupation number in red. b,d,f Occupation number for the electron-positron scattering with a confining potential of $\chi = 0.15 \kappa$. g Evolution of the central electric flux during the scattering without (green) and with (orange) confinement. The experimental data from which these figures were created are given in the Supplementary Information.
• Figure 3: Dynamics of the particle occupation number for electron-positron scatterings with a mass quench at $t=12 \kappa^{-1}$ from the initial mass $m_i = 1.5 \kappa$ to a final mass of $m_f = 0.0 \kappa$ (a-c), $m_f = m_c$ (d-f), and $m_f = 0.8\kappa$ (g-i), respectively. a,d,g Classical reference calculations performed with MPS. b,e,h Mitigated results obtained on quantum hardware. c,f,i Different representation of the same data. Electron occupation number is shown in blue, positron occupation number in red. j Evolution of the central electric flux during the scattering including a mass quench to $m_f = 0.0\kappa$ (green), $m_f = m_c$ (orange), and $m_f = 0.8\kappa$ (purple). The central electric flux before the mass quench is shown in black. For all simulations, the chosen value for the confining potential is $\chi = 0.0 \kappa$. The experimental data from which these figures were created are given in the Supplementary Information.
• Figure 4: Dynamics of the particle occupation number for a meson-meson collision for $m = 1.5 \kappa$ and $\chi = 0.01 \kappa$. a Classical reference calculation performed with MPS. b Mitigated results obtained on quantum hardware. c Different representation of the data in (b). Electron occupation number is shown in blue, and positron occupation number in red. d Evolution of the central electric flux. The experimental data from which these figures were created are given in the Supplementary Information.
• Figure S1: Measured (orange) and mitigated (green) electric flux for the electron-positron scattering without confining potential. Time steps 1 to 15. Classical reference values (black) obtained with MPS simulations.