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arXiv:2505.21240 · Physical Review Research

Scalable quantum algorithm for meson scattering in a lattice gauge theory

Yahui Chai, Yibin Guo, Stefan Kühn

Published Jul 13, 2026• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/f93h-rlzy

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Simulating Meson Scattering in (1+1)D Z2\mathbb{Z}_2Z2​ Lattice Gauge Theory: Efficient Operator Construction and Quantum Circuit Implementation
We present a framework for efficiently preparing meson wave packets for a lattice gauge theory on quantum devices. The method is demonstrated using a (1+1)D Z2 lattice gauge theory coupled to Kogut-Susskind staggered fermions as a testbed. Our approach systematically constructs mesonic excitations on top of the ground state with well-defined momentum. Using a quantum subspace expansion approach with a symmetry-preserving basis, we obtain explicit operators for creating such excitations, which in turn allow us to construct localized wave packets. By simulating the scattering process of two meson wave packets with Tensor Network States, we identify both elastic and inelastic scattering processes during the dynamics. In addition, we also provide a resource-efficient decomposition for the operators creating mesonic wave packets into elementary quantum gates, thus enabling quantum simulation of meson scattering in the (1+1)D Z2 lattice gauge theory.
We present a framework for efficiently preparing meson wave packets for a lattice gauge theory on quantum devices. The method is demonstrated using a (1+1)D Z2 lattice gauge theory coupled to Kogut-Susskind staggered fermions as a testbed. Our approach systematically constructs mesonic excitations on top of the ground state with well-defined momentum. Using a quantum subspace expansion approach with a symmetry-preserving basis, we obtain explicit operators for creating such excitations, which in turn allow us to construct localized wave packets. By simulating the scattering process of two meson wave packets with Tensor Network States, we identify both elastic and inelastic scattering processes during the dynamics. In addition, we also provide a resource-efficient decomposition for the operators creating mesonic wave packets into elementary quantum gates, thus enabling quantum simulation of meson scattering in the (1+1)D Z2 lattice gauge theory.
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We present a digital quantum computation of two-hadron scattering in a Z2Z_2Z2​ lattice gauge theory in 1+1 dimensions. We prepare well-separated single-particle wave packets with desired momentum-space wavefunctions, and simulate their collision through digitized time evolution. Multiple hadronic wave packets can be produced using the efficient, systematically improvable algorithm of this work, achieving high fidelity with the target initial state. Specifically, employing a trapped-ion quantum computer (IonQ Forte), we prepare up to three meson wave packets using 11 and 27 system qubits, and simulate collision dynamics of two meson wave packets for the smaller system. Results for local observables are consistent with numerical simulations at early times, but decoherence effects limit evolution into long times. We demonstrate the critical role of high-fidelity initial states for precision measurements of state-sensitive observables, such as SSS-matrix elements. Our work establishes the potential of quantum computers in simulating hadron-scattering processes in strongly interacting gauge theories.
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.
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.