Description
Scattering processes in gauge theories are fundamental to high-energy physics but remain challenging for classical simulations due to the sign problem and entanglement growth in real-time dynamics. Quantum computing offers a promising alternative for simulating such processes.
In this work, we study meson scattering in a (1+1)-dimensional $\mathbb{Z}_2$ lattice gauge theory coupled to staggered fermions. We develop a resource-efficient method to construct meson creation operators using the quantum subspace expansion (QSE), achieving higher fidelity than previous VQE-based approaches. The meson wave packets are constructed using these operators, and time evolution of the scattering process is simulated using Trotterized quantum circuits. By the classical simulation, we observed both elastic and inelastic scattering processes with rich physical phenomena, including the new particle production, entanglement entropy growth, and longer flux string generation and breaking.
Furthermore, we propose an efficient quantum circuit decomposition for meson wave packet preparation based on Givens rotations, significantly reducing the circuit depth from $\mathcal{O}(L^3)$ to $\mathcal{O}(L)$ and CNOT gates from $\mathcal{O}(L^3)$ to $\mathcal{O}(L^2)$ compared to previous methods, where $L$ is the system size. Our results provide a concrete pathway for simulating inelastic meson scattering on near-term quantum devices and offer new insights into meson dynamics in confining gauge theories.
