Real-Time Scattering Processes with Continuous-Variable Quantum Computers

We propose a framework for simulating the real-time dynamics of quantum field theories (QFTs) using continuous-variable quantum computing (CVQC). Focusing on ($1+1$)-dimensional $\varphi^4$ scalar field theory, the approach employs the Hamiltonian formalism to map the theory onto a spatial lattice, with fields represented as quantum harmonic oscillators. Using measurement-based quantum computing, we implement non-Gaussian operations for CQVC platforms. The study introduces methods for preparing initial states with specific momenta and simulating their evolution under the $\varphi^4$ Hamiltonian. Key quantum objects, such as two-point correlation functions, validate the framework against analytical solutions. Scattering simulations further illustrate how mass and coupling strength influence field dynamics and energy redistribution. Thus, we demonstrate CVQC's scalability for larger lattice systems and its potential for simulating more complex field theories.