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Quantum computers can simulate highly entangled quantum systems efficiently, enabling the exploration of dynamical processes in Quantum Field Theories (QFTs), which would otherwise be impossible using classical techniques. In this talk, I describe an alternative approach to traditional methods for simulating the real-time evolution in QFTs, employing Hamiltonian truncation (HT). Our approach is validated by simulating the evolution of the vacuum state of the Schwinger Model following a quench, and by preparing scattering states in scalar $\phi^4$ theory. I present results obtained using both superconducting transmon and trapped ion hardware, and comment on promising future applications.