  Quantum computers can efficiently simulate highly entangled quantum systems,
offering a solution to challenges facing classical simulation of Quantum Field
Theories (QFTs). This paper presents an alternative to traditional methods for
simulating the real-time evolution in QFTs by leveraging Hamiltonian Truncation
(HT). As a use case, we study the Schwinger model, systematically reducing the
complexity of the Hamiltonian via HT while preserving essential physical
properties. For the observables studied in this paper, the HT approach
converges quickly with the number of qubits, allowing for the interesting
physics processes to be captured without needing many qubits. Identifying the
truncated free Hamiltonian's eigenbasis with the quantum device's computational
basis avoids the need for complicated and costly state preparation routines,
reducing the algorithm's overall circuit depth and required coherence time. As
a result, the HT approach to simulating QFTs on a quantum device is well suited
to Noisy-Intermediate Scale Quantum (NISQ) devices, which have a limited number
of qubits and short coherence times. We validate our approach by running
simulations on a NISQ device, showcasing strong agreement with theoretical
predictions. We highlight the potential of HT for simulating QFTs on quantum
hardware.
