  Quantum field theory (QFT) simulations are a potentially important
application for noisy intermediate scale quantum (NISQ) computers. The ability
of a quantum computer to emulate a QFT, therefore, constitutes a natural
application-centric benchmark. Foundational quantum algorithms to simulate QFT
processes rely on fault-tolerant computational resources, but to be useful on
NISQ machines, error-resilient algorithms are required. Here we outline and
implement a hybrid algorithm to calculate the lowest energy levels of the
paradigmatic 1+1--dimensional interacting scalar QFT. We calculate energy
splittings and compare results with experimental values obtained on currently
available quantum hardware. We show that the accuracy of mass-renormalization
calculations represents a useful metric with which near-term hardware may be
benchmarked. We also discuss the prospects of scaling the algorithm to full
simulation of interacting QFTs on future hardware.
