Quantum Algorithms for Fermionic Quantum Field Theories

Extending previous work on scalar field theories, we develop a quantum
algorithm to compute relativistic scattering amplitudes in fermionic field
theories, exemplified by the massive Gross-Neveu model, a theory in two
spacetime dimensions with quartic interactions. The algorithm introduces new
techniques to meet the additional challenges posed by the characteristics of
fermionic fields, and its run time is polynomial in the desired precision and
the energy. Thus, it constitutes further progress towards an efficient quantum
algorithm for simulating the Standard Model of particle physics.