  In quantum algorithms discovered so far for simulating scattering processes
in quantum field theories, state preparation is the slowest step. We present a
new algorithm for preparing particle states to use in simulation of Fermionic
Quantum Field Theory (QFT) on a quantum computer, which is based on the matrix
product state ansatz. We apply this to the massive Gross-Neveu model in one
spatial dimension to illustrate the algorithm, but we believe the same
algorithm with slight modifications can be used to simulate any one-dimensional
massive Fermionic QFT. In the case where the number of particle species is one,
our algorithm can prepare particle states using $O\left(
\epsilon^{-3.23\ldots}\right)$ gates, which is much faster than previous known
results, namely $O\left(\epsilon^{-8-o\left(1\right)}\right)$. Furthermore,
unlike previous methods which were based on adiabatic state preparation, the
method given here should be able to simulate quantum phases unconnected to the
free theory.
