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(ε\−3.23\…) gates, which is much faster than previous known results, namely O(ε\−8\−o(1)). 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.

}, doi = {https://doi.org/10.1103/PhysRevA.98.012332}, url = {https://arxiv.org/abs/1711.04006}, author = {Moosavian, Ali Hamed and Stephen Jordan} }