Faster Quantum Algorithm to simulate Fermionic Quantum Field Theory

TitleFaster Quantum Algorithm to simulate Fermionic Quantum Field Theory
Publication TypeJournal Article
Year of Publication2018
AuthorsMoosavian, AHamed, Jordan, S
JournalPhys. Rev. A 98, 012332 (2018)
Date Published2018/05/04

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.