Quantum Imaginary Time Evolution Algorithm for Quantum Field Theories with Continuous Variables

We calculate the energy levels and corresponding eigenstates of an interacting scalar quantum fi?eld theory on a lattice using a continuous-variable version of the quantum imaginary time evolution algorithm. Only a single qumode is needed for the simulation of the ?eld at each point on the lattice. Our quantum algorithm avoids the use of non-Gaussian quantum gates and relies, instead, on detectors projecting onto eigenstates of the photon-number operator. Using Xanadu's Strawberry Fields simulator, we obtain results on energy levels that are in very good agreement with results from exact calculations. We propose an experimental setup that can be realized with existing technology.