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

TL;DR

This paper introduces a continuous-variable quantum imaginary time evolution algorithm for simulating scalar quantum field theories on a lattice, achieving accurate energy level calculations with minimal quantum resources.

Contribution

It presents a novel quantum algorithm that uses only Gaussian operations and photon-number measurements, avoiding non-Gaussian gates for quantum field theory simulations.

Findings

Results agree well with exact calculations

Single qumode per lattice point suffices for simulation

Proposed experimental setup feasible with current technology

Abstract

We calculate the energy levels and corresponding eigenstates of an interacting scalar quantum field 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 field 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.