Quantum computation of phase transition in interacting scalar quantum field theory

It has been demonstrated that the critical point of the phase transition in scalar quantum field theory with a quartic interaction in one space dimension can be approximated via a Gaussian Effective Potential (GEP). We discuss how this critical point can be estimated using quantum hardware. Performing quantum computations with various lattice sizes, we obtain evidence of a transition from a symmetric to a symmetry-broken phase using both discrete- and continuous-variable quantum computation. The ten-site case is implemented on IBM quantum hardware using the Variational Quantum Eigensolver algorithm to minimize the GEP and identify lattice level crossings. These are extrapolated via simulations to find the continuum critical point.