Quantum Computation of Phase Transition in φ⁴Scalar Field Theory

It has been demonstrated that the critical point of the phase transition in φ⁴ scalar quantum field theory in one space and time dimension can be approximated via a Gaussian Effective Potential (GEP). Here we demonstrate how this critical point may be estimated on quantum hardware. We perform quantum computations with various lattice sizes and show that there is evidence of a transition from a symmetric phase to a symmetry-broken phase. The two-site case is implemented on actual quantum hardware, while we show via simulations that the continuum critical point lies at λ/m² ∼ 61.2, where λ is the coupling and m is the renormalized mass. To compute the effective potential we first use the Variational Quantum Eigensolver algorithm (VQE) to determine the parameters for the Gaussian states. We then use these parameters to compute the effective potential as a function of 〈φ〉, using varying levels of hybrid quantum-classical computation. By modifying the Ansatz state, one can extend this procedure beyond GEP’s in order to demonstrate the second-order nature of the true phase transition, as the GEP transition is only first-order.