A Euclidean Monte-Carlo-informed route to ground-state preparation for quantum simulation of scalar field theory

TL;DR

This paper introduces a method that uses classical Euclidean Monte-Carlo data to efficiently prepare ground states for quantum simulations of scalar field theories, bridging classical and quantum approaches.

Contribution

It proposes variational ansatzes optimized with Monte-Carlo data that can be efficiently implemented on quantum circuits, enabling better initial state preparation for quantum field theory simulations.

Findings

Ansatzes achieve comparable ground-state energies with distinct correlations.

Quantum circuits derived have polynomial gate complexity.

Method bridges Euclidean Monte-Carlo data with quantum state preparation.

Abstract

Quantum simulators hold great promise for studying real-time (Minkowski) dynamics of quantum field theories. Nonetheless, preparing non-trivial initial states remains a major obstacle. Euclidean-time Monte-Carlo methods yield ground-state spectra and static correlation functions that can, in principle, guide state preparation. In this work, we exploit this classical information to bridge Euclidean and Minkowski descriptions for a (1+1)-dimensional interacting scalar field theory. We propose variational ansatz families which achieve comparable ground-state energies, yet exhibit distinct correlations and local non-Gaussianity. By optimizing selected wavefunction moments with Monte-Carlo data, we obtain ansatzes that can be efficiently translated into quantum circuits. Our algorithmic cost analysis shows these circuits' gate complexity scales polynomially in system size. Our work paves the way for systematically leveraging classically-computed information to prepare initial states in quantum field theories of interest in nature.