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

TL;DR

This paper introduces a classical pipeline that leverages Euclidean Monte Carlo data to efficiently prepare ground states for quantum simulations of scalar field theories, enhancing initial state accuracy.

Contribution

It presents a novel method combining classical Euclidean data with variational ansatz and quantum circuit translation for ground-state preparation in quantum field theory.

Findings

States have comparable energy estimates but different correlations.

The quantum circuit preparation cost is polynomial in system size.

Classical Euclidean data effectively inform quantum state initialization.

Abstract

Quantum simulators offer great potential for investigating dynamical properties of quantum field theories. However, preparing accurate non-trivial initial states for these simulations is challenging. Classical Euclidean-time Monte-Carlo methods provide a wealth of information about states of interest to quantum simulations. Thus, it is desirable to facilitate state preparation on quantum simulators using this information. To this end, we present a fully classical pipeline for generating efficient quantum circuits for preparing the ground state of an interacting scalar field theory in 1+1 dimensions. The first element of this pipeline is a variational ansatz family based on the stellar hierarchy for bosonic quantum systems. The second element of this pipeline is the classical moment-optimization procedure that augments the standard variational energy minimization by penalizing deviations in selected sets of ground-state correlation functions (i.e., moments). The values of ground-state moments are sourced from classical Euclidean methods. The resulting states yield comparable ground-state energy estimates but exhibit distinct correlations and local non-Gaussianity. The third element of this pipeline is translating the moment-optimized ansatz into an efficient quantum circuit with an asymptotic cost that is polynomial in system size. This work opens the way to systematically applying classically obtained knowledge of states to prepare accurate initial states in quantum field theories of interest in nature.