Strategies for quantum-optimized construction of interpolating operators in classical simulations of lattice quantum field theories

TL;DR

This paper explores quantum computer-assisted methods to optimize interpolating operators in lattice quantum field theories, demonstrating two approaches—fidelity maximization and energy minimization—in a (1+1)-dimensional Schwinger model simulation.

Contribution

It develops and implements two quantum-inspired methods for constructing interpolating operators, showing their effectiveness in classical simulations of lattice quantum field theories.

Findings

Energy minimization is more robust to quantum gate errors than fidelity maximization.

Quantum-optimized operators improve the accuracy of lattice QFT calculations.

Proof-of-concept demonstrated in a (1+1)-dimensional Schwinger model.

Abstract

It has recently been argued that noisy intermediate-scale quantum computers may be used to optimize interpolating operator constructions for lattice quantum field theory (LQFT) calculations on classical computers. Here, two concrete realizations of the method are developed and implemented. The first approach is to maximize the overlap, or fidelity, of the state created by an interpolating operator acting on the vacuum state to the target eigenstate. The second is to instead minimize the energy expectation value of the interpolated state. These approaches are implemented in a proof-of-concept calculation in (1+1)-dimensions for a single-flavor massive Schwinger model to obtain quantum-optimized interpolating operator constructions for a vector meson state in the theory. Although fidelity maximization is preferable in the absence of noise due to quantum gate errors, it is found that energy minimization is more robust to these effects in the proof-of-concept calculation. This work serves as a concrete demonstration of how quantum computers in the intermediate term might be used to accelerate classical LQFT calculations.