Strategies for Quantum-Accelerated Interpolator Construction in Classical Simulations of Lattice Field Theories*

Optimized interpolating operators have the potential to accelerate the computation of hadron and nuclear matrix elements in lattice QCD. With decreased overlap onto low-lying excited states, optimized interpolated states require less euclidean time evolution to suppress unwanted contributions. This makes for a more efficient preparation of initial and final states in matrix elements, reducing computational costs.

However, classical interpolator optimization itself may be computationally expensive. In this proof-of-principle work, we show that optimal interpolator constructions can be determined in a small-scale quantum simulation. We use a small-scale quantum Hamiltonian simulation of the Schwinger model to variationally optimize an interpolator construction for a pseudoscalar meson state in the theory, and then employ that construction in a classical path-integral Monte-Carlo calculation, where systematically improvable continuum-limit scaling is possible.