Hybrid Classical-Quantum Sampling for Lattice Scalar Field Theory

TL;DR

This paper explores a hybrid approach combining classical and quantum methods to sample lattice scalar field theories, utilizing a quantum annealer to handle quartic interactions and improve sampling efficiency.

Contribution

It introduces three novel schemes to encode quartic interactions as quadratic polynomials using auxiliary qubits, enabling quantum annealing for scalar field theory sampling.

Findings

Quantum annealer-generated distributions closely match classical results.

The proposed schemes effectively encode quartic interactions for quantum annealing.

Hybrid sampling improves efficiency over purely classical methods.

Abstract

We investigate lattice scalar field theory in two-dimensional Euclidean space via a quantum annealer. To accommodate the quartic interaction terms, we introduce three schemes for rewriting them as quadratic polynomials through the use of auxiliary qubits. These methods are applied on D-Wave quantum annealer, and their effectiveness is assessed by examining the annealer-generated distributions. Using these distributions, we perform Monte Carlo sampling via the Metropolis-Hastings algorithm and compare the outcomes with those from classical Metropolis simulations.