Signal/noise enhancement strategies for stochastically estimated correlation functions

Abstract

We develop strategies for enhancing the signal/noise ratio for stochastically sampled correlation functions. The techniques are general and offer a wide range of applicability. We demonstrate the potential of the approach with a generic two-state system, and then explore the practical applicability of the method for single hadron correlators in lattice quantum chromodynamics. In the latter case, we determine the ground state energies of the pion, proton, and delta baryon, as well as the ground and first excited state energy of the rho meson using matrices of correlators computed on an exemplary ensemble of anisotropic gauge configurations. In the majority of cases, we find a modest reduction in the statistical uncertainties on extracted energies compared to conventional variational techniques. However, in the case of the delta baryon, we achieve a factor of three reduction in statistical uncertainties. The variety of outcomes achieved for single hadron correlators illustrates an inherent dependence of the method on the properties of the system under consideration and the operator basis from which the correlators are constructed.

40 pages, 21 figures; revisions made to the abstract and Section VI C, one additional figure and five tables added; published version

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• Strategies for quantum-optimized construction of interpolating operators in classical simulations of lattice quantum field theories
• Nuclear correlation functions using first-principle calculations of lattice quantum chromodynamics
• Formal Developments for Lattice QCD with Applications to Hadronic Systems