Title: Taming the Signal-to-Noise Problem in Lattice QCD by Phase Reweighting,
Abstract: Path integrals describing quantum many-body systems can be calculated with
Monte Carlo sampling techniques, but average quantities are often subject to
signal-to-noise ratios that degrade exponentially with time. A
phase-reweighting technique inspired by recent observations of random walk
statistics in correlation functions is proposed that allows energy levels to be
extracted from late-time correlation functions with time-independent
signal-to-noise ratios. Phase reweighting effectively includes dynamical
refinement of source magnitudes but introduces a bias associated with the
phase. This bias can be removed by performing an extrapolation, but at the
expense of re-introducing a signal-to-noise problem. Lattice Quantum
Chromodynamics calculations of the $\rho$ and nucleon masses and of the
$\Xi\Xi$ binding energy show consistency between standard results obtained
using earlier-time correlation functions and phase-reweighted results using
late-time correlation functions inaccessible to standard statistical analysis
methods.