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Path integrals describing quantum many-body systems can be calculated withMonte Carlo sampling techniques, but average quantities are often subject tosignal-to-noise ratios that degrade exponentially with time. Aphase-reweighting technique inspired by recent observations of random walkstatistics in correlation functions is proposed that allows energy levels to beextracted from late-time correlation functions with time-independentsignal-to-noise ratios. Phase reweighting effectively includes dynamicalrefinement of source magnitudes but introduces a bias associated with thephase. This bias can be removed by performing an extrapolation, but at theexpense of re-introducing a signal-to-noise problem. Lattice QuantumChromodynamics calculations of the $\rho$ and nucleon masses and of the$\Xi\Xi$ binding energy show consistency between standard results obtainedusing earlier-time correlation functions and phase-reweighted results usinglate-time correlation functions inaccessible to standard statistical analysismethods.

Taming the Signal-to-Noise Problem in Lattice QCD by Phase Reweighting