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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 $XiXi$ 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.
The theory of quantum chromodynamics (QCD) encodes the strong interactions that bind quarks and gluons into nucleons and that bind nucleons into nuclei. Predictive control of QCD would allow nuclear structure and reactions as well as properties of su
A systematic analysis of the structure of single-baryon correlation functions calculated with lattice QCD is performed, with a particular focus on characterizing the structure of the noise associated with quantum fluctuations. The signal-to-noise pro
Lattice QCD simulations of multi-baryon correlation functions can predict the structure and reactions of nuclei without encountering the baryon chemical potential sign problem. However, they suffer from a signal-to-noise problem where Monte Carlo est
The reweighting method is widely used in numerical studies of QCD, in particular, for the cases in which the conventional Monte-Carlo method cannot be applied directly, e.g., finite density QCD. However, the application range of the reweighing method
Gauge theories are of paramount importance in our understanding of fundamental constituents of matter and their interactions. However, the complete characterization of their phase diagrams and the full understanding of non-perturbative effects are st