Can multi-level Monte-Carlo address the sign problem in a finite-density Bose gas?
Numerical simulation of field theories with complex actions is frustrated by the sign problem, which causes an exponential growth in statistical sampling noise. A key example of such a theory is QCD at finite baryon chemical potential, which has important applications to the structure of atomic nuclei and neutron stars. Until now, the sign problem has precluded the possibility of first-principles numerical calculations that could provide key insight into these important physical systems. In this work, we propose an approach to avoiding this limitation by applying a reweighting procedure coupled with a multi-level Monte-Carlo sampling algorithm that offers an exponential enhancement of statistics to counteract the sign problem. We test the approach on a simpler model that displays the same sign problem at finite chemical potential. Our results demonstrate the promise of the proposed approach, significantly increasing the range over which precise calculations are possible, and providing improvements all the way up to the phase transition.