  As an intrinsically unbiased method, the quantum Monte Carlo (QMC) method is
of unique importance in simulating interacting quantum systems. Although the
QMC method often suffers from the notorious sign problem, the sign problem of
quantum models may be mitigated by finding better choices of the simulation
scheme. However, a general framework for identifying optimal QMC schemes has
been lacking. Here, we propose a general framework using automatic
differentiation to automatically search for the best QMC scheme within a given
ansatz of the Hubbard-Stratonovich transformation, which we call "automatic
differentiable sign optimization" (ADSO). We apply the ADSO framework to the
honeycomb lattice Hubbard model with Rashba spin-orbit coupling and demonstrate
that ADSO is remarkably effective in mitigating and even solving its sign
problem. Specifically, ADSO finds a sign-free point in the model which was
previously thought to be sign-problematic. For the sign-free model discovered
by ADSO, its ground state is shown by sign-free QMC simulations to possess
spiral magnetic ordering; we also obtained the critical exponents
characterizing the magnetic quantum phase transition.
