  The Berry curvature and its descendant, the Berry phase, play an important
role in quantum mechanics. They can be used to understand the Aharonov-Bohm
effect, define topological Chern numbers, and generally to investigate the
geometric properties of a quantum ground state manifold. While Berry curvature
has been well-studied in the regimes of few-body physics and non-interacting
particles, its use in the regime of strong interactions is hindered by the lack
of numerical methods to solve it. In this paper we fill this gap by
implementing a quantum Monte Carlo method to solve for the Berry curvature,
based on interpreting Berry curvature as a leading correction to imaginary time
ramps. We demonstrate our algorithm using the transverse-field Ising model in
one and two dimensions, the latter of which is non-integrable. Despite the fact
that the Berry curvature gives information about the phase of the wave
function, we show that our algorithm has no sign or phase problem for standard
sign-problem-free Hamiltonians. Our algorithm scales similarly to conventional
methods as a function of system size and energy gap, and therefore should prove
a valuable tool in investigating the quantum geometry of many-body systems.
