  We show how the worldline quantum Monte Carlo procedure, which usually relies
on an artificial time discretization, can be formulated directly in continuous
time, rendering the scheme exact. For an arbitrary system with discrete Hilbert
space, none of the configuration update procedures contain small parameters. We
find that the most effective update strategy involves the motion of worldline
discontinuities (both in space and time), i.e., the evaluation of the Green's
function. Being based on local updates only, our method nevertheless allows one
to work with the grand canonical ensemble and non-zero winding numbers, and to
calculate any dynamic correlation function as easily as expectation values of,
e.g., total energy. The principles found for the update in continuous time
generalize to any continuous variables in the space of discrete virtual
transitions, and in principle also make it possible to simulate continuous
systems exactly.
