  The development and implementation of increasingly accurate methods for
electronic structure calculations mean that, for many atomistic simulation
problems, treating light nuclei as classical particles is now one of the most
serious approximations. Even though recent developments have significantly
reduced the overhead for modelling the quantum nature of the nuclei, the cost
is still prohibitive when combined with advanced electronic structure methods.
Here we present how multiple time step integrators can be combined with
ring-polymer contraction techniques (effectively, multiple time stepping in
imaginary time) to reduce virtually to zero the overhead of modelling nuclear
quantum effects, while describing inter-atomic forces at high levels of
electronic structure theory. This is demonstrated for a combination of MP2 and
semi-local DFT applied to the Zundel cation. The approach can be seamlessly
combined with other methods to reduce the computational cost of path integral
calculations, such as high-order factorizations of the Boltzmann operator, or
generalized Langevin equation thermostats.
