  We present new maximally local two-nucleon interactions derived in
$\Delta$-less chiral effective field theory up to
next-to-next-to-next-to-leading order (N$^3$LO), which include all contact and
pion-exchange contributions to the nuclear Hamiltonian up to this order. Our
interactions are fit to nucleon-nucleon phase shifts using a Bayesian
statistical approach, and explore a wide cutoff range from $0.6-0.9$ fm
($\approx 660 - 440$ MeV). These interactions can be straightforwardly employed
in quantum Monte Carlo methods, such as the auxiliary field diffusion Monte
Carlo method. Together with local three-nucleon forces, calculations with these
new interactions will provide improved benchmarks for the structure of atomic
nuclei and serve as crucial input to analyses of astrophysical phenomena of
neutron stars, such as binary neutron-star mergers.
