  We develop an efficient algorithm to implement the recently introduced binary
tree state (BTS) ansatz on a classical computer. BTS allows a simple
approximation to permanents arising from the computationally intractable
antisymmetric product of interacting geminals and respects size-consistency. We
show how to compute BTS overlap and reduced density matrices efficiently. We
also explore two routes for developing correlated BTS approaches: Jastrow
coupled cluster on BTS and linear combinations of BT states. The resulting
methods show great promise in benchmark applications to the reduced
Bardeen-Cooper-Schrieffer Hamiltonian and the one-dimensional XXZ Heisenberg
Hamiltonian.
