  The performance of computational methods for many-body physics and chemistry
is strongly dependent on the choice of basis used to cast the problem; hence,
the search for better bases and similarity transformations is important for
progress in the field. So far, tools from theoretical quantum information have
been not thoroughly explored for this task. Here we take a step in this
direction by presenting efficiently computable Clifford similarity
transformations for quantum chemistry Hamiltonians, which expose bases with
reduced entanglement in the corresponding molecular ground states. These
transformations are constructed via block diagonalization of a hierarchy of
truncated molecular Hamiltonians, preserving the full spectrum of the original
problem. We show that the bases introduced here allow for more efficient
classical and quantum computation of ground state properties. First, we find a
systematic reduction of bipartite entanglement in molecular ground states as
compared to standard problem representations. This entanglement reduction has
implications in classical numerical methods such as ones based on the density
matrix renormalization group. Then, we develop variational quantum algorithms
that exploit the structure in the new bases, showing again improved results
when the hierarchical Clifford transformations are used.
