  Zombie States are a recently introduced formalism to describe coupled
coherent Fermionic states which address the Fermionic sign problem in a
computationally tractable manner. Previously it has been shown that Zombie
States with fractional occupations of spin-orbitals obeyed the correct
Fermionic creation and annihilation algebra and presented results for real-time
evolution [Dmitrii V. Shalashilin, J. Chem. Phys. 148, 194109 (2018)]. In this
work we extend and build on this formalism by developing efficient algorithms
for evaluating the Hamiltonian and other operators between Zombie States and
address their normalization. We also show how imaginary time propagation can be
used to find the ground state of a system. We also present a biasing method,
for setting up a basis set of random Zombie States, that allow much smaller
basis sizes to be used while still accurately describing the electronic
structure Hamiltonian and its ground state and describe a technique of wave
function "cleaning" which removes the contributions of configurations with the
wrong number of electrons, improving the accuracy further. We also show how
low-lying excited states can be calculated efficiently using a Gram-Schmidt
orthogonalization procedure.The proposed algorithm of imaginary time
propagation on a biased random grids of Zombie States may present an
alternative to existing Quantum Monte Carlo methods.
