Electronic energies from coupled fermionic "Zombie" states' imaginary time evolution

Zombie states are a recently introduced formalism to describe coupled coherent fermionic states that 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 [D. 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 allows 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" that 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 biased random grids of Zombie states may present an alternative to the existing quantum Monte Carlo methods.