  Quantum computation promises to provide substantial speedups in many
practical applications with a particularly exciting one being the simulation of
quantum many-body systems. Adiabatic state preparation (ASP) is one way that
quantum computers could recreate and simulate the ground state of a physical
system. In this paper we explore a novel approach for classically simulating
the time dynamics of ASP with high accuracy, and with only modest computational
resources via an adaptive sampling configuration interaction (ASCI) scheme for
truncating the Hilbert space to only the most important determinants. We verify
that this truncation introduces negligible error, and use this new approach to
simulate ASP for sets of small molecular systems and Hubbard models. Further,
we examine two approaches to speeding up ASP when performed on quantum
hardware: (i) using the complete active space configuration interaction (CASCI)
wavefunction instead of the Hartree-Fock initial state and (ii)~a non-linear
interpolation between initial and target Hamiltonians. We find that starting
with a CASCI wavefunction with a limited active space yields substantial
speedups for many of the systems examined while non-linear interpolation does
not. Additionally, we observe interesting trends in the minimum gap location
(based on the initial state) as well as how critical time can depend on certain
molecular properties such as the number of valence electrons. Importantly, we
find that the required state preparation times do not show an immediate
exponential wall that would preclude an efficient run of ASP on actual
hardware.
