We present a comprehensive approach to quantum simulations at both zero and
finite temperatures, employing a quantum information theoretic perspective and
utilizing the Clifford + kRz transformations. We introduce the "quantum magic
ladder", a natural hierarchy formed by systematically augmenting Clifford
transformations with the addition of Rz gates. These classically simulable
similarity transformations allow us to reduce the quantumness of our system,
conserving vital quantum resources. This reduction in quantumness is essential,
as it simplifies the Hamiltonian and shortens physical circuit-depth,
overcoming constraints imposed by limited error correction. We improve the
performance of both digital and analog quantum computers on ground state and
finite temperature molecular simulations, not only outperforming the
Hartree-Fock solution, but also achieving consistent improvements as we ascend
the quantum magic ladder. By facilitating more efficient quantum simulations,
our approach enables near-term and early fault-tolerant quantum computers to
address novel challenges in quantum chemistry.Comment: 12 pages, 9 figure