  An accurate assessment of how quantum computers can be used for chemical
simulation, especially their potential computational advantages, provides
important context on how to deploy these future devices. In order to perform
this assessment reliably, quantum resource estimates must be coupled with
classical simulations attempting to answer relevant chemical questions and to
define the classical simulation frontier. Herein, we explore the quantum and
classical resources required to assess the electronic structure of cytochrome
P450 enzymes (CYPs) and thus define a classical-quantum advantage boundary.
This is accomplished by analyzing the convergence of DMRG+NEVPT2 and coupled
cluster singles doubles with non-iterative triples (CCSD(T)) calculations for
spin-gaps in models of the CYP catalytic cycle that indicate multireference
character. The quantum resources required to perform phase estimation using
qubitized quantum walks are calculated for the same systems. Compilation into
the surface-code provides runtime estimates to compare directly to DMRG
runtimes and to evaluate potential quantum advantage. Both classical and
quantum resource estimates suggest that simulation of CYP models at scales
large enough to balance dynamic and multiconfigurational electron correlation
has the potential to be a quantum advantage problem and emphasizes the
important interplay between classical simulations and quantum algorithms
development for chemical simulation.
