  We propose the regularized compressed double factorization (RC-DF) method to
classically compute compressed representations of molecular Hamiltonians that
enable efficient simulation with noisy intermediate scale (NISQ) and error
corrected quantum algorithms. We find that already for small systems with 12 to
20 qubits, the resulting NISQ measurement scheme reduces the number of
measurement bases by roughly a factor of three and the shot count to reach
chemical accuracy by a factor of three to six compared to truncated double
factorization (DF) and we see order of magnitude improvements over Pauli
grouping schemes. We demonstrate the scalability of our approach by performing
RC-DF on the CpdI species of cytochrome P450 with 58 orbitals and find that
using the resulting compressed Hamiltonian cuts the run time of qubitization
and truncated DF based error corrected algorithms almost in half and even
outperforms the lambda parameters achievable with tensor hypercontraction (THC)
while at the same time reducing the CCSD(T) energy error heuristic by an order
of magnitude.
