Accelerating Quantum Computations of Chemistry Through Regularized Compressed Double Factorization

Abstract: 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.