Tailored and Externally Corrected Coupled Cluster with Quantum Inputs.

We propose to use wave function overlaps obtained from a quantum computer as inputs for the classical split-amplitude techniques, tailored and externally corrected coupled cluster, to achieve balanced treatment of static and dynamic correlation effects in molecular electronic structure simulations. By combining insights from statistical properties of matchgate shadows, which are used to measure quantum trial state overlaps, with classical correlation diagnostics, we can provide quantum resource estimates well into the classically no longer exactly solvable regime. We find that rather imperfect wave functions and remarkably low shot counts are sufficient to cure qualitative failures of plain coupled cluster singles doubles and to obtain chemically precise dynamic correlation energy corrections.

Efficient quantum analytic nuclear gradients with double factorization.

Efficient representations of the Hamiltonian, such as double factorization, drastically reduce the circuit depth or the number of repetitions in error corrected and noisy intermediate-scale quantum (NISQ) algorithms for chemistry. We report a Lagrangian-based approach for evaluating relaxed one- and two-particle reduced density matrices from double factorized Hamiltonians, unlocking efficiency improvements in computing the nuclear gradient and related derivative properties. We demonstrate the accuracy and feasibility of our Lagrangian-based approach to recover all off-diagonal density matrix elements in classically simulated examples with up to 327 quantum and 18 470 total atoms in QM/MM simulations with modest-sized quantum active spaces.