Quantum Information Harvesting with the Parallel Quantum Flow Algorithm

The quantum flow (QFlow) algorithm provides a resource-efficient framework for describing correlated many-body systems on hybrid quantum-classical architectures. By enabling the parallel utilization of quantum and classical resources, QFlow offers a scalable pathway toward simulations of realistic systems. In this Letter, we report a distributed-memory parallel implementation of the QFlow formalism based on a single- and double-excitationmodel. We demonstrate its performance for target spaces comprising 82 and 114 orbitals, where every active space in the flow contains 6 active electrons in 6 active orbitals, as well as the dissociation of the HF molecule to investigate both weakly and strongly correlated regimes. In the largest QFlow simulations, we optimized 1.17 million wave function parameters using the equivalent of 12 qubits. We introduce an ensemble-weighted averaging strategy that restores the correct potential energy behavior for strongly correlated regimes where a simple arithmetic mean of active-space energies can break down. Despite the modest qubit requirements of the underlying active-space approximations, the method recovers over 95% of the total correlation energy obtained with the coupled cluster singles and doubles (CCSD) approach for systems across different correlation regimes, whether dominated by static or dynamic correlation effects, which remain challenging for existing quantum algorithms. We further show that the QFlow formalism retains high accuracy in extended basis sets with diffuse functions, highlighting its potential for realistic, large-scale quantum chemistry simulations.