Resource-adaptive quantum flow algorithms for quantum simulations of many-body systems: sub-flow embedding procedures

In this study, we utilized the quantum flow (QFlow) method to perform quantum simulations of correlated systems. The QFlow approach allows for sampling large sub-spaces of the Hilbert space by solving coupled variational problems in reduced dimensionality active spaces. Our research demonstrates that the circuits for evaluating the low dimensionality subproblems of the QFlow algorithms on quantum computers are significantly less complex than the parent (large subspace of the Hilbert space) problem, opening up possibilities for scalable and constant-circuit-depth quantum computing. Our simulations indicate that QFlow can be used to optimize a large number of wave function parameters without an increase in the required number of qubits. We were able to showcase that a variation of the QFlow procedure can optimize 1,100 wave function parameters using modest quantum resources. Furthermore, we investigated an adaptive approach known as the sub-flow approach, which involves a limited number of active spaces in the quantum flow process. Our findings shed light on the potential of QFlow in efficiently handling correlated systems via quantum simulations.