Lyapunov control-inspired quantum algorithms for ground state preparation

The Feedback-based Algorithm for Quantum OptimizatioN (FALQON) was recently proposed as a strategy for performing combinatorial optimization on quantum computers.?The key feature of this approach is that it?does not?require any classical optimization, which differentiates it from QAOA and other variational quantum algorithms. Instead, quantum circuit parameter values are set using a deterministic feedback law derived from quantum Lyapunov control principles. This feedback law guarantees a monotonic improvement in solution quality with respect to the depth of the quantum circuit. In this talk, we discuss how this framework can be adapted to applications beyond combinatorial optimization. To this end, we introduce a generalized formulation of feedback-based quantum algorithms for preparing ground states of quantum systems in a manner that is optimization-free. We investigate its performance for finding ground states of the Fermi-Hubbard model for strongly correlated quantum systems, and present a variety of numerical analyses exploring its robustness and convergence properties, the effect of parameter variation, and the impact of different modifications to the standard FALQON approach. Sandia National Labs is managed and operated by NTESS under DOE NNSA contract DENA0003525. SAND2022-14643 A.