Robust Variational Ground-State Solvers via Dissipative Quantum Feedback Models

Abstract: We propose a variational framework for solving ground-state problems of open quantum systems governed by quantum stochastic differential equations (QSDEs). This formulation naturally accommodates bosonic operators, as commonly encountered in quantum chemistry and quantum optics. By parameterizing a dissipative quantum optical system, we minimize its steady-state energy to approximate the ground state of a target Hamiltonian. The system converges to a unique steady state regardless of its initial condition, and the design inherently guarantees physical realizability. To enhance robustness against persistent disturbances, we incorporate H-infinity control into the system architecture. Numerical comparisons with the quantum approximate optimization algorithm (QAOA) highlight the method's structural advantages, stability, and physical implementability. This framework is compatible with experimental platforms such as cavity quantum electrodynamics (QED) and photonic crystal circuits.