Nested-Loop Trajectory-Informed Variational Quantum Solver for Interior-Point OPF
Optimal power flow (OPF) solved by an interior-point method (IPM) requires repeatedly solving Newton linear systems. When variational quantum linear solvers (VQLS) are used, each IPM iteration involves an additional nested inner variational optimization loop, which can significantly slow the overall quantum-assisted IPM convergence. To address this challenge, this paper proposes a dual-level trainable quantum IPM framework for OPF that leverages early solver-generated trajectories rather than relying on single-point prediction. The key observation is that early IPM iterates provide informative primal-dual, slack, and barrier-variable evolution about the path to optimality, while early VQLS parameter updates provide useful information about the later variational search. At the quantum-solver level, a trainable parameter model uses a short prefix of the VQLS parameter trajectory to project the remaining variational search toward a lower-cost region. At the OPF-solver level, a second trainable model uses early primal-dual IPM iterates to project a later central path state, which is restored to an admissible point before IPM refinement continues. Simulation studies show that the proposed approach reduces the number of variational updates by up to $95\%$ while maintaining OPF objective values close to the classical IPM reference. A 2-bus demonstration on real quantum hardware is also included to validate the implementation of the proposed workflow.