Configuration-Aware Natural Gradient Optimization for Variational Quantum Circuits

P.K. Bharadwaj

Published Apr 24, 2026• 0 citations

Abstract

Variational quantum algorithms (VQAs) are commonly developed under the assumption that a parameterized circuit corresponds to a single, well-defined physical realization. In practice, this assumption is not satisfied. Differences in compilation, gate ordering, and hardware-level perturbations lead to multiple admissible circuit realizations, each associated with a distinct objective over the same parameter space. The resulting optimization problem is therefore not defined by a single loss function, but by a family of configuration-dependent objectives whose aggregate behaviour must be considered. This study formulates optimization explicitly at the level of such configuration families. A consistent extension of natural-gradient methods is developed in which both the descent direction and the local geometric structure are obtained through averaging across configurations. The resulting update preserves the structure of quantum natural gradient methods while ensuring alignment with the family-defined objective. The approach is evaluated using exact statevector simulations on transverse-field Ising and Heisenberg Hamiltonians under controlled variability. Across all tested regimes, the method produces lower average loss, substantially reduced dispersion across configurations, and improved worst-case performance relative to both configuration-specific optimization and gradient-averaged baselines. These results show that when the objective depends on a set of admissible circuit realizations, optimization must be constructed at the same level to obtain stable and reliable solutions.

DOI: 10.5281/zenodo.19438251

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