  We introduce SantaQlaus, a resource-efficient optimization algorithm tailored
for variational quantum algorithms (VQAs), including applications in the
variational quantum eigensolver (VQE) and quantum machine learning (QML).
Classical optimization strategies for VQAs are often hindered by the complex
landscapes of local minima and saddle points. Although some existing
quantum-aware optimizers adaptively adjust the number of measurement shots,
their primary focus is on maximizing gain per iteration rather than
strategically utilizing quantum shot-noise (QSN) to address these challenges.
Inspired by the classical Stochastic AnNealing Thermostats with Adaptive
momentum (Santa) algorithm, SantaQlaus explicitly leverages inherent QSN for
optimization. The algorithm dynamically adjusts the number of quantum
measurement shots in an annealing framework: fewer shots are allocated during
the early, high-temperature stages for efficient resource utilization and
landscape exploration, while more shots are employed later for enhanced
precision. Numerical simulations on VQE and QML demonstrate that SantaQlaus
outperforms existing optimizers, particularly in mitigating the risks of
converging to poor local optima, all while maintaining shot efficiency. This
paves the way for efficient and robust training of quantum variational models.
