Dynamic Estimation Loss Control in Variational Quantum Sensing via Online Conformal Inference

Abstract: Quantum sensing exploits non-classical effects to overcome limitations of classical sensors, with applications ranging from gravitational-wave detection to nanoscale imaging. However, practical quantum sensors built on noisy intermediate-scale quantum (NISQ) devices face significant noise and sampling constraints, and current variational quantum sensing (VQS) methods lack rigorous performance guarantees. This paper proposes an online control framework for VQS that dynamically updates the variational parameters while providing deterministic error bars on the estimates. By leveraging online conformal inference techniques, the approach produces sequential estimation sets with a guaranteed long-term risk level. Experiments on a quantum magnetometry task confirm that the proposed dynamic VQS approach maintains the required reliability over time, while still yielding precise estimates. The results demonstrate the practical benefits of combining variational quantum algorithms with online conformal inference to achieve reliable quantum sensing on NISQ devices.