This paper explores hybrid quantum-classical algorithms, specifically focusing on their application in quantum metrology. These Variational Quantum Algorithms (VQAs) show promise for implementation on early quantum devices that cannot yet run quantum error correction. While experimental demonstrations have occurred on various quantum hardware platforms, practical quantum advantage remains an outstanding challenge.
The authors investigate quantum metrology, which uses quantum effects like entanglement to exceed classical limits on measurement precision. They extend previous research to optical phase estimation using squeezed coherent states and homodyne measurements – a combination successfully used in gravitational wave detection, magnetic field sensing, and biological imaging beyond classical limits.
Their experiment demonstrates how a variational algorithm can optimize a quantum sensing setup by finding the optimal probe state and measurement basis despite real-world imperfections like phase fluctuations and loss. The approach optimizes classical Fisher information, a key factor in metrological precision, using parameter shift rules adapted for continuous variable systems.
Two optimization approaches were implemented:
- A gradient-based method that estimates the gradient of classical Fisher information through additional measurements
- A gradient-free Bayesian optimizer for fine-tuning
The results confirm variational techniques’ potential for quantum sensing while highlighting practical challenges. The gradient-based approach handles slow drifts better but requires more time overhead for gradient calculation. The gradient-free method enables faster convergence but needs more fine-tuning of exploration/exploitation parameters.
The experiment consists of three stages: preparing a displaced squeezed state with adjustable parameters, applying a phase shift (the parameter to be sensed), and performing homodyne detection with another adjustable parameter. The optimization happens in real-time, with continuous measurement, cost function estimation, and parameter adjustment.
This approach offers advantages over conventional methods by adapting to actual physical conditions without requiring a complete theoretical model, allowing the protocol to implicitly account for unmodeled effects that could negatively impact performance.
Reference: Nielsen, J.A.H., Kicinski, M.J., Arge, T.N. et al. Variational quantum algorithm for enhanced continuous variable optical phase sensing. npj Quantum Inf 11, 70 (2025). doi:10.1038/s41534-024-00947-1
