Four Generations of Quantum Biomedical Sensors

Quantum sensors offer significant advantages over classical devices in spatial resolution and sensitivity, enabling transformative applications across materials science, healthcare, and beyond. Their practical performance, however, is often constrained by unmodelled effects, including noise, imperfect state preparation, and non-ideal control fields. In this work, we report the first experimental implementation of a graybox modelling strategy for a solid-state open quantum system. The graybox framework integrates a physics-based system model with a data-driven description of experimental imperfections, achieving higher fidelity than purely analytical (whitebox) approaches while requiring fewer training resources than fully deep-learning blackbox models. We experimentally validate the method on the task of estimating a static magnetic field using a single-spin quantum sensor, performing Bayesian inference with a graybox model trained on prior experimental data. Using roughly 10,000 training datapoints, the graybox model yields several orders of magnitude improvement in mean squared error over the corresponding physics-only model, as well as significant improvement over a blackbox model with comparable size. These results are broadly applicable to a wide range of quantum sensing platforms, not limited to single-spin systems, and are particularly valuable for real-time adaptive protocols, where model inaccuracies can otherwise lead to suboptimal control and degraded performance.

Quantum technology has the potential to transform scientific discovery, but quantum advantages often require processing capabilities well beyond the reach of experimental platforms. We show that coupling a single controllable qubit to an otherwise conventional sensor can exponentially reduce the number of measurements required to learn classical signals. These rigorous quantum advantages apply to fundamental sensing tasks, including learning Fourier coefficients, extracting temporal correlations from time-varying signals, and estimating transformations of physical observables. Using a superconducting cavity--qubit architecture, we experimentally demonstrate $10^7$-fold reductions in the number of measurements required for Fourier-amplitude and time-varying signal learning. Our $\textit{quantum feature sensing}$ algorithms further enable orders-of-magnitude improvements in simulations of weak-signal dark matter detection and wireless communication applications. These quantum advantages are derived from Quantum Phase-Space Inference (Q$Ψ$), a unifying theory of quantum-enhanced experiments that simultaneously converts a set of experimental objectives and constraints into tight lower bounds and optimal quantum-enhanced learning algorithms while producing a certificate of quantum advantage. Q$Ψ$ extends beyond the regimes captured by quantum Fisher information and provides a framework for systematically identifying rigorous quantum advantages in practical experimental tasks. Together, our results establish that near-term quantum technology can exponentially enhance our ability to learn from classical signals.

In this paper, a learning framework is introduced which incorporates principles of probabilistic inference, variational optimization, and geometry-preserving operations inspired by quantum transformations. The central innovation of this quantum-inspired variational convolution (QiVC) lies in its quantum-inspired rotated ensemble (QiRE) mechanism. QiRE performs differentiable low-dimensional subspace rotations of convolutional weights. By drawing a mathematical analogy from unitary evolution, this approach enables structured uncertainty modeling that respects the intrinsic geometry of the parameter space. To demonstrate its practical potential, the concept is instantiated in a QiVC-based convolutional network (QiVC-Net) and evaluated in the context of biosignal classification, focusing on phonocardiogram (PCG) recordings. The proposed QiVC-Net integrates an architecture in which the QiVC layer does not introduce additional parameters, instead performing an ensemble rotation of the convolutional weights through a structured mechanism ensuring robustness without added highly computational burden. Experiments on two benchmark datasets, PhysioNet CinC 2016 and PhysioNet CirCor DigiScope 2022, show that QiVC-Net achieves state-of-the-art performance, reaching accuracies of 97.84% and 97.89%, respectively. These findings highlight the versatility of the QiVC framework and its promise for advancing uncertainty-aware modeling in real-world biomedical signal analysis. The implementation of the QiVConv layer is available in GitHub for public use.