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

TL;DR

This work addresses reliable sequential estimation in variational quantum sensing on NISQ devices by marrying online conformal inference with adaptive quantum sensing. The proposed framework outputs a time-varying estimation set with a guaranteed long-term risk level while updating both the variational probe parameters and the estimator. The key innovations include online threshold calibration, a smooth surrogate for set size to enable online gradient updates, and a formal bound ensuring $\bar{L}(T)\le\alpha+O(1/T)$. Experimental validation on a quantum magnetometry task shows maintained reliability over time and tighter estimation sets compared to non-adaptive approaches, highlighting the practical impact for trustworthy quantum sensing on noisy hardware.

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.

Figures (5)

• Figure 1: (a) Illustration of the variational quantum sensing (VQS) system under study. A probe quantum state is generated by a $n$-qubit quantum circuit parametrised by the vector $\theta$. The probe state interacts with the parameter of interest $x_t$, and the perturbed state $\rho_{\theta}(x_t)$ is then measured with a given fixed POVM $\{\Pi^s\}$. The set of measurements $s$ is finally fed to a classical estimator, which produces an estimation set $\hat{\mathcal{X}}_t$. (b) The goal is to control the size of the estimation set $\hat{\mathcal{X}}_t$ so as to meet a long-term deterministic reliability level.
• Figure 2: Time-averaged coverage of the proposed dynamic scheme as a function of the time steps $t$ for target average loss values $\alpha=0.2$, $\alpha=0.3$ and $\alpha=0.4$.
• Figure 3: Time-averaged coverage of the proposed dynamic scheme and of the benchmarks as a function of the time step $t$ for $\alpha=0.3$. The target coverage is shown in a dashed line.
• Figure 4: Time-averaged set size of the proposed dynamic scheme and of the benchmarks as a function of the time step $t$ for $\alpha=0.3$.
• Figure 5: Time-averaged coverage as a function of the number of time steps $t$ for the proposed dynamic scheme with different decoder models.

Theorems & Definitions (1)

• Proposition 1