The performance of a quantum sensor is fundamentally limited by noise. This noise is particularly damaging when it becomes correlated with the readout of a target signal, caused by fluctuations of the sensor's operating parameters. These uncertainties limit sensitivity in a way that can be understood with multiparameter estimation theory. We develop a new approach, adaptable to any quantum platform, for designing robust sensing protocols that leverages multiparameter estimation theory and machine learning to decorrelate a target signal from fluctuating off-target (``nuisance'') parameters. Central to our approach is the identification of information-theoretic goals that guide a machine learning agent through an otherwise intractably large space of potential sensing protocols. As an illustrative example, we apply our approach to a reconfigurable optical lattice to design an accelerometer whose sensitivity is decorrelated from lattice depth noise. We demonstrate the effect of decorrelation on outcomes and Bayesian inferencing through statistical analysis in parameter space, and discuss implications for future applications in quantum metrology and computing.
The performance of a quantum sensor is fundamentally limited by noise. This noise is particularly damaging when it becomes correlated with the readout of a target signal, caused by fluctuations of the sensor's operating parameters. These uncertainties limit sensitivity in a way that can be understood with multiparameter estimation theory. We develop a new approach, adaptable to any quantum platform, for designing robust sensing protocols that leverages multiparameter estimation theory and machine learning to decorrelate a target signal from fluctuating off-target (``nuisance'') parameters. Central to our approach is the identification of information-theoretic goals that guide a machine learning agent through an otherwise intractably large space of potential sensing protocols. As an illustrative example, we apply our approach to a reconfigurable optical lattice to design an accelerometer whose sensitivity is decorrelated from lattice depth noise. We demonstrate the effect of decorrelation on outcomes and Bayesian inferencing through statistical analysis in parameter space, and discuss implications for future applications in quantum metrology and computing.
Critical quantum metrology relies on the extreme sensitivity of a system's eigenstates near the critical point of a quantum phase transition to Hamiltonian perturbations. This means that these eigenstates are extremely sensitive to all the parameters of the Hamiltonian. In realistic settings, there is always some degree of uncertainty in the control parameters used to tune the system to criticality. These uncertainties, while not the target of estimation, can significantly affect the attainable precision, effectively acting as nuisance parameters in the estimation process. Despite being a practically relevant source of noise, their impact on critical metrology has been largely overlooked. In this work we present a general framework that interpolates between single- and multiparameter estimation settings, enabling a systematic analysis of how such uncertainties influence sensitivity. We apply this framework to the paradigmatic transverse field Ising and Lipkin-Meshkov-Glick models, explicitly demonstrating how uncertainty in control parameters affects the metrological performance of critical sensors. For finite-size systems, we identify a fundamental trade-off between robustness to uncertainty and the ability to retain a quantum advantage at the critical point. Our results contribute to a deeper understanding of the practical limitations of critical quantum metrology and provide a route toward its more resilient implementation.
We propose and analyze a versatile and efficient multiparameter quantum sensing protocol, which simultaneously estimates many non-commuting and time-dependent signals that are coherently or incoherently coupled to sensing particles. Even in the presence of control imperfections and readout errors, our approach can detect exponentially many parameters in the system size while maintaining the optimal scaling of sensitivity. To accomplish this, scrambling dynamics are leveraged to map distinct signals to unique patterns of bitstring measurements, which distinguishes a large number of signals without significant sensitivity loss. Based on this principle, we develop a computationally efficient protocol utilizing random global Clifford unitaries and evaluate its performance both analytically and numerically. Our protocol naturally extends to scrambling dynamics generated by random local Clifford circuits, local random unitary circuits (RUCs), and ergodic Hamiltonian evolution--commonly realized in near-term quantum hardware--and opens the door to applications ranging from precise noise benchmarking of quantum dynamics to learning time-dependent Hamiltonians.
Abstract The quest for precision in parameter estimation is a fundamental task in different scientific areas. The relevance of this problem thus provided the motivation to develop methods for the application of quantum resources to estimation protocols. Within this context, Bayesian estimation offers a complete framework for optimal quantum metrology techniques, such as adaptive protocols. However, the use of the Bayesian approach requires extensive computational resources, especially in the multiparameter estimations that represent the typical operational scenario for quantum sensors. Hence, the requirement to characterize protocols implementing Bayesian estimations can become a significant challenge. This work focuses on the crucial task of robustly benchmarking the performances of these protocols in both single and multiple-parameter scenarios. By comparing different figures of merits, evidence is provided in favor of using the median of the quadratic error in the estimations in order to mitigate spurious effects due to the numerical discretization of the parameter space, the presence of limited data, and numerical instabilities. These results, providing a robust and reliable characterization of Bayesian protocols, find natural applications to practical problems within the quantum estimation framework.
High-sensitivity accelerometers and gravimeters, achieving the ultimate limits of measurement sensitivity are key tools for advancing both fundamental and applied physics. While numerous platforms have been proposed to achieve this goal, from atom interferometers to optomechanical systems, all of these studies neglect the effects of intrinsic quantum uncertainty in time estimation. Starting from the Hamiltonian of a generic linear quantum sensor, we derive the two-parameter quantum Fisher information matrix and establish the corresponding Cram'er-Rao bound, treating time as an uncertain (nuisance) parameter. Our analysis reveals a fundamental coupling between time and signal estimation that inherently degrades measurement sensitivity, with the standard single-parameter quantum limit recovered only at specific interrogation times or under special decoupling conditions. We then apply these results to an optomechanical gravimeter and explicitly derive an optimal decoupling condition under which the effects of time uncertainty are averaged out in a continuous measurement scheme. Our approach is general and can be readily extended to a broad class of quantum sensors.
Recent years have witnessed a growing interest in understating the limitations imposed by quantum noise in precision measurements and devising techniques to reduce it. The attention is currently turning to the simultaneously estimation of several parameters of interest, driven by its promising potential across a wide range of sensing applications as well as fueled by experimental progress in various optical and atomic platforms. Here, we provide a comprehensive overview of key research directions in multiparameter quantum sensing and metrology, highlighting both opportunities and challenges. We introduce the basic framework, discuss ultimate sensitivity bounds, optimal measurement strategies, and the role of quantum incompatibility, showing important differences with respect to single-parameter estimation. Additionally, we discuss emerging experimental implementations in distributed quantum sensing, including cutting-edge optimization techniques. This review aims to bridge the gap between theory and experiments, paving the way for the next-generation of quantum sensors and their integration with other quantum technologies.
Quantum sensing offers sensitivities surpassing classical limits, yet practical deployment is often constrained by noise and inefficient signal extraction. This systematic review synthesizes literature from 2015 to 2025 and maps the landscape of data-driven signal processing across diverse platforms, including nitrogen-vacancy (NV) centers and cold atom interferometers. Emerging methodologies are categorized and emphasis is placed on the dominance of hybrid quantum-classical architectures where classical machine learning manages high-dimensional data processing while quantum processors execute specific primitives like feature mapping. Our findings demonstrate that advanced statistical frameworks such as Variational Bayesian Inference (VBI) enable scalable multi-parameter estimation with polynomial complexity, allowing dozens of sensor parameters to be estimated within minutes. Meanwhile, quantum sensing missions in GPS-denied navigation have achieved operational gains through AI-automated software designed to manage quantum hardware drifts and environmental noise, despite a persistent reality gap for generalized quantum machine learning. We further analyze the critical sensitivity-robustness dilemma inherent in entangled sensors and discuss mitigation strategies such as covariant quantum error-correcting codes. We also distinguish between theoretical Quantum Fisher Information (QFI) and realized Mean Squared Error (MSE) of sensor outputs to resolve benchmarking inconsistencies in quantum metrology, and propose a "Gold Standard" reproducibility framework tailored for the Noisy Intermediate-Scale Quantum (NISQ) era to promote automated workflows and hardware calibration transparency. This review provides a strategic roadmap for researchers to bridge the gap between theoretical sensitivity and reliable, software-defined operational utility in quantum sensing.