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arXiv:2512.11671

Tailored Error Mitigation for Single-Qubit Magnetometry

Miriam Resch, Dennis Herb, Mirko Rossini, Joachim Ankerhold, Dominik Maile

quant-phcond-mat.mes-hallSubmitted Dec 12, 2025• Announced Dec 15, 2025• 0 citations
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Abstract

Quantum sensing is an emerging field with the potential to outperform classical methods in both precision and spatial resolution. However, the sensitivity of the underlying quantum platform also makes the sensors highly susceptible to their environmental noise. To address this issue, techniques from the field of quantum error mitigation use information about the noise to improve measurement results. We present a novel mitigation technique for quantum sensors to efficiently reverse the effects of any noise that can be described by a completely positive trace preserving map. The method leverages the knowledge acquired by a pre-characterization step of the device to automatically adapt to the complexity of the dissipative evolution and to indicate optimal sensing times $τ$ to achieve the most accurate results. We demonstrate that our method reaches the best achievable sensitivity in noisy single-NV-center magnetometry. This work marks a further step toward more resilient quantum sensors with the smallest scale of resolution.

Comments
7 pages, 3 figures (main), 18 pages, 15 figures (supplementary)

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Quantum sensing is an emerging field with the potential to outperform classical methods in both precision and spatial resolution. However, the sensitivity of the underlying quantum platform also makes the sensors highly susceptible to their environmental noise. To address this issue, techniques from the field of quantum error mitigation use information about the noise to improve measurement results. We present a novel mitigation technique for quantum sensors to efficiently reverse the effects of any noise that can be described by a completely positive trace preserving map. The method leverages the knowledge acquired by a pre-characterization step of the device to automatically adapt to the complexity of the dissipative evolution and to indicate optimal sensing times τττ to achieve the most accurate results. We demonstrate that our method reaches the best achievable sensitivity in noisy single-NV-center magnetometry.
This work marks a further step toward more resilient quantum sensors with the smallest scale of resolution.
Quantum sensors take advantage of the inherent sensitivity of quantum systems to external environment perturbations to precisely measure target signals. The same interaction with the environment, however, limits the device sensitivity by reducing the coherence of the quantum states. Quantum control can play a crucial role in improving the sensor performance. We explore quantum control tools to improve the performance of a NitrogenVacancy (NV) center as a single-qubit sensor of ultra-weak magnetic fields in noisy environments. We present a method to obtain a precise spectroscopic characterization of the NV environment, instrumental to design robust sensing strategies with improved noise protection. Then, we exploit optimal quantum control based on a set of numerical methods to optimize the temporal dependence of the sensor driving field adapted to quantum sensing purposes, and prove its advantage to achieve best compromises between signal acquisition and noise cancellation.
Nitrogen-vacancy (NV) centers in diamond can serve as highly sensitive solid-state quantum sensors for high-sensitivity magnetometry. However, in the noisy intermediate-scale quantum (NISQ) era, extracting reliable information from noisy, finite-shot, and measurement-limited sensing data remains a considerable challenge. Whereas, quantum machine learning (QML) offers a potential path to improve parameter estimation by learning nonlinear relationships between quantum-sensing data and the underlying physical signal. In this work, we investigate the role of QML in magnetic-field estimation within an NV center-inspired magnetometry setting. We formulated magnetic field sensing as a supervised regression task. We compared the performance of several classical machine learning models trained on measurement-based classical data with that of quantum kernel-based models trained on pre-measurement coherent quantum states. Our objective is to isolate the impact of measurement-induced information loss and therefore provide a theoretical upper bound on the sensing performance. The upper bound is achievable only when coherent quantum information is directly available to the learning model. Our results show that QML-based sensing performance improves significantly with coherent quantum-state information, and not much with changes in model complexity or learning paradigm. This observation underscores the importance of learning pipelines that tightly integrate quantum sensors and QML models to enhance magnetic field sensing under realistic constraints.
Quantum sensing is one of the most promising applications for quantum technologies . However, reaching the ultimate sensitivities enabled by the laws of quantum mechanics can be a challenging task in realistic scenarios where noise is present. While several strategies have been proposed to deal with the detrimental effects of noise, these come at the cost of an extra shot budget. Given that shots are a precious resource for sensing – as infinite measurements could lead to infinite precision – care must be taken to truly guarantee that any shot not being used for sensing is actually leading to some metrological improvement. In this work, we study whether investing shots in error-mitigation, inference techniques, or combinations thereof, can improve the sensitivity of a noisy quantum sensor on a (shot) budget. We present a detailed bias–variance error analysis for various sensing protocols. Our results show that the costs of zero-noise extrapolation techniques outweigh their benefits. We also find that pre-characterizing a quantum sensor via inference techniques leads to the best performance, under the assumption that the sensor is sufficiently stable.
Quantum systems can be used to measure various quantities in their environment with high precision. Often, however, their sensitivity is limited by the decohering effects of this same environment. Dynamical decoupling schemes are widely used to filter environmental noise from signals, but their performance is limited by the spectral properties of the signal and noise at hand. Quantum error correction schemes have therefore emerged as a complementary technique without the same limitations. To date, however, they have failed to correct the dominant noise type in many quantum sensors, which couples to each qubit in a sensor in the same way as the signal. Here we show how quantum error correction can correct for such noise, which dynamical decoupling can only partially address. Whereas dynamical decoupling exploits temporal noise correlations in signal and noise, our scheme exploits spatial correlations. We give explicit examples in small quantum devices and demonstrate a method by which error-correcting codes can be tailored to their noise.
Abstract Quantum systems can be used to measure various quantities in their environment with high precision. Often, however, their sensitivity is limited by the decohering effects of this same environment. Dynamical decoupling schemes are widely used to filter environmental noise from signals, but their performance is limited by the spectral properties of the signal and noise at hand. Quantum error correction schemes have therefore emerged as a complementary technique without the same limitations. To date, however, they have failed to correct the dominant noise type in many quantum sensors, which couples to each qubit in a sensor in the same way as the signal. Here we show how quantum error correction can correct for such noise, which dynamical decoupling can only partially address. Whereas dynamical decoupling exploits temporal noise correlations in signal and noise, our scheme exploits spatial correlations. We give explicit examples in small quantum devices and demonstrate a method by which error-correcting codes can be tailored to their noise.
Abstract New quantum computing architectures consider integrating qubits as sensors to provide actionable information useful for calibration or decoherence mitigation on neighboring data qubits, but little work has addressed how such schemes may be efficiently implemented in order to maximize information utilization. Techniques from classical estimation and dynamic control, suitably adapted to the strictures of quantum measurement, provide an opportunity to extract augmented hardware performance through automation of low-level characterization and control. In this work, we present an adaptive learning framework, Noise Mapping for Quantum Architectures (NMQA), for scheduling of sensor–qubit measurements and efficient spatial noise mapping (prior to actuation) across device architectures. Via a two-layer particle filter, NMQA receives binary measurements and determines regions within the architecture that share common noise processes; an adaptive controller then schedules future measurements to reduce map uncertainty. Numerical analysis and experiments on an array of trapped ytterbium ions demonstrate that NMQA outperforms brute-force mapping by up to 20× (3×) in simulations (experiments), calculated as a reduction in the number of measurements required to map a spatially inhomogeneous magnetic field with a target error metric. As an early adaptation of robotic control to quantum devices, this work opens up exciting new avenues in quantum computer science.