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Quantum metrology based on superconducting qubits

Anton Kolosvetov, Nikolay Gusarov, Vladimir Slepnev, Michael Perelshtein, Vasilii Sevriuk, Azat R. Gubaydullin, V. M. Vinokur

Published Jun 4, 2026• 1 citation
Publisher

Abstract

Quantum metrology based on superconducting qubits offers unprecedented precision in measuring fundamental physical quantities, particularly magnetic fields. In this study, we develop a modified quantum phase estimation algorithm utilizing superconducting qubits, enhanced by optimized initial state preparation, significantly improving measurement sensitivity and reducing estimation times compared to conventional techniques. To ensure practical applicability and robustness, we incorporate advanced noise modeling, including intrinsic decoherence effects such as flux-induced noise and Purcell losses. Through detailed analytical modeling and numerical simulations, we systematically evaluate sensitivity and practical implementation constraints across various superconducting qubit architectures—transmon, fluxonium, conventional flux, and C-shunt flux qubits. Our approach quantifies the critical trade-offs between coherence, measurement dynamics, and sensitivity, identifying optimal operational regimes for high-performance quantum sensing. We introduce custom circuit simulation methods enabling the analysis and optimization of arbitrary superconducting quantum devices. Our findings provide a framework for advancing quantum-enhanced magnetometry and promise to facilitate next-generation quantum sensors for fundamental physics research, gravitational field measurements, and quantum-assisted searches for dark matter candidates.

DOI
10.1038/s41534-026-01285-0

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Quantum metrology based on superconducting qubits offers unprecedented precision in measuring fundamental physical quantities, particularly magnetic fields. In this study, we develop a modified quantum phase estimation algorithm utilizing superconducting qubits, enhanced by optimized initial state preparation, significantly improving measurement sensitivity and reducing estimation times compared to conventional techniques. To ensure practical applicability and robustness, we incorporate advanced noise modeling, including intrinsic decoherence effects such as flux-induced noise and Purcell losses. Through detailed analytical modeling and numerical simulations, we systematically evaluate sensitivity and practical implementation constraints across various superconducting qubit architectures—transmon, fluxonium, conventional flux, and C-shunt flux qubits. Our approach quantifies the critical trade-offs between coherence, measurement dynamics, and sensitivity, identifying optimal operational regimes for high-performance quantum sensing. We introduce custom circuit simulation methods enabling the analysis and optimization of arbitrary superconducting quantum devices. Our findings provide a framework for advancing quantum-enhanced magnetometry and promise to facilitate next-generation quantum sensors for fundamental physics research, gravitational field measurements, and quantum-assisted searches for dark matter candidates.
Abstract Sensing and metrology are crucial in both fundamental science and practical applications. They meet the constant demand for precise data, enabling more dependable assessments of theoretical models’ validity. Sensors, now a common feature in many fields, play a vital role in applications like gravity imaging, geology, navigation, security, timekeeping, spectroscopy, chemistry, magnetometry, healthcare, and medicine. The advancements in quantum technologies have sparked interest in employing quantum systems as sensors, offering enhanced capabilities and new possibilities. This article describes the optimization of the quantum-enhanced sensing of magnetic fluxes with a Kitaev phase estimation algorithm based on frequency tunable transmon qubits. It provides the optimal flux biasing point for sensors with different qubit transition frequencies and gives an estimation of decoherence rates and achievable sensitivity. The use of 2- and 3-qubit entangled states are compared in simulation with the single-qubit case. The flux sensing accuracy reaches 10 − 8 ⋅ Φ 0 and scales inversely with time, which proves the speed-up of sensing with high ultimate accuracy.
We develop the quantum approach to magnetometry utilizing phase estimation algorithms, demonstrating improvements in the estimation of magnetic flux in both precision and dynamical range. We propose the modifications to conventional algorithms including the signal modulation and proximity time measurements. We demonstrate that our approach extends the dynamical range and improves the precision of magnetic flux detection. We show that our approach enhances performance of superconducting qubits and enables higher information gain without compromising dynamical range, paving the way toward achieving the Heisenberg limit. Combining adaptive algorithms with device-specific calibration, our methods bridge the gap between theoretical advancements and practical quantum sensing applications, offering a powerful framework for metrology using superconducting qubits.
High-precision magnetometers have found wide applications in medicine, geological exploration, material property studies, and other fields of human activity. Recently, there has been significant development in magnetometers based on the evolution of quantum system states under the influence of an external magnetic field. A notable example of such a quantum system is the fluxonium superconducting qubit. In this paper, we evaluate the performance of a low-frequency magnetic field sensor based on the fluxonium qubit. The analysis utilizes parameters from qubits implemented by various experimental groups. We compare the performance of a fluxonium-based magnetometer with that of superconducting quantum interference devices. Our calculations show that fluxonium-based magnetometers are capable of high-precision measurements and that the high intrinsic inductance of the fluxonium loop allows efficient coupling with auxiliary antennas. Moreover, we propose the algorithm upgrade for low-frequency magnetic field measurements using qubits, which could enhance measurement accuracy by approximately a factor of two compared to existing qubit-based algorithms.
Quantum magnetometry based on adaptive phase estimation allows for Heisenberg precision while avoiding creation and maintenance of complex entangled states. However, the absolute sensitivity is limited by the nonoptimal use of quantum resources provided by multiple-qubit devices and algorithmic realizations of the protocol. Here, addressing both issues, we advance the time-ascending phase estimation protocol by numerical improvements of Bayesian learning, i.e., sequential updating of the field distribution, and optimal exploitation of resources provided by unentangled qubits with limited coherence. Such algorithmic improvements are used to evaluate the absolute sensitivity both on a simulator and by pulsed-transmon experiments conducted on the IBMQ platform, where we take advantage of high coherence time. In addition, we compare the proficiency of separable and entangled states for magnetometry and show that, in practice, separable states provide superior performance. Flux-sensing emulation experiments demonstrate that a sensitivity of $(0.17--1.74)\ensuremath{\mu}{\mathrm{\ensuremath{\Phi}}}_{0}\phantom{\rule{4pt}{0ex}}{(\sqrt{\mathrm{Hz}})}^{\ensuremath{-}1}$ (where ${\mathrm{\ensuremath{\Phi}}}_{0}$ is the flux quantum) for a single-qubit magnetometer and $(0.06--0.65)\ensuremath{\mu}{\mathrm{\ensuremath{\Phi}}}_{0}\phantom{\rule{4pt}{0ex}}{(\sqrt{\mathrm{Hz}})}^{\ensuremath{-}1}$ for a five-qubit magnetometer can be achieved for slowly oscillating 1−−10kHz1--10\phantom{\rule{4pt}{0ex}}\mathrm{kHz}1−−10kHz magnetic fields, which is comparable to more established experimental platforms for magnetometry.
Phase estimation algorithms are key protocols in quantum information processing. Besides applications in quantum computing, they can also be employed in metrology as they allow for fast extraction of information stored in the quantum state of a system. Here, we implement two suitably modified phase estimation procedures, the Kitaev and the semiclassical Fourier-transform algorithms, using an artificial atom realized with a superconducting transmon circuit. We demonstrate that both algorithms yield a flux sensitivity exceeding the classical shot-noise limit of the device, allowing one to approach the Heisenberg limit. Our experiment paves the way for the use of superconducting qubits as metrological devices which are potentially able to outperform the best existing flux sensors with a sensitivity enhanced by few orders of magnitude.
A measurement of a single-qubit quantum sensor reveals at most 1 bit of information about the signal that was sensed. To perform a classification task on the signal, the conventional approach is to repeat a sensing protocol many times, averaging the measurement results to obtain a high-precision estimate of the sensed signal, and then to apply classical postprocessing. Quantum computational sensing (QCS) is an alternative approach that breaks with the paradigm of first obtaining a classical estimate of the signal and then computing a function of the estimated signal in postprocessing. QCS instead combines quantum sensing with quantum computing to concentrate information about the signal relevant to the task into the solitary bit revealed by each measurement. Here, we report on the experimental demonstration of QCS where sensing and computing were both performed by the same single superconducting transmon qubit. We consider various binary classification tasks based on static and oscillating magnetic fields induced by current through a flux line. The fields were sensed through a double-junction superconducting quantum interference device (SQUID) loop that was part of the qubit. We used a protocol based on quantum signal processing to preprocess the sensed signals in the quantum domain prior to measurement. For tasks on static magnetic fields, our protocol outperformed the conventional baseline of Ramsey-based phase estimation by as much as 15 percentage points. For tasks on oscillating magnetic fields, we classified signal amplitude and frequency with up to 20 and 15 percentage points higher accuracy, respectively, compared to the conventional baseline of optimized dynamical-decoupling protocols. Our results illustrate how quantum computing can enhance quantum sensing even with a minimally sized quantum system subject to the practical limitations of decoherence and error-prone operations.