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Physical Review A

Optimized emulation of quantum magnetometry via superconducting qubits

Nikolay Gusarov, Michael Romanovich Perelshtein, Pertti Juhani Hakonen, Gheorghe Sorin Paraoanu

Published May 19, 2023• 8 citations
Publisher

Abstract

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 $1--10\phantom{\rule{4pt}{0ex}}\mathrm{kHz}$ magnetic fields, which is comparable to more established experimental platforms for magnetometry.

DOI
10.1103/physreva.107.052609

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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.
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.
Quantum metrology promises enhanced precision by harnessing entanglement and quantum algorithms. Yet, realizing such gains on current noisy quantum hardware remains a significant challenge. Here, we investigate quantum-enhanced magnetometry using phase estimation algorithms on superconducting quantum processors the IQM Garnet and Rigetti Ankaa-3. We experimentally compare the performance of different entangled, parallel and combined sensing strategies. While the entangled states should provide improvements in sensitivity in ideal conditions, we find that their advantage is less in practice on currently available systems. Instead, partitioning qubits into smaller entangled subsets and operating them in parallel achieves near-optimal sensitivity. We derive a general expression for magnetometric precision as a function of total qubit number and subset entanglement size, based on the attenuation of the system, identifying optimal configurations under realistic noise constraints.
Quantum sensing has become a key technology for precision measurement, with applications spanning magnetometry, gravitational sensing, navigation and geodesy, materials and device diagnostics, and biomedical detection. This motivates the study of quantum-enhanced magnetometry with entangled states. We focus on Greenberger–Horne–Zeilinger (GHZ) and Dicke states operated within a Kitaev phase estimation algorithm (PEA). We consider superconducting fluxonium-qubit sensors, which are modelled with relaxation and dephasing noise. Using a Bayesian update procedure, we evaluate the estimation performance and compare the GHZ and Dicke sensors in terms of sensitivity, dynamical range, and information gain. GHZ probes achieve the highest local sensitivity, while Dicke probes maintain comparable sensitivity over a substantially wider bias interval and exhibit improved tolerance to bias errors and edge effects in PEA sequence. Our results demonstrate a trade-off between local peak sensitivity and the achievable dynamical range and robustness under noise.
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.
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.