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arXiv:2505.22395 · Physical Review A

Configuration-dependent precision in magnetometry and thermometry using multiqubit quantum sensors

Asghar Ullah, Özgür Esat Müstecaplıoğlu, Matteo G. A. Paris

Published Dec 18, 2025• 2 citations
arXivHTMLPDF

Abstract

We study the performance of quantum sensors composed of four qubits arranged in different geometries for magnetometry and thermometry. The qubits interact via the transverse-field Ising model with both ferromagnetic and antiferromagnetic couplings, maintained in thermal equilibrium with a heat bath under an external magnetic field. Using quantum Fisher information, we evaluate the metrological precision of these sensors. For ferromagnetic couplings, weakly connected graphs (e.g., the chain graph, P_4) perform optimally in estimating weak magnetic fields, whereas highly connected graphs (e.g., the complete graph, K_4) excel at strong fields. Conversely, K_4 achieves the highest sensitivity for temperature estimation in the weak-field regime. In the antiferromagnetic case, we uncover a fundamental trade-off dictated by spectral degeneracy: configurations with non-degenerate energy spectra - such as the pan-like graph (three qubits in a triangle with the fourth attached) - exhibit strong magnetic field sensitivity due to their pronounced response to perturbations. In contrast, symmetric structures like the square graph, featuring degenerate energy levels (particularly ground-state degeneracy), are better suited for precise thermometry. Notably, our four-qubit sensors achieve peak precision in the low-temperature, weak-field regime. Finally, we introduce a spectral sensitivity measure that quantifies energy spectrum deformations under small perturbations, providing a simple heuristic indicator of metrological sensitivity.

DOI
10.1103/zn5v-rcgd

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Quantum thermometry leveraging quantum sensors is investigated with an emphasis on fundamental precision bounds derived from quantum estimation theory. The proposed sensing platform consists of two dissimilar qubits coupled via capacitor, which induce quantum oscillations in the presence of a thermal environment. Thermal equilibrium states are modeled using the Gibbs distribution. The precision limits are assessed through the Quantum Fisher Information (QFI) and the Hilbert-Schmidt Speed (HSS), serving as stringent criteria for sensor sensitivity. Systematic analysis of the dependence of QFI and HSS on tunable parameters -such as qubit energies and coupling strengths- provides optimization pathways for maximizing temperature sensitivity. Furthermore, we explore two distinct quantum thermometry paradigms: (I) local temperature estimation directly performed by Alice, who possesses the quantum sensor interfacing with the thermal bath, and (II) remote temperature estimation conducted by Bob, facilitated via quantum teleportation. In the latter scenario, temperature information encoded in the qubit state is transmitted through a single-qubit quantum thermal teleportation protocol. Our findings indicate that direct measurement yields superior sensitivity compared to remote estimation, primarily due to the inherent advantage of direct sensor-environment interaction. The analysis reveals that increasing Josephson energies diminishes sensor sensitivity, whereas augmenting the mutual coupling strength between the qubits enhances it.