Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Frontiers in Quantum Science and Technology

Quantum walks on a ring as a versatile single-parameter sensor

Lorenzo Zanoli, Giovanni Ragazzi, Paolo Bordone, Matteo G. A. Paris

Published Aug 4, 2026• 0 citations
Publisher

Abstract

Continuous-time quantum walks (QWs) on cycle graphs are investigated as a versatile metrological platform. The parameters of interest are a local on-site potential (electric-like perturbation) and the overall chiral phase (magnetic-like perturbation). For single-parameter estimation, we compare static strategies, in which information is encoded in the ground state, with dynamical protocols, in which the system evolves from the unperturbed ground state under the perturbed Hamiltonian. For the electric perturbation, the dynamical approach yields a quantum Fisher information (QFI) that scales quadratically in time, saturating the Heisenberg limit. In contrast, estimation of the magnetic perturbation alone is unfeasible in both static and dynamical settings as the eigenstates are independent of the chiral phase. Assisted estimation (in which a known perturbation is used to enhance sensitivity to the other) restores quadratic scaling for both fields, with optimal performance achieved by tuning the assisting parameter near critical values. Conversely, joint estimation of both fields performs rather poorly: the model exhibits substantial sloppiness over large parameter ranges, indicating sensitivity only to specific parameter combinations. Finally, the magnetically perturbed ring is re-analyzed as a quantum thermometer. The magnetic flux tunes the energy gap, enabling near-optimal low-temperature sensitivity that follows the Landau bound. Overall, quantum walks on cycle graphs represent a flexible class of sensors ideally suited for (assisted) single-parameter estimation.

DOI
10.3389/frqst.2026.1894991

Related papers

Continuous-time quantum walks in the presence of a quadratic perturbation

Alessandro Candeloro, Luca Razzoli, Simone Cavazzoni +2 more

We address the properties of continuous-time quantum walks with Hamiltonians of the form $\mathcal{H}=L+\ensuremath{\lambda}{L}^{2}$, with $L$ the Laplacian matrix of the underlying graph and the perturbation $\ensuremath{\lambda}{L}^{2}$ motivated by its potential use to introduce next-nearest-neighbor hopping. We consider cycle, complete, and star graphs as paradigmatic models with low and high connectivity and/or symmetry. First, we investigate the dynamics of an initially localized walker. Then we devote attention to estimating the perturbation parameter $\ensuremath{\lambda}$ using only a snapshot of the walker dynamics. Our analysis shows that a walker on a cycle graph spreads ballistically independently of the perturbation, whereas on complete and star graphs one observes perturbation-dependent revivals and strong localization phenomena. Concerning the estimation of the perturbation, we determine the walker preparations and the simple graphs that maximize the quantum Fisher information. We also assess the performance of position measurement, which turns out to be optimal, or nearly optimal, in several situations of interest. Besides fundamental interest, our study may find applications in designing enhanced algorithms on graphs.

arXiv:2005.06351•Physical Review A•Oct 14, 2020•10 citations

Quantum metrology for a general Hamiltonian parameter

Shengshi Pang, Todd A. Brun

Quantum metrology enhances the sensitivity of parameter estimation using the distinctive resources of quantum mechanics such as entanglement. It has been shown that the precision of estimating an overall multiplicative factor of a Hamiltonian can be increased to exceed the classical limit, yet little is known about estimating a general Hamiltonian parameter. In this paper, we study this problem in detail. We find that the scaling of the estimation precision with the number of systems can always be optimized to the Heisenberg limit, while the time scaling can be quite different from that of estimating an overall multiplicative factor. We derive the generator of local parameter translation on the unitary evolution operator of the Hamiltonian, and use it to evaluate the estimation precision of the parameter and establish a general upper bound on the quantum Fisher information. The results indicate that the quantum Fisher information generally can be divided into two parts: one is quadratic in time, while the other oscillates with time. When the eigenvalues of the Hamiltonian do not depend on the parameter, the quadratic term vanishes, and the quantum Fisher information will be bounded in this case. To illustrate the results, we give an example of estimating a parameter of a magnetic field by measuring a spin-$\frac{1}{2}$ particle and compare the results for estimating the amplitude and the direction of the magnetic field.

arXiv:1407.6091•Physical Review A•Aug 25, 2014•175 citations

Stable metrological precision of quantum sensing in a common classical environment

Seyed Mohammad Hosseiny, Milad Norouzi

This study examines a quantum sensor consisting of two qubits modeled in an XXZ Heisenberg spin chain under a homogeneous magnetic field, for use in quantum thermometry and magnetometry. The sensor is subjected to a common classical environment driven by static noise and is in thermal equilibrium with a heat bath. We analyze the impact of spin–spin, Dzyaloshinskii–Moriya, and Kaplan–Shekhtman–Entin-Wohlman–Aharony interactions, as well as the static noise characterized by the disorder parameter, on the sensor's time-evolved state. We also assess the influence of magnetic field homogeneity on performance. Employing quantum Fisher information criteria, we determine the sensor's metrological precision. The performance of the proposed sensor in estimating the external magnetic field and temperature in weak and strong field regimes is different over time with temperature variations. In the strong magnetic field regime, static noise reduces the sensitivity of quantum sensing, while in the weak field regime, this effect is negligible. Our sensor achieves optimal sensitivity and precision for temperature and magnetic field estimation in the presence of static noise and in the weak magnetic field and low temperature regime. Finally, we demonstrate that the quantum sensor achieves a stable sensitivity and precision in its performance over time in quantum magnetometry and thermometry, which can be very valuable in quantum sensing. Moreover, we propose some experimental platforms for the realization of our quantum sensor.

AVS Quantum Science•Jan 5, 2026•0 citations

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

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

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.

arXiv:2505.22395•Physical Review A•Dec 18, 2025•2 citations

From spectral structure to sensing limits in quantum thermometry

Youssef Aiache, Simone Cavazzoni, Abderrahim El Allati +2 more

The precision of a quantum thermometer is fundamentally constrained by the spectral structure of the probe itself, and a systematic mapping between the configurations of energy levels and thermometric performance provides relevant information to design optimized devices. In this work, we establish such a mapping by analyzing a broad class of quantum systems, ranging from finite spin ensembles and degenerate atoms to confining potentials, quantum walks, and continuous-spectrum models. We derive exact scaling laws for the quantum Fisher information, revealing two distinct high-temperature universality classes: finite-spectrum probes exhibit a $T^{-4}$ decay, while unbounded or continuous spectra yield a slower $T^{-2}$ decay. At low temperatures, we show that sensitivity, though universally exponentially suppressed, can be enhanced arbitrarily by engineering degenerate excited states or a quantum walk on a fully connected topology. By contrast, specific quantum walk topologies provide a distinct enhancement mechanism based on gap engineering, whereby an optimal network size yields an optimized $T^{-2}$ low-temperature scaling. Furthermore, power-law spectra enable tunable scaling of thermometric performance with system size, offering a design principle for optimal probes in specific temperature windows. Our results contribute to transform spectral information into a resource for quantum thermometry, providing both fundamental bounds and practical guidelines to tailored temperature sensing.

quant-pharXiv:2606.25933•Jun 25, 2026•0 citations

Quantum critical environment assisted quantum magnetometer

Noufal Jaseem, S. Omkar, Anil Shaji

Abstract A central qubit coupled to an Ising ring of N qubits, operating close to a critical point is investigated as a potential precision quantum magnetometer for estimating an applied transverse magnetic field. We compute the quantum Fisher information for the central, probe qubit with the Ising chain initialized in its ground state or in a thermal state. The non-unitary evolution of the central qubit due to its interaction with the surrounding Ising ring enhances the accuracy of the magnetic field measurement. Near the critical point of the ring, Heisenberg-like scaling of the precision in estimating the magnetic field is obtained when the ring is initialized in its ground state. However, for finite temperatures, the Heisenberg scaling is limited to lower ranges of N values.

arXiv:1707.03738•Journal of Physics A Mathematical and Theoretical•Mar 21, 2018•5 citations
Continuous-time quantum walks (QWs) on cycle graphs are investigated as a versatile metrological platform. The parameters of interest are a local on-site potential (electric-like perturbation) and the overall chiral phase (magnetic-like perturbation). For single-parameter estimation, we compare static strategies, in which information is encoded in the ground state, with dynamical protocols, in which the system evolves from the unperturbed ground state under the perturbed Hamiltonian. For the electric perturbation, the dynamical approach yields a quantum Fisher information (QFI) that scales quadratically in time, saturating the Heisenberg limit. In contrast, estimation of the magnetic perturbation alone is unfeasible in both static and dynamical settings as the eigenstates are independent of the chiral phase. Assisted estimation (in which a known perturbation is used to enhance sensitivity to the other) restores quadratic scaling for both fields, with optimal performance achieved by tuning the assisting parameter near critical values. Conversely, joint estimation of both fields performs rather poorly: the model exhibits substantial sloppiness over large parameter ranges, indicating sensitivity only to specific parameter combinations. Finally, the magnetically perturbed ring is re-analyzed as a quantum thermometer. The magnetic flux tunes the energy gap, enabling near-optimal low-temperature sensitivity that follows the Landau bound. Overall, quantum walks on cycle graphs represent a flexible class of sensors ideally suited for (assisted) single-parameter estimation.
We address the properties of continuous-time quantum walks with Hamiltonians of the form $\mathcal{H}=L+\ensuremath{\lambda}{L}^{2}$, with LLL the Laplacian matrix of the underlying graph and the perturbation $\ensuremath{\lambda}{L}^{2}$ motivated by its potential use to introduce next-nearest-neighbor hopping. We consider cycle, complete, and star graphs as paradigmatic models with low and high connectivity and/or symmetry. First, we investigate the dynamics of an initially localized walker. Then we devote attention to estimating the perturbation parameter $\ensuremath{\lambda}$ using only a snapshot of the walker dynamics. Our analysis shows that a walker on a cycle graph spreads ballistically independently of the perturbation, whereas on complete and star graphs one observes perturbation-dependent revivals and strong localization phenomena. Concerning the estimation of the perturbation, we determine the walker preparations and the simple graphs that maximize the quantum Fisher information. We also assess the performance of position measurement, which turns out to be optimal, or nearly optimal, in several situations of interest. Besides fundamental interest, our study may find applications in designing enhanced algorithms on graphs.
Quantum metrology enhances the sensitivity of parameter estimation using the distinctive resources of quantum mechanics such as entanglement. It has been shown that the precision of estimating an overall multiplicative factor of a Hamiltonian can be increased to exceed the classical limit, yet little is known about estimating a general Hamiltonian parameter. In this paper, we study this problem in detail. We find that the scaling of the estimation precision with the number of systems can always be optimized to the Heisenberg limit, while the time scaling can be quite different from that of estimating an overall multiplicative factor. We derive the generator of local parameter translation on the unitary evolution operator of the Hamiltonian, and use it to evaluate the estimation precision of the parameter and establish a general upper bound on the quantum Fisher information. The results indicate that the quantum Fisher information generally can be divided into two parts: one is quadratic in time, while the other oscillates with time. When the eigenvalues of the Hamiltonian do not depend on the parameter, the quadratic term vanishes, and the quantum Fisher information will be bounded in this case. To illustrate the results, we give an example of estimating a parameter of a magnetic field by measuring a spin-12\frac{1}{2}21​ particle and compare the results for estimating the amplitude and the direction of the magnetic field.
This study examines a quantum sensor consisting of two qubits modeled in an XXZ Heisenberg spin chain under a homogeneous magnetic field, for use in quantum thermometry and magnetometry. The sensor is subjected to a common classical environment driven by static noise and is in thermal equilibrium with a heat bath. We analyze the impact of spin–spin, Dzyaloshinskii–Moriya, and Kaplan–Shekhtman–Entin-Wohlman–Aharony interactions, as well as the static noise characterized by the disorder parameter, on the sensor's time-evolved state. We also assess the influence of magnetic field homogeneity on performance. Employing quantum Fisher information criteria, we determine the sensor's metrological precision. The performance of the proposed sensor in estimating the external magnetic field and temperature in weak and strong field regimes is different over time with temperature variations. In the strong magnetic field regime, static noise reduces the sensitivity of quantum sensing, while in the weak field regime, this effect is negligible. Our sensor achieves optimal sensitivity and precision for temperature and magnetic field estimation in the presence of static noise and in the weak magnetic field and low temperature regime. Finally, we demonstrate that the quantum sensor achieves a stable sensitivity and precision in its performance over time in quantum magnetometry and thermometry, which can be very valuable in quantum sensing. Moreover, we propose some experimental platforms for the realization of our quantum sensor.
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.
The precision of a quantum thermometer is fundamentally constrained by the spectral structure of the probe itself, and a systematic mapping between the configurations of energy levels and thermometric performance provides relevant information to design optimized devices. In this work, we establish such a mapping by analyzing a broad class of quantum systems, ranging from finite spin ensembles and degenerate atoms to confining potentials, quantum walks, and continuous-spectrum models. We derive exact scaling laws for the quantum Fisher information, revealing two distinct high-temperature universality classes: finite-spectrum probes exhibit a T−4T^{-4}T−4 decay, while unbounded or continuous spectra yield a slower T−2T^{-2}T−2 decay. At low temperatures, we show that sensitivity, though universally exponentially suppressed, can be enhanced arbitrarily by engineering degenerate excited states or a quantum walk on a fully connected topology. By contrast, specific quantum walk topologies provide a distinct enhancement mechanism based on gap engineering, whereby an optimal network size yields an optimized T−2T^{-2}T−2 low-temperature scaling. Furthermore, power-law spectra enable tunable scaling of thermometric performance with system size, offering a design principle for optimal probes in specific temperature windows. Our results contribute to transform spectral information into a resource for quantum thermometry, providing both fundamental bounds and practical guidelines to tailored temperature sensing.
Abstract A central qubit coupled to an Ising ring of N qubits, operating close to a critical point is investigated as a potential precision quantum magnetometer for estimating an applied transverse magnetic field. We compute the quantum Fisher information for the central, probe qubit with the Ising chain initialized in its ground state or in a thermal state. The non-unitary evolution of the central qubit due to its interaction with the surrounding Ising ring enhances the accuracy of the magnetic field measurement. Near the critical point of the ring, Heisenberg-like scaling of the precision in estimating the magnetic field is obtained when the ring is initialized in its ground state. However, for finite temperatures, the Heisenberg scaling is limited to lower ranges of N values.