Year: 2026
Type: article
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.
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,353
OpenAlex ID: W7172442082