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arXiv:2508.14409 · 中国科学通报：英文版

Non-equilibrium criticality-enhanced quantum sensing with superconducting qubits

Hao Li, Yaoling Yang, Yun‐Hao Shi, Zheng‐An Wang, Ziting Wang, Jintao Li, Yipeng Zhang, Kui Zhao, Yue-Shan Xu, Cheng-Lin Deng, Yu Liu, Wei-Guo Ma, Tian-Ming Li, Jiachi Zhang, Cai-Ping Fang, Jia-Cheng Song, Hao-Tian Liu, Si-Yun Zhou, Zheng-He Liu, B. Chen, Gui-Han Liang, Xiaohui Song, Zhongcheng Xiang, Kai‐Da Xu, Kaixuan Huang, Abolfazl Bayat, Heng Fan

Published May 18, 2026• 1 citation
arXivHTMLPDF

Abstract

Exploiting quantum features allows for estimating external parameters with precision well beyond the capacity of classical sensors, a phenomenon known as quantum-enhanced precision. Quantum criticality has been identified as a resource for achieving such enhancements with respect to the probe size. However, such protocols demand complex probe preparation and measurement, and the achievable enhancement is ultimately restricted to narrow parameter regimes. On the other hand, non-equilibrium probes harness dynamics, enabling quantum-enhanced precision with respect to time over a wide range of parameters through simple probe initialization. Here, we unify these approaches through a Stark-Wannier localization platform, where competition between a linear gradient field and particle tunneling enables quantum-enhanced sensitivity across an extended parameter regime. The probe is implemented on a 9-qubit superconducting quantum device, in both single- and double-excitation subspaces, where we explore its performance in the extended phase, the critical point and the localized phase. Despite employing only computational-basis measurements, we have been able to achieve near-Heisenberg-limited precision by combining outcomes at distinct evolution times. In addition, we demonstrate that the performance of the probe in the entire extended phase significantly outperforms the performance in the localized regime. Our results highlight Stark-Wannier systems as versatile platforms for quantum sensing, where the combination of criticality and non-equilibrium dynamics enhances precision over a wide range of parameters without stringent measurement requirements.

DOI
10.1016/j.scib.2026.05.023

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Exploiting quantum features allows for estimating external parameters with precision well beyond the capacity of classical sensors, a phenomenon known as quantum-enhanced precision. Quantum criticality has been identified as a resource for achieving such enhancements with respect to the probe size. However, such protocols demand complex probe preparation and measurement, and the achievable enhancement is ultimately restricted to narrow parameter regimes. On the other hand, non-equilibrium probes harness dynamics, enabling quantum-enhanced precision with respect to time over a wide range of parameters through simple probe initialization. Here, we unify these approaches through a Stark-Wannier localization platform, where competition between a linear gradient field and particle tunneling enables quantum-enhanced sensitivity across an extended parameter regime. The probe is implemented on a 9-qubit superconducting quantum device, in both single- and double-excitation subspaces, where we explore its performance in the extended phase, the critical point and the localized phase. Despite employing only computational-basis measurements, we have been able to achieve near-Heisenberg-limited precision by combining outcomes at distinct evolution times. In addition, we demonstrate that the performance of the probe in the entire extended phase significantly outperforms the performance in the localized regime. Our results highlight Stark-Wannier systems as versatile platforms for quantum sensing, where the combination of criticality and non-equilibrium dynamics enhances precision over a wide range of parameters without stringent measurement requirements.
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Stark systems in which a linear gradient field is applied across a many-body system have recently been proposed for quantum sensing. Here, we explore sensing capacity of Stark probes, in both single-particle and many-body interacting systems, for estimating nonlinear forms of the gradient fields. Our analysis reveals that, this estimation can achieve super-Heisenberg scaling precision that grows linearly by increasing the nonlinearity. Specifically, we find a universal algebraic relation between the scaling of the precision and the degree of the nonlinearity. This universal behavior remains valid in both single-particle and many-body interacting probes and reflects itself in the properties of the phase transition from an extended to a localized phase, obtained through establishing a comprehensive finite-size scaling analysis. Considering a parabolic gradient potential composed of both linear and nonlinear fields, we used multiparameter estimation methodology to estimate the components of the gradient potential. The phase diagram of the system is determined in terms of both linear and nonlinear gradient fields showing how the nonlocalized phase turns into a localized one as the Stark fields increase. The sensing precision of both linear and nonlinear Stark fields follows the same universal algebraic relation that was found for the case of single parameter sensing. We demonstrate that simple and experimentally available measurements can reach the theoretical precision bounds. Finally, we show that quantum enhanced sensitivity is still achievable even when we incorporate the preparation time of the probe into our resource analysis.
Wannier-Stark localization has been proven to be a resource for quantum-enhanced sensitivity for precise estimation of a gradient field. An extremely promising feature of such probes is their ability to showcase such enhanced scaling even dynamically with system size, on top of the quadratic scaling in time. In this paper, we address the issue of decoherence that occurs during time evolution and characterize how that affects the sensing performance. We determine the parameter domains in which the enhancement is sustained under dephasing dynamics. In addition, we consider an effective non-Hermitian description of the open quantum system dynamics for describing the effect of decoherence on the sensing performance of the probe. By investigating the static and dynamic properties of the non-Hermitian Hamiltonians, we show that quantum-enhanced sensitivity can indeed be sustained over a certain range of decoherence strength for Wannier-Stark probes. This is demonstrated with two examples of non-Hermitian systems with nonreciprocal couplings.
Quantum metrology, a cornerstone of quantum technologies, exploits entanglement and superposition to achieve higher precision than classical protocols in parameter-estimation tasks. When combined with critical phenomena such as phase transitions, the divergence of quantum fluctuations is predicted to enhance the performance of quantum sensors. Here, we implement a critical quantum sensor using a superconducting parametric (i.e., two-photon driven) Kerr resonator. The sensor, a linear resonator terminated by a superconducting quantum interference device, operates near the critical point of a finite-component second-order dissipative phase transition obtained by scaling the system parameters. We analyze the performance of a frequency-estimation protocol and show that quadratic precision scaling with respect to the system size can be achieved with finite values of the Kerr nonlinearity. Since each photon emitted from the cavity carries more information about the parameter to be estimated compared to its classical counterpart, our protocol opens up perspectives for faster or more precise metrological protocols. Our results demonstrate that quantum advantage in a sensing protocol can be achieved by exploiting a phase transition.
We investigate the sensing capacity of non-equilibrium dynamics in quantum systems exhibiting Bloch oscillations. By focusing on the resource efficiency of the probe, quantified by quantum Fisher information, we find different scaling behaviors in two different phases, namely localized and extended. Our results provide a quantitative ansatz for quantum Fisher information in terms of time, probe size, and the number of excitations. In the long-time regime, the quantum Fisher information is a quadratic function of time, touching the Heisenberg limit. The system size scaling drastically depends on the phase changing from quantum-enhanced scaling in the extended phase to size-independent behavior in the localized phase. Furthermore, increasing the number of excitations always enhances the precision of the probe, although, in the interacting systems the enhancement becomes less eminent than the non-interacting probes. This is due to the induced localization by increasing the interaction between the excitations. We show that a simple particle configuration measurement together with a maximum likelihood estimation can closely reach the ultimate precision limit in both single- and multi-particle probes.