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

arXiv:2605.29173

Modular non-Hermitian topology and its application to critical sensing

Saubhik Sarkar, Chiranjib Mukhopadhyay, Abolfazl Bayat

quant-phcond-mat.str-elSubmitted May 27, 2026• Announced May 29, 2026
arXivHTMLPDF

Abstract

Non-Hermitian topological systems have attracted a lot of research activities in recent times, both theoretically and experimentally, due to their unique physical properties and association with open quantum systems. We show that modular structures, where specific couplings at regular intervals take distinct values, enrich the unique topological attributes of these systems such as the non-Hermitian skin effect and the breakdown of conventional bulk-boundary correspondence. These systems also possess the capability of displaying criticality-enhanced sensitivity for precision metrology. We establish how the modular structure enhances their sensing performance near spectral topological phase transitions and show that the enhancement can be achieved in multi-parameter estimation scenarios as well.

Comments
11 pages, 5 figs, comments welcome

Related papers

Critical non-Hermitian topology induced quantum sensing

Saubhik Sarkar, Francesco Ciccarello, Angelo C. M. Carollo +1 more

Abstract Non-Hermitian (NH) physics predicts open quantum system dynamics with unique topological features such as exceptional points and the NH skin effect. We show that this new paradigm of topological systems can serve as probes for bulk Hamiltonian parameters with quantum-enhanced sensitivity reaching Heisenberg scaling. Such enhancement occurs close to a spectral topological phase transition, where the entire spectrum undergoes a delocalization transition. We provide an explanation for this enhanced sensitivity based on the closing of point gap, which is a genuinely NH energy gap with no Hermitian counterpart. This establishes a direct connection between energy-gap closing and quantum enhancement in the NH realm. Our findings are demonstrated through several paradigmatic NH topological models in various dimensions and potential experimental implementations.

arXiv:2311.12756•New Journal of Physics•Jun 27, 2024•19 citations

Topological Eigenvalues: Unveiling Non-Hermitian Spectral Singularities

PAULO SÉRGIO DE ANDRADE

This paper explores the novel concept of topological eigenvalues within the realm of non-Hermitian quantum mechanics, focusing on their role in unveiling spectral singularities. Unlike conventional Hermitian systems, non-Hermitian Hamiltonians, which describe open systems with gain and loss, exhibit complex eigenvalues and unique spectral features such as exceptional points (EPs) where eigenvalues and their corresponding eigenvectors coalesce. We introduce the idea that certain eigenvalues in non-Hermitian systems possess an inherent topological character, dictated by the geometry of the parameter space and the winding properties of the characteristic polynomial. These topological eigenvalues are shown to be intimately linked to spectral singularities, which are non-Hermitian generalizations of bound states in the continuum or points of perfect reflection/transmission, characterized by infinite scattering amplitudes. We develop a theoretical framework to identify and characterize these topological eigenvalues, demonstrating how they emerge from the interplay of non-Hermiticity and underlying symmetries. Our findings reveal that the robust nature of these topological eigenvalues provides a new lens through which to understand the exotic phenomena observed in non-Hermitian systems, including the non-Hermitian skin effect and the breakdown of traditional bulk-boundary correspondence. This work opens new avenues for designing robust non-Hermitian devices and understanding fundamental aspects of open quantum systems.

•Nov 22, 2025•0 citations

Tunable topological enhancement of covariant quantum Fisher information via non-Bloch skin effect in non-Hermitian SSH lattices

Qi-Cheng Wu, Yan-Hui Zhou, Tong Liu +2 more

The covariant quantum Fisher information (CQFI) has recently been established as the ultimate precision benchmark for pseudo-Hermitian sensors [Phys. Rev. Lett. 136, 080802 (2026)], yet existing analyses are limited to single-mode systems. Here we extend the CQFI formalism to multi-mode non-Hermitian Su-Schrieffer-Heeger lattices and reveal tunable topological enhancement enabled by the non-Hermitian skin effect (NHSE). Under open boundary conditions, the NHSE deforms the conventional Brillouin zone into a generalized Brillouin zone of radius r = exp(\k{appa}), where \k{appa} denotes the non-Bloch decay rate. While the total CQFI scales linearly with system size N, its prefactor depends critically on \k{appa}, yielding an enhancement factor E(N) = F_OBC / F_PBC that exceeds 30 for N ~ 30, substantially outperforming periodic-boundary sensors. The enhancement is robust against moderate local disorder and supports multi-parameter estimation, with the joint Cramér-Rao bound reduced by up to 15 orders of magnitude. These findings establish a spatial-domain mechanism for quantum metrology that complements time-domain strategies and is experimentally accessible using topoelectrical circuits, photonic lattices, and superconducting circuits with current technology.

quant-pharXiv:2609.03421•Sep 4, 2026•0 citations

Observation of Criticality-Enhanced Quantum Sensing in Nonunitary Quantum Walks

Lei Xiao, Saubhik Sarkar, Kunkun Wang +2 more

Quantum physics enables parameter estimation with precisions beyond the capability of classical sensors. Quantum criticality is a key resource for this quantum-enhanced sensing, but experimental realization has been challenging due to the complexity of ground-state preparation and the long time required to reach the steady state near criticality. Here, we experimentally demonstrate critical enhancement in a non-Hermitian topological system using a photonic quantum walk setup. Our system supports two distinct phase transitions at which enhanced sensitivity is observed even at transient times for which the Bayesian inference shows excellent estimation and precision. It is a direct demonstration of criticality-enhanced scaling laws with nonunitary dynamics.

arXiv:2506.16133•Physical Review Letters•Jan 20, 2026•1 citation

Exponentially-enhanced quantum sensing with non-Hermitian lattice dynamics

Alexander McDonald, Aashish A. Clerk

Non-Hermitian systems exhibit markedly different phenomena than their conventional Hermitian counterparts. Several such features, such as the non-Hermitian skin effect, are only present in spatially extended systems. Potential applications of these effects in many-mode systems however remains largely unexplored. Here, we study how unique features of non-Hermitian lattice systems can be harnessed to improve Hamiltonian parameter estimation in a fully quantum setting. While the quintessential non-Hermitian skin effect does not provide any distinct advantage, alternate effects yield dramatic enhancements. We show that certain asymmetric non-Hermitian tight-binding models with a [Formula: see text] symmetry yield a pronounced sensing advantage: the quantum Fisher information per photon increases exponentially with system size. We find that these advantages persist in regimes where non-Markovian and non-perturbative effects become important. Our setup is directly compatible with a variety of quantum optical and superconducting circuit platforms, and already yields strong enhancements with as few as three lattice sites.

arXiv:2004.00585•Nature Communications•Oct 23, 2020•223 citations

Entanglement spectrum dynamics as a probe for non-Hermitian bulk-boundary correspondence in systems with periodic boundaries

Pablo Bayona-Pena, Ryo Hanai, Takashi Mori +1 more

It has recently been established that open quantum systems may exhibit a strong spectral sensitivity to boundary conditions, known as the non-Hermitian/Liouvillian skin effect (NHSE/LSE), making the topological properties of the system boundary-condition sensitive. In this Letter, we ask the query: Can topological phase transitions of open quantum systems, captured by open boundary conditioned invariants, be observed in the dynamics of a system under periodic boundary conditions, even in the presence of NHSE/LSE? We affirmatively respond to this question, by considering the quench dynamics of entanglement spectrum in a periodic open quantum fermionic system. We demonstrate that the entanglement spectrum exhibits zero-crossings only when this periodic system is quenched from a topologically trivial to nontrivial phase, defined from the spectrum under open boundary conditions, even in systems featuring LSE. Our results reveal that non-Hermitian topological phases leave a distinctive imprint on the unconditional dynamics within a subsystem of fermionic systems.

arXiv:2409.07279•Physical review. B./Physical review. B•Apr 7, 2025•4 citations
Non-Hermitian topological systems have attracted a lot of research activities in recent times, both theoretically and experimentally, due to their unique physical properties and association with open quantum systems. We show that modular structures, where specific couplings at regular intervals take distinct values, enrich the unique topological attributes of these systems such as the non-Hermitian skin effect and the breakdown of conventional bulk-boundary correspondence. These systems also possess the capability of displaying criticality-enhanced sensitivity for precision metrology. We establish how the modular structure enhances their sensing performance near spectral topological phase transitions and show that the enhancement can be achieved in multi-parameter estimation scenarios as well.
Abstract Non-Hermitian (NH) physics predicts open quantum system dynamics with unique topological features such as exceptional points and the NH skin effect. We show that this new paradigm of topological systems can serve as probes for bulk Hamiltonian parameters with quantum-enhanced sensitivity reaching Heisenberg scaling. Such enhancement occurs close to a spectral topological phase transition, where the entire spectrum undergoes a delocalization transition. We provide an explanation for this enhanced sensitivity based on the closing of point gap, which is a genuinely NH energy gap with no Hermitian counterpart. This establishes a direct connection between energy-gap closing and quantum enhancement in the NH realm. Our findings are demonstrated through several paradigmatic NH topological models in various dimensions and potential experimental implementations.
This paper explores the novel concept of topological eigenvalues within the realm of non-Hermitian quantum mechanics, focusing on their role in unveiling spectral singularities. Unlike conventional Hermitian systems, non-Hermitian Hamiltonians, which describe open systems with gain and loss, exhibit complex eigenvalues and unique spectral features such as exceptional points (EPs) where eigenvalues and their corresponding eigenvectors coalesce. We introduce the idea that certain eigenvalues in non-Hermitian systems possess an inherent topological character, dictated by the geometry of the parameter space and the winding properties of the characteristic polynomial. These topological eigenvalues are shown to be intimately linked to spectral singularities, which are non-Hermitian generalizations of bound states in the continuum or points of perfect reflection/transmission, characterized by infinite scattering amplitudes. We develop a theoretical framework to identify and characterize these topological eigenvalues, demonstrating how they emerge from the interplay of non-Hermiticity and underlying symmetries. Our findings reveal that the robust nature of these topological eigenvalues provides a new lens through which to understand the exotic phenomena observed in non-Hermitian systems, including the non-Hermitian skin effect and the breakdown of traditional bulk-boundary correspondence. This work opens new avenues for designing robust non-Hermitian devices and understanding fundamental aspects of open quantum systems.
The covariant quantum Fisher information (CQFI) has recently been established as the ultimate precision benchmark for pseudo-Hermitian sensors [Phys. Rev. Lett. 136, 080802 (2026)], yet existing analyses are limited to single-mode systems. Here we extend the CQFI formalism to multi-mode non-Hermitian Su-Schrieffer-Heeger lattices and reveal tunable topological enhancement enabled by the non-Hermitian skin effect (NHSE). Under open boundary conditions, the NHSE deforms the conventional Brillouin zone into a generalized Brillouin zone of radius r = exp(\k{appa}), where \k{appa} denotes the non-Bloch decay rate. While the total CQFI scales linearly with system size N, its prefactor depends critically on \k{appa}, yielding an enhancement factor E(N) = F_OBC / F_PBC that exceeds 30 for N ~ 30, substantially outperforming periodic-boundary sensors. The enhancement is robust against moderate local disorder and supports multi-parameter estimation, with the joint Cramér-Rao bound reduced by up to 15 orders of magnitude. These findings establish a spatial-domain mechanism for quantum metrology that complements time-domain strategies and is experimentally accessible using topoelectrical circuits, photonic lattices, and superconducting circuits with current technology.
Quantum physics enables parameter estimation with precisions beyond the capability of classical sensors. Quantum criticality is a key resource for this quantum-enhanced sensing, but experimental realization has been challenging due to the complexity of ground-state preparation and the long time required to reach the steady state near criticality. Here, we experimentally demonstrate critical enhancement in a non-Hermitian topological system using a photonic quantum walk setup. Our system supports two distinct phase transitions at which enhanced sensitivity is observed even at transient times for which the Bayesian inference shows excellent estimation and precision. It is a direct demonstration of criticality-enhanced scaling laws with nonunitary dynamics.
Non-Hermitian systems exhibit markedly different phenomena than their conventional Hermitian counterparts. Several such features, such as the non-Hermitian skin effect, are only present in spatially extended systems. Potential applications of these effects in many-mode systems however remains largely unexplored. Here, we study how unique features of non-Hermitian lattice systems can be harnessed to improve Hamiltonian parameter estimation in a fully quantum setting. While the quintessential non-Hermitian skin effect does not provide any distinct advantage, alternate effects yield dramatic enhancements. We show that certain asymmetric non-Hermitian tight-binding models with a [Formula: see text] symmetry yield a pronounced sensing advantage: the quantum Fisher information per photon increases exponentially with system size. We find that these advantages persist in regimes where non-Markovian and non-perturbative effects become important. Our setup is directly compatible with a variety of quantum optical and superconducting circuit platforms, and already yields strong enhancements with as few as three lattice sites.
It has recently been established that open quantum systems may exhibit a strong spectral sensitivity to boundary conditions, known as the non-Hermitian/Liouvillian skin effect (NHSE/LSE), making the topological properties of the system boundary-condition sensitive. In this Letter, we ask the query: Can topological phase transitions of open quantum systems, captured by open boundary conditioned invariants, be observed in the dynamics of a system under periodic boundary conditions, even in the presence of NHSE/LSE? We affirmatively respond to this question, by considering the quench dynamics of entanglement spectrum in a periodic open quantum fermionic system. We demonstrate that the entanglement spectrum exhibits zero-crossings only when this periodic system is quenched from a topologically trivial to nontrivial phase, defined from the spectrum under open boundary conditions, even in systems featuring LSE. Our results reveal that non-Hermitian topological phases leave a distinctive imprint on the unconditional dynamics within a subsystem of fermionic systems.