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Communications Physics

Hybrid non-Hermitian singularities and mapped-state concurrence in a superconducting-circuit dynamical matrix

Yang Xiao, Hao-Long Zhang, Ri‐Hua Zheng, Yu Wang, Jie Song, Ye‐Hong Chen, Yi‐Hao Kang, Yan Xia

Published Sep 21, 2026• 0 citations
Publisher

Abstract

Non-Hermitian spectral singularities have attracted considerable interest, but how such structures emerge from a concrete microscopic system and connect to measurable observables remains an important question. Here, we study a coupled double-cavity system mediated by a superconducting qutrit and show that, although the effective two-mode Hamiltonian is Hermitian, the corresponding four-component Bogoliubov operator dynamics is governed by a non-Hermitian dynamical matrix. Starting from the microscopic circuit model, we derive the effective bosonic Hamiltonian and construct the dynamical matrix from the Heisenberg equations of motion. We show that this dynamical matrix hosts exceptional points, exceptional lines, and hybrid diabolical-exceptional points, also known as diabolically degenerate exceptional points. We further present a quadrature-based, model-assisted protocol for extracting the dynamical-matrix spectrum from measurable cavity-field observables. Finally, we introduce a virtual two-qubit representation of the four-component dynamical vector and use the mapped-state concurrence as a diagnostic of eigenvector nonseparability and its dynamical evolution. Our results provide a concrete route to connect Hermitian bosonic dynamics, non-Hermitian dynamical-matrix singularities, spectrum reconstruction, and virtual two-qubit diagnostics in a superconducting-circuit platform.

DOI
10.1038/s42005-026-02871-6

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Exceptional points (EPs) are conventionally identified through eigenvector coalescence, inaccessible in classical platforms lacking a Hamiltonian spectrum. We introduce classical observable coalescence as a diagnostic identifying EPs directly from physical configurations, and demonstrate it in a known non-Hermitian Ising chain with coupling JJJ and staggered imaginary field γγγ, chosen for verifiability against established quantum results. A mean-field reduction of the Heisenberg dynamics yields equilibrium branches organising into two symmetry-related families whose fusion at the boundary of the EP supersurface ∣γ∣=∣J∣|γ|=|J|∣γ∣=∣J∣ exhibits the characteristic J2−γ2\sqrt{J^2-γ^2}J2−γ2​ branch-point structure and two-sheeted Riemann topology. Crucially, the degeneracy at $γ=0,η=0 $ is shown to be a diabolic point, producing no observable coalescence, establishing the diagnostic as discriminating rather than merely suggestive. An exact Jordan-Wigner and Bogoliubov-de Gennes treatment confirms eigenvector coalescence at the same threshold, and a coupled gain-loss circuit realisation is proposed, establishing classical observables as experimentally accessible signatures of non-Hermitian criticality.
We analyze the existence and degeneracies of quantum exceptional, diabolical, and hybrid points in simple bosonic systems – comprising up to six modes with damping and/or amplification – under two complementary scenarios to those described in arXiv:2405.01666: (i) nonconventional PT-symmetric dynamics confined to a subspace of the full Liouville space, and (ii) systems featuring unidirectional coupling. The system dynamics described by quadratic non-Hermitian Hamiltonians is governed by the Heisenberg-Langevin equations. Conditions for the observation of inherited quantum hybrid points with up to sixth-order exceptional and second-order diabolical degeneracies are revealed, though relevant only for short-time dynamics. This raises the question of whether higher-order inherited singularities exist in bosonic systems under general conditions. Nevertheless, for short times, unidirectional coupling of various types enables the concatenation of simple bosonic systems with second- and third-order exceptional degeneracies such that arbitrarily high exceptional degeneracies are reached. Methods for numerical identifying the quantum exceptional and hybrid points together with their degeneracies are addressed. Following arXiv:2405.01666 rich dynamics of second-order field-operator moments is analyzed from the point of view of the presence of exceptional and diabolical points and their degeneracies.
Non-Hermitian Hamiltonians are a fascinating class of many-body models that describe the effective dynamics of quantum systems interacting with the environment through particle, energy, or information exchange. Although their theoretical framework is well established, the controlled engineering of such Hamiltonians in the context of quantum simulations remains challenging, even more so when the non-Hermitian part describes a kkk-body interaction. Qudit quantum simulators offer a compelling framework to implement such models. We theoretically investigate the dynamics of a one-dimensional chain of qudits undergoing hybrid unitary-projective evolution, where suitably designed measurements constrain the dynamics to a Zeno subspace. As we illustrate for the case of qutrits, within the Zeno subspace the dynamics is governed by an effective non-Hermitian Hamiltonian for an ensemble of pseudo-spins 1/21/21/2, which can inherit non-Hermitian two-body interactions with the same connectivity as the full qutrit chain. We derive an analytical relation linking the monitored qutrits' evolution to a desired target non-Hermitian Hamiltonian and validate the effective description through numerical simulations of a representative model. Our scheme provides a constructive route for the realization of a large class of interacting non-Hermitian many-body Hamiltonians in experimentally relevant multilevel quantum platforms, including trapped ions and superconducting circuits.