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Frontiers of Physics

Parity detection based on non-Hermitian spectral phase transition

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

Published Jan 1, 2026• 1 citation
Publisher

Abstract

We present a protocol for realizing parity detection of a bipartite system based on non-Hermitian spectral phase transition. The system comprises two superconducting qubits as information carriers and an auxiliary superconducting resonator. We derive a parity-dependent effective Hamiltonian, where the frequency of the resonator is shifted when the qubits are in even-parity states. The frequency shift results in a spectral phase transition in the non-Hermitian dynamical matrix in the Heisenberg picture, where the spectrum turns from purely imaginary to purely real. With a proper frequency shift, the spectral distinction between the even- and odd-parity cases leads to markedly different photon number dynamics, i.e., exponential growth for the odd-parity case, and bounded oscillations for the even-parity case. By measuring the photon number in the resonator after a fixed evolution time, the parity of the qubits can be reliably discriminated. Numerical simulations further demonstrate that the protocol is robust against systematic imperfections and decoherence, including the spontaneous emission and dephasing of the qubits, as well as cavity decay. These results establish a practical route to parity detection via non-Hermitian dynamics. This approach provides a scalable building block for superconducting-circuit quantum information processing.

DOI
10.15302/frontphys.2026.115201

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We present a protocol for realizing parity detection of a bipartite system based on non-Hermitian spectral phase transition. The system comprises two superconducting qubits as information carriers and an auxiliary superconducting resonator. We derive a parity-dependent effective Hamiltonian, where the frequency of the resonator is shifted when the qubits are in even-parity states. The frequency shift results in a spectral phase transition in the non-Hermitian dynamical matrix in the Heisenberg picture, where the spectrum turns from purely imaginary to purely real. With a proper frequency shift, the spectral distinction between the even- and odd-parity cases leads to markedly different photon number dynamics, i.e., exponential growth for the odd-parity case, and bounded oscillations for the even-parity case. By measuring the photon number in the resonator after a fixed evolution time, the parity of the qubits can be reliably discriminated. Numerical simulations further demonstrate that the protocol is robust against systematic imperfections and decoherence, including the spontaneous emission and dephasing of the qubits, as well as cavity decay. These results establish a practical route to parity detection via non-Hermitian dynamics. This approach provides a scalable building block for superconducting-circuit quantum information processing.
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.
Abstract The evolution of entanglement in a non-Hermitian quantum system may behave differently compared to its Hermitian counterpart. In this paper, we investigate the entanglement dynamics of two coupled and driven non-Hermitian qubits. Through calculating the concurrence of the system, we find that the evolution of the bipartite entanglement manifests two distinct patterns in the parameter space. In the low non-Hermiticity regime, the concurrence oscillates significantly, while in the opposite regime the same quantity would trend to a stable value. We attribute this phenomenon to parity-time ( PT ) symmetry phase transition. We also study the effect of decoherence on the entanglement dynamics. Our work provides a method to stabilize entanglement by exploiting non-Hermiticity.
PT\mathcal{PT}PT-like phase transitions from square roots of supersymmetric Hamiltonians
We introduce a general framework for realizing PT\mathcal{PT}PT-like phase transitions in non-Hermitian systems without imposing explicit parity--time (PT\mathcal{PT}PT) symmetry. The approach is based on constructing a Hamiltonian as the square root of a supersymmetric partner energy-shifted by a constant. This formulation naturally leads to bipartite dynamics with balanced gain and loss and can incorporate non-reciprocal couplings. The resulting systems exhibit entirely real spectra over a finite parameter range precisely when the corresponding passive Hamiltonian lacks a zero mode. As the non-Hermitian parameter representing gain and loss increases, the spectrum undergoes controlled real-to-complex transitions at second-order exceptional points. We demonstrate the versatility of this framework through several examples, including well-known models such as the Hatano--Nelson (HN) and complex Su--Schrieffer--Heeger (cSSH) lattices. Extending the formalism to qqq-commuting matrices further enables the systematic realization of higher-order exceptional points in systems with unidirectional couplings. Overall, this work uncovers new links between non-Hermitian physics and supersymmetry, offering a practical route to engineer photonic arrays with tunable spectral properties beyond what is achievable with explicit PT\mathcal{PT}PT-symmetry.
We propose a scheme for realizing parity measurement of cat-state qubits based on a topological quantum phase transition. The cat-state qubits, formed by the bosonic modes in the Kerr-nonlinear resonators with two-photon squeezing drives, couple with a superconducting qubit in the center. We demonstrate that the resonator-qubit couplings with proper strengths can induce a topological quantum phase transition when the cat-state qubits are initial in the even-parity states. The topological quantum phase transition provides an approach to distinguish the even-parity states from the odd-parity states by measuring a topological invariant, namely the Chern number. Due to the robustness of the Chern number, the scheme shows great tolerance for multiple types of disturbing factors, including the systematic errors of the control fields and the coupling strengths, the inter-resonator crosstalk, and decoherence. Therefore, the scheme may be useful to construct an error-tolerant parity detector of cat-state qubits.
Abstract Non-Hermitian quantum systems showcase many distinct and intriguing features with no Hermitian counterparts. One of them is the exceptional point which marks the PT (parity and time) symmetry phase transition, where an enhanced spectral sensitivity arises and leads to novel quantum engineering. Here we theoretically study the multipartite entanglement properties in non-Hermitian superconducting qubits, where high-fidelity entangled states can be created under strong driving fields or strong couplings among the qubits. Under an interplay between driving fields, couplings, and non-Hermiticity, we focus on generations of GHZ states or GHZ classes in three and four qubits with all-to-all couplings, which allows a fidelity approaching unity when relatively low non-Hermitian decay rates are considered. This presents an ultimate capability of non-Hermitian qubits to host a genuine and maximal multipartite entanglement. Our results can shed light on novel quantum engineering of multipartite entanglement generations in non-Hermitian qubit systems.
In many classical and quantum systems described by an effective non-Hermitian Hamiltonian, spectral phase transitions, from an entirely real-energy spectrum to a complex spectrum, can be observed as a non-Hermitian parameter in the system is increased above a critical value. A paradigmatic example is provided by systems possessing parity-time (PT\mathcal{PT}PT) symmetry, where the energy spectrum remains entirely real in the unbroken PT\mathcal{PT}PT phase while a transition to complex energies is observed in the broken PT\mathcal{PT}PT phase. Such spectral phase transitions are universally sharp. However, when the system is slowly and periodically cycled, the phase transition can become smooth, i.e., imperfect, owing to the complex Berry phase associated to the cyclic adiabatic evolution of the system. This remarkable phenomenon is illustrated by considering the spectral phase transition of the Wannier-Stark ladders in a PT\mathcal{PT}PT-symmetric class of two-band non-Hermitian lattices subjected to an external dc field, revealing that a nonvanishing imaginary part of the Zak phase---the Berry phase picked up by a Bloch eigenstate evolving across the entire Brillouin zone---is responsible for imperfect spectral phase transitions.