Exceptional points (EPs), the degeneracy points of non-Hermitian systems, have recently attracted great attention because of their potential of enhancing the sensitivity of quantum sensors. Unlike the usual degeneracies in Hermitian systems, at EPs, both the eigenenergies and eigenvectors coalesce. Although EPs have been widely explored, the range of EPs studied is largely limited by the underlying systems, for instance, higher-order EPs are hard to achieve. Here we propose an extendable method to simulate non-Hermitian systems and study EPs with quantum circuits. The system is inherently parity-time (PT) broken due to the non-symmetric controlling effects of the circuit. Inspired by the quantum Zeno effect, the circuit structure guarantees the success rate of the post-selection. A sample circuit is implemented in a quantum programming framework, and the phase transition at EP is demonstrated. Considering the scalable and flexible nature of quantum circuits, our model is capable of simulating large-scale systems with higher-order EPs.
Exceptional points (EPs), the degeneracy points of non-Hermitian systems, have recently attracted great attention because of their potential of enhancing the sensitivity of quantum sensors. Unlike the usual degeneracies in Hermitian systems, at EPs, both the eigenenergies and eigenvectors coalesce. Although EPs have been widely explored, the range of EPs studied is largely limited by the underlying systems, for instance, higher-order EPs are hard to achieve. Here we propose an extendable method to simulate non-Hermitian systems and study EPs with quantum circuits. The system is inherently parity-time (PT) broken due to the non-symmetric controlling effects of the circuit. Inspired by the quantum Zeno effect, the circuit structure guarantees the success rate of the post-selection. A sample circuit is implemented in a quantum programming framework, and the phase transition at EP is demonstrated. Considering the scalable and flexible nature of quantum circuits, our model is capable of simulating large-scale systems with higher-order EPs.
Abstract The nontrivial degeneracies in non-Hermitian systems, exceptional points (EPs), have attracted extensive attention due to intriguing phenomena. Compared with commonly observed second-order EPs, high-order EPs show rich physics due to their extended dimension and parameter space, ranging from the coalescence of EPs into higher-order EPs to potential applications in topological properties. However, these features also pose challenges in controlling multiple coherent and dissipative elements in a scaled system. Here we experimentally demonstrate a native programmable control to simulate a high-order non-Hermitian Hamiltonian in a multi-dimensional trapped ion system. We simulate a series of non-Hermitian systems with varied parameters and observe the coalescence of second-order EPs into fourth-order EPs. Our results pave the way for scalable quantum simulation of high-dimensional dissipative systems and can be beneficial for the application of high-order EPs in quantum sensing and quantum control.
Abstract Exceptional points (EPs) occur in non-Hermitian systems where eigenvalues and eigenvectors coalesce. In open quantum systems, EPs are typically studied via non-Hermitian effective Hamiltonians or Liouvillians, but these omit the full generality of quantum dynamics, which requires description using quantum channels. Here, we introduce a general strategy for generating quantum-channel EPs in the single-qubit setting. We show that quantum channels naturally fall into two distinct phases, purely real or complex-conjugate eigenvalues, without the need of enforcing additional symmetries, and interpolating between different phases induces a phase transition where EPs can emerge. We experimentally simulate such channels on a nuclear magnetic resonance quantum computer, observing second-order quantum-channel EPs with 93% fidelity, and extend the approach to three channels to uncover exceptional lines and a third-order quantum-channel EP. Our results promise potential applications from enhanced quantum sensing to quantum control, such as Jordan-chain mediated asymmetric conversion.
Open photonic systems provide a versatile platform for non-Hermitian physics, enabling control over complex spectra, transport, and light-matter interactions. Exceptional points (EPs), at which eigenvalues and eigenvectors coalesce and the governing operator becomes defective, play a central role because they combine branch-point spectral topology, nonanalytic perturbative response, and controllable eigenstate conversion. This Review provides a unified framework for EP photonics by systematically distinguishing exceptional degeneracies according to the underlying operator, spectral variable, boundary conditions, and experimentally accessible observables. We discuss Hamiltonian EPs, absorbing EPs associated with scattering zeros, real-frequency scattering-matrix and Jones-matrix EPs, Bloch and Floquet EPs, and Liouvillian EPs in open quantum systems. We review their spectral topology, static and dynamical encircling, higher-order exceptional structures, and coexistence with bound states in the continuum, together with applications in sensing, lasing, coherent absorption, directional scattering, polarization and wavefront control, nonlinear optics, optical storage, nonreciprocal photonics, and quantum photonics. We also critically assess the current limitations, practical challenges, and future perspectives of EP-based photonic technologies, with particular attention to robustness, noise, scalability, and experimentally measurable performance.
Exceptional points (EPs) occur in non-Hermitian systems where eigenvalues and eigenvectors coalesce. In open quantum systems, EPs are typically studied via non-Hermitian effective Hamiltonians or Liouvillians, but these omit the full generality of quantum dynamics, which requires description using quantum channels. Here, we introduce a general strategy for generating quantum-channel EPs in the single-qubit setting. We show that quantum channels naturally fall into two distinct phases, purely real or complex-conjugate eigenvalues, without the need of enforcing additional symmetries, and interpolating between different phases induces a phase transition where EPs can emerge. We experimentally simulate such channels on a nuclear magnetic resonance quantum computer, observing second-order quantum-channel EPs with 93% fidelity, and extend the approach to three channels to uncover exceptional lines and a third-order quantum-channel EP. Our results promise potential applications from enhanced quantum sensing to quantum control, such as Jordan-chain mediated asymmetric conversion.
Non-Hermitian systems with parity-time (PT) symmetry give rise to exceptional points (EPs) with exceptional properties that arise due to the coalescence of eigenvectors. Such systems have been extensively explored in the classical domain, where second- or higher-order EPs have been proposed or realized. In contrast, quantum information studies of PT-symmetric systems have been confined to systems with a two-dimensional Hilbert space. Here, by using a single-photon interferometry setup, we simulate the quantum dynamics of a four-dimensional PT-symmetric system across a fourth-order exceptional point. By tracking the coherent, nonunitary evolution of the density matrix of the system in PT-symmetry unbroken and broken regions, we observe the entropy dynamics for both the entire system, and the gain and loss subsystems. Our setup is scalable to the higher-dimensional PT-symmetric systems, and our results point towards the rich dynamics and critical properties.
In this paper we study exceptional-point (EP) effects and quantum sensing in a parity-time (PT)-symmetric two-qubit system with the Ising-type interaction. We explore EP properties of the system by analyzing degeneracy of energy eigenvalues or entanglement of eigenstates. We investigate entanglement dynamics of the two qubits in detail. In particular, we demonstrate that the system can create the steady-state entanglement in the PT-broken phase and collapse-revival phenomenon of entanglement in the PT-symmetric phase during the long-time evolution. We show that entanglement can be generated more quickly than the corresponding Hermitian system. Finally, we prove that the sensitivity of eigenstate quantum sensing for the parameters exhibits the remarkable enharncement at EPs, and propose a quantum-coherence measurement to witness the existence of EPs.