. However, it has always been a great challenge to complete such a task because of decoherence and disorder. Here, we propose theoretically and demonstrate experimentally an effective scheme to realize robust operation of quantum entanglement states by designing quadruple degeneracy exceptional points. By encircling the exceptional points on two overlapping Riemann energy surfaces, we have realized a chiral switch for entangled states with high fidelity. Owing to the topological protection conferred by the Riemann surface structure, this switching of chirality exhibits strong robustness against perturbations in the encircling path. Furthermore, we have experimentally validated such a scheme on a quantum walk platform. Our work opens up a new way for the application of non-Hermitian physics in the field of quantum information.
. However, it has always been a great challenge to complete such a task because of decoherence and disorder. Here, we propose theoretically and demonstrate experimentally an effective scheme to realize robust operation of quantum entanglement states by designing quadruple degeneracy exceptional points. By encircling the exceptional points on two overlapping Riemann energy surfaces, we have realized a chiral switch for entangled states with high fidelity. Owing to the topological protection conferred by the Riemann surface structure, this switching of chirality exhibits strong robustness against perturbations in the encircling path. Furthermore, we have experimentally validated such a scheme on a quantum walk platform. Our work opens up a new way for the application of non-Hermitian physics in the field of quantum information.
Abstract Exceptional points (EPs) are non‐Hermitian degeneracies or branch points where eigenvalues and their corresponding eigenvectors coalesce. Due to the complex non‐trivial topology of Riemann surfaces associated with non‐Hermitian Hamiltonians, the dynamical encirclement or proximity of EPs in parameter space has been shown to lead to topological mode conversions and some novel physical phenomena. In fact, degeneracies can also form continuous line geometries, which are called exceptional lines (ELs). The problem is whether the state transfer around the ELs can show different characteristics from the EPs, which is less explored. Here, novel properties of quantum state transfer around the ELs based on a quantum walk platform are explored. It is found that the evolutionary state around the ELs is independent of the initial state and evolution direction, and the transfer of quantum state is more efficient than the case around the EPs. Furthermore, based on such a property, an entangled state generation insensitive to the incident state is realized experimentally. The work opens up a new way for the application of non‐Hermitian physics in the field of quantum information.
Dissipation always exists in real environments, and it can cause decoherence during transfer of quantum states. To avoid decoherence, dissipation is usually shielded. However, dissipation is difficult to avoid in real cases. Thus, how to achieve efficient quantum state transfer in dissipation environments, although it will receive great attention, remains a challenge. Here we demonstrate that dissipation can be utilized to realize robust control of quantum state transfer instead of being avoided. Our scheme is realized by constructing Liouvillian exceptional point (LEP). By tuning dissipation, the exchange of eigenvectors and nonadiabatic transition near the LEP can be modulated, thereby controlling transfer and chirality of topological quantum state. Furthermore, we have experimentally validated such a scheme on a quantum walk platform. Our work opens up a different avenue for quantum information process in real systems.
We theoretically investigate the interplay of topology and localized non-Hermiticity in a finite Su-Schrieffer-Heeger chain characterized by non-Hermitian potentials at its boundaries. By tuning the boundary gain and loss parameters, we exploit the finite-size hybridization of two mid-gap topological edge states to analytically derive the exact coordinates of boundary-induced exceptional points (EPs), ΓEP=±ivN/wN−1, at which these states undergo coalescence. We demonstrate that dynamically encircling these boundary EPs facilitates a robust, chiral edge state-transfer protocol. Depending on the orientation of the encircling loop, this protocol allows a topological edge state localized at one boundary to be either transferred to the opposite edge with perfect fidelity or returned to its starting position through a double switching process. Importantly, since the non-Hermiticity remains strictly confined to the boundaries, this chiral transport occurs without affecting the energy spectrum of the bulk bands. These results establish a minimal framework for a large-scale topological chiral switch that is experimentally verifiable and capable of being controlled through boundary non-Hermitian driving.
This paper investigates the protection of quantum entanglement states through topological principles. The core claim is that embedding entangled states within systems exhibiting non-trivial topological properties can lead to enhanced long-term fidelity. The fundamental mechanism involves leveraging the topological robustness of these structures to suppress the detrimental effects of local perturbations on the delicate entangled correlations. We explore various topological systems, focusing on their ability to shield entangled states from decoherence. The theoretical framework presented here offers a novel approach to building robust quantum information processing architectures, particularly for quantum computing applications. We demonstrate, through mathematical analysis, that the topological protection significantly improves the preservation of entanglement against environmental noise. Specifically, we consider a model system—a chain of interacting spin-1/2 particles—and derive the equations governing the evolution of the entangled state under the influence of both Hamiltonian terms and external perturbations. Our results highlight the potential of topological protection for achieving high-fidelity quantum entanglement over extended periods. The key equation governing the evolution of the entangled state is given by: ψ(t) = U(t)ψ(0) where ψ(t) is the state vector at time t, ψ(0) is the initial state vector, and U(t) is the time-evolution operator. We also explore the concept of topological invariants, such as the braid group, to characterize the topological properties of the system. The braiding of these topological elements can be used to manipulate the entangled state without destroying the entanglement. The preservation of entanglement is quantified by the fidelity, defined as: F(t) = |⟨ψ(t)|ψ(0)⟩|2 where ⟨ψ(t)|ψ(0)⟩ represents the overlap between the final and initial states. Our analysis demonstrates that the fidelity decays much slower in topological systems compared to non-topological systems. Furthermore, we investigate different types of topological protection, including chiral edge states and non-abelian braiding. We present a general framework for assessing the topological protection of any quantum system, emphasizing the importance of understanding the interplay between the topological structure and the quantum state. Finally, we discuss the challenges and future directions in realizing topological quantum computation. ---
Chirality is more than a geometric curiosity; it governs measurable asymmetries across nature, from enantiomer-selective drugs and left-handed fermions in particle physics to handed charge transport in Weyl semimetals. We extend this universal concept to non-Hermitian systems by defining topological chirality, an invariant that emerges whenever an exceptional-points (EP) pair is present. Built from the non-commutative fundamental group and its braid representation, topological chirality acts as a singularity selector: clockwise EP loops occupy a homotopy class that avoids EPs, whereas counter-clockwise mirrors are equivalent only if they cross the EPs themselves. We confirm this binary rule in an optical microcavity and a non-Hermitian topological band. The same two-sheeted topology governs EP pairs in spin systems, photonic crystals and hybrid light-matter structures, where EP encirclements have already been demonstrated, so the framework transfers without alteration and confirms its experimental viability. Our findings lay the cornerstone for interpreting loop-sensitive observables such as spectral vorticity, the complex Berry phase and the non-Abelian holonomy. Finally, a gluing-of-planes construction extends the invariant to an n-sheeted surface hosting 2m EPs, unifying higher-order EP pairs.
Topologically ordered phases have robust degenerate ground states against the local perturbations, providing a promising platform for fault-tolerant quantum computation. Despite of the non-local feature of the topological order, we find that local non-Hermitian perturbations can induce the transition between the topologically ordered ground states. In this work, we study the toric code in the presence of non-Hermitian perturbations. By controlling the non-Hermiticity, we show that non-orthogonal ground states can exhibit an eigenstate coalescence and have the spectral singularity, known as an exceptional point (EP). We explore the potential of the EPs in the control of topological order. Adiabatic encircling EPs allows for the controlled switching of eigenstates, enabling dynamic manipulation between the ground state degeneracy. Interestingly, we show a property of our scheme that arbitrary strengths of local perturbations can induce the EP and eigenstate switching. Finally, we also show the orientation-dependent behavior of non-adiabatic transitions (NAT) during the dynamic encirclement around an EP. Our work shows that control of the non-Hermiticity can serve as a promising strategy for fault-tolerant quantum information processing.