相关论文: Robustness of Topological Order in the Toric Code …
Topologically ordered phases in $2+1$ dimensions are generally characterized by three mutually-related features: fractionalized (anyonic) excitations, topological entanglement entropy, and robust ground state degeneracy that does not…
Quantum Ising model in a transverse field is of the simplest quantum many body systems used for studying universal properties of quantum phase transitions. Interestingly, it is well-known that such phase transitions can be mapped to…
We present the first examples of topological phases of matter with uniform power for measurement-based quantum computation. This is possible thanks to a new framework for analyzing the computational properties of phases of matter that is…
We study the entanglement structure of topological orders subject to decoherence on the bipartition boundary. Focusing on the toric codes in $d$ space dimensions for $d=2,3,4$, we explore whether the boundary decoherence may be able to…
We introduce a class of cyclic quantum codes, basing the construction not on the simplicity of the stabilizers, but rather on the simplicity of preparation of a code state (at least in the absence of noise). We show how certain known codes,…
It is known that noisy topological quantum codes are related to random bond Ising models where the order-disorder phase transition in the classical model is mapped to the error threshold of the corresponding topological code. On the other…
In this chapter we discuss aspects of the quantum critical behavior that occurs at a quantum phase transition separating a topological phase from a conventionally ordered one. We concentrate on a family of quantum lattice models, namely…
The bulk-boundary correspondence is a generic feature of topological states of matter, reflecting the intrinsic relation between topological bulk and boundary states. For example, robust edge states propagate along the edges and corner…
To observe synchronization in a large network of classical or quantum systems demands both excellent control of the interactions between the nodes and very accurate preparation of the initial conditions due to the involved nonlinearities…
We investigate the robustness of Majorana edge modes under disorder and interactions. We exploit a recently found mapping of the interacting Kitaev chain in the symmetric region ($\mu = 0$, $t = \Delta$) to free fermions. Extending the…
The concepts of topology have a profound impact on physics research spanning the fields of condensed matter, photonics and acoustics and predicting topological states that provide unprecedented versatility in routing and control of waves of…
The discovery of topological order has revolutionized the understanding of quantum matter in modern physics and provided the theoretical foundation for many quantum error correcting codes. Realizing topologically ordered states has proven…
We study topological order in a toric code in three spatial dimensions, or a 3+1D Z_2 gauge theory, at finite temperature. We compute exactly the topological entropy of the system, and show that it drops, for any infinitesimal temperature,…
We characterize phases of the compass ladder model by using degenerate perturbation theory, symmetry fractionalization, and numerical techniques. Through degenerate perturbation theory we obtain an effective Hamiltonian for each phase of…
Robustness of machine learning models to various adversarial and non-adversarial corruptions continues to be of interest. In this paper, we introduce the notion of the boundary thickness of a classifier, and we describe its connection with…
Topologically ordered quantum spin systems have become an area of great interest, as they may provide a fault-tolerant means of quantum computation. One of the simplest examples of such a spin system is Kitaev's toric code. Naaijkens made…
As a prototype model of topological quantum memory, two-dimensional toric code is genuinely immune to generic local static perturbations, but fragile at finite temperature and also after non-equilibrium time evolution at zero temperature.…
The 2D toric code is a prototypical example that exhibits non-trivial topological properties and a ground state possessing a non-trivial topological order. Until now, all the cases studied in the literature have been in the stable…
Topological order is now being established as a central criterion for characterizing and classifying ground states of condensed matter systems and complements categorizations based on symmetries. Fractional quantum Hall systems and quantum…
Many examples from quantum and classical physics are known where topological protection is responsible for the robustness of the dynamics. Less explored is the role of topological protection in the context of classical oscillatory systems.…