Related papers: Universal topological phase of 2D stabilizer codes
We have calculated order parameters for the phases of the Kitaev chain with interaction and dimerization at a special symmetric point applying the Jordan-Wigner and other duality transformations. We use string order parameters (SOPs)…
Universal two-particle entanglement processes are analyzed in arbitrary dimensional Hilbert spaces. On the basis of this analysis the class of possible optimal universal entanglement processes is determined whose resulting output states do…
Here we show the connection between topological order and the geometric entanglement, as measured by the logarithm of the overlap between a given state and its closest product state of blocks, for the topological universality class of the…
We investigate the topological-to-non-topological quantum phase transitions (QPTs) occurring in the Kitaev code under local perturbations in the form of local magnetic field and spin-spin interactions of the Ising-type using fidelity…
Deciding if a given family of quantum states is topologically ordered is an important but nontrivial problem in condensed matter physics and quantum information theory. We derive necessary and sufficient conditions for a family of graph…
We study a quantum phase transition between a phase which is topologically ordered and one which is not. We focus on a spin model, an extension of the toric code, for which we obtain the exact ground state for all values of the coupling…
This Letter discusses topological quantum computation with gapped boundaries of two-dimensional topological phases. Systematic methods are presented to encode quantum information topologically using gapped boundaries, and to perform…
In a graph, we say that two nodes are topologically equivalent if their sets of first neighbors, excluding the two nodes, coincide. We prove that nonlinearly coupled heterogeneous oscillators located on a group of topologically equivalent…
In this work, we consider 2D $\mathbb{Z}_2$ topologically ordered phases ($\mathbb{Z}_2$ toric code and the modified surface code) on a simple hyperbolic lattice. Introducing a 2D lattice consisting of the product of a 1D Cayley tree and a…
Topologically non-trivial phases have recently been reported on self-similar structures. Here, we investigate the effect of local structure, specifically the role of the coordination number, on the topological phases on self-similar…
A particularly simple model belonging to a wide class of coupled maps which obey a local conservation law is studied. The phase structure of the system and the types of the phase transitions are determined. It is argued that the structure…
The multi-scale entanglement renormalisation ansatz (MERA) is argued to provide a natural description for topological states of matter. The case of Kitaev's toric code is analyzed in detail and shown to possess a remarkably simple MERA…
We show how good quantum error-correcting codes can be constructed using generalized concatenation. The inner codes are quantum codes, the outer codes can be linear or nonlinear classical codes. Many new good codes are found, including both…
Generic 2D Hamiltonian systems possess partial barriers in their chaotic phase space that restrict classical transport. Quantum mechanically the transport is suppressed if Planck's constant h is large compared to the classical flux, h >>…
We consider the analogy between the topological phase transition which occurs as a function of spatial coordinate on a surface of a non-trivial insulator, and the one which occurs in the bulk due to the change of internal parameters (such…
Topological quantum memory can protect information against local errors up to finite error thresholds. Such thresholds are usually determined based on the success of decoding algorithms rather than the intrinsic properties of the mixed…
We study topological properties of phase transition points of one-dimensional topological quantum phase transitions by assigning winding numbers defined on closed circles around the gap closing points in the parameter space of momentum and…
Stability of synchronization in unidirectionally coupled time-delay systems is studied using the Krasovskii-Lyapunov theory. We have shown that the same general stability condition is valid for different cases, even for the general…
Here we investigate the connection between topological order and the geometric entanglement, as measured by the logarithm of the overlap between a given state and its closest product state of blocks. We do this for a variety of…
We prove the existence of topological quantum error correcting codes with encoding rates $k/n$ asymptotically approaching the maximum possible value. Explicit constructions of these topological codes are presented using surfaces of…