Related papers: Topological line in frustrated Toric code models

In this paper, the degenerate ground states of Z2 topological order on a plane with holes (the so-called surface codes) are used as the protected code subspace to build a topological quantum computer by tuning their quantum tunneling…

Turbo codes are a very efficient method for communicating reliably through a noisy channel. There is no theoretical understanding of their effectiveness. In [1] they are mapped onto a class of disordered spin models. The analytical…

We investigate the quantum phase diagram of the $K$-layer Ising toric code corresponding to $K$ layers of two-dimensional toric codes coupled by Ising interactions. While for small Ising interactions the system displays $\mathbb{Z}_2^K$…

The Kitaev honeycomb model is an approximate topological quantum error correcting code in the same phase as the toric code, but requiring only a 2-body Hamiltonian. As a frustrated spin model, it is well outside the commuting models of…

Ground-state phase diagram of the toric code model in a parallel magnetic field has three distinct phases: topological, charge-condensed, and vortex-condensed states. To study it we consider an implicit local order parameter characterizing…

We consider a system consisting of a 2D network of links between Majorana fermions on superconducting islands. We show that the fermionic Hamiltonian modeling this system is topologically-ordered in a region of parameter space. In…

Geometric phases, accumulated when a quantum system traces a cycle in quantum state space, do not depend on the parametrization of the cyclic path, but do depend on the path itself. In the presence of noise that deforms the path, the phase…

Topological phases, edge states, and flat bands in synthetic quantum systems are a key resource for topological quantum computing and noise-resilient information processing. We introduce a scheme based on step-dependent quantum walks on…

The relation between thermodynamic phase transitions in classical systems and topology changes in their configuration space is discussed for a one-dimensional, analytically tractable solid-on-solid model. The topology of a certain family of…

Geometric frustration appears in a broad range of systems, generally emerging as disordered ground configurations, thereby impeding understanding of the phenomenon's underlying mechanics. We report on a continuum system featuring locally…

We study the stability of anyonic models on lattices to perturbations. We establish a cluster expansion for the energy of the perturbed models and use it to study the stability of the models to local perturbations. We show that the spectral…

We analyze the computational aspects of detecting topological order in a quantum many-body system. We contrast the widely used topological entanglement entropy with a recently introduced operational definition for topological order based on…

Quantum spin liquids, exotic phases of matter with topological order, have been a major focus of explorations in physical science for the past several decades. Such phases feature long-range quantum entanglement that can potentially be…

In this paper, we explore topological quantum computation augmented by subphases and phase transitions. We commence by investigating the anyon tunneling map, denoted as $\varphi$, between subphases of the quantum double model…

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 introduce a new set of one dimensional quantum lattice models which we refer to as The quantum torus chain. These models have discrete global symmetry, and projective on-site representations. They possess an integer-valued parameter…

In recent experiments, time-dependent periodic fields are used to create exotic topological phases of matter with potential applications ranging from quantum transport to quantum computing. These nonequilibrium states, at high driving…

We show that topology can protect exponentially localized, zero energy edge modes at critical points between one-dimensional symmetry protected topological phases. This is possible even without gapped degrees of freedom in the bulk ---in…

Topology and nonlinearity are deeply connected. However, whether topological effects can arise solely from the structure of nonlinear interaction terms, and the nature of the resulting topological phases, remain to large extent open…

We demonstrate that two toric code layers on the square lattice coupled by an Ising interaction display two distinct phases with intrinsic topological order. The second-order quantum phase transition between the weakly-coupled…