Related papers: Efficient computation of topological order
Topological order is a new type order that beyond Landau's symmetry breaking theory. The topological entanglement entropy provides a universal quantum number to characterize the topological order in a system. The topological entanglement…
Systems displaying quantum topological order feature robust characteristics that are very attractive to quantum computing schemes. Topological quantum field theories have proven to be powerful in capturing the quintessential attributes of…
Topological order has been proposed to go beyond Landau symmetry breaking theory for more than twenty years. But it is still a challenging problem to generally detect it in a generic many-body state. In this paper, we will introduce a…
We study the topological entanglement entropy and scalar chirality of a topologically ordered skyrmion formed in a two-dimensional triangular lattice. Scalar chirality remains a smooth function of the magnetic field in both helical and…
Topological quantum computation is a promising technique to achieve large-scale, error-corrected computation. Quantum hardware is used to create a large, 3-dimensional lattice of entangled qubits while performing computation requires…
Entanglement is one of the fundamental properties of a quantum state and is a crucial differentiator between classical and quantum computation. There are many ways to define entanglement and its measure, depending on the problem or…
Topological states of matter are promising resources for composing fault-tolerant quantum computers, advancing beyond the limitations of current noisy intermediate-scale quantum devices. To enable this progress, a deep understanding of…
Topologically ordered systems exhibit large-scale correlation in their ground states, which may be characterized by quantities such as topological entanglement entropy. We propose that the concept of irreducible many-body correlation, the…
Entanglement entropy has become an important theoretical concept in condensed matter physics, because it provides a unique tool for characterizing quantum mechanical many-body phases and new kinds of quantum order. However, the experimental…
A characterization of topological order in terms of bi-partite entanglement was proposed recently [A. Kitaev and J. Preskill, Phys. Rev. Lett. 96, 110404 (2006); M. Levin and X.-G. Wen, ibid, 110405]. It was argued that in a topological…
The modern conception of phases of matter has undergone tremendous developments since the first observation of topologically ordered states in fractional quantum Hall systems in the 1980s. In this paper, we explore the question: How much…
We calculate exactly the von Neumann and topological entropies of the toric code as a function of system size and temperature. We do so for systems with infinite energy scale separation between magnetic and electric excitations, so that the…
Concepts of information theory are increasingly used to characterize collective phenomena in condensed matter systems, such as the use of entanglement entropies to identify emergent topological order in interacting quantum many-body…
Topological quantum error correction codes are currently among the most promising candidates for efficiently dealing with the decoherence effects inherently present in quantum devices. Numerically, their theoretical error threshold can be…
We compute the topological entropy of the toric code models in arbitrary dimension at finite temperature. We find that the critical temperatures for the existence of full quantum (classical) topological entropy correspond to the…
In this paper we explore how non trivial boundary conditions could influence the entanglement entropy in a topological order in 2+1 dimensions. Specifically we consider the special class of topological orders describable by the quantum…
We introduce a many-body topological invariant, called the topological disorder parameter (TDP), to characterize gapped quantum phases with global internal symmetry in (2+1)d. TDP is defined as the constant correction that appears in the…
Entanglement entropy provides a powerful characterization of two-dimensional gapped topological phases of quantum matter, intimately tied to their description by topological quantum field theories (TQFTs). Fracton topological orders are…
In topological quantum computing, information is encoded in "knotted" quantum states of topological phases of matter, thus being locked into topology to prevent decay. Topological precision has been confirmed in quantum Hall liquids by…
Calculation of topological order parameters, such as the topological entropy and topological mutual information, are used to determine whether states possess topological order. Their calculation is expected to give reliable results when the…