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Entanglement, one of the most intriguing features of quantum theory and a main resource in quantum information science, is expected to play a crucial role also in the study of quantum phase transitions, where it is responsible for the appearance of long-range correlations. We investigate, through a microscopic calculation, the scaling properties of… (More)

- Michael H Freedman, Alexei Kitaev, Michael J Larsen, Zhenghan Wang
- 1996

The theory of quantum computation can be constructed from the abstract study of anyonic systems. In mathematical terms, these are unitary topological modular functors. They underlie the Jones polynomial and arise in Witten-Chern-Simons theory. The braiding and fusion of anyonic excitations in quantum Hall electron liquids and 2D-magnets are modeled by… (More)

- Eric Dennis, Alexei Kitaev, Andrew Landahl, John Preskill
- 2002

We analyze surface codes, the topological quantum error-correcting codes introduced by Kitaev. In these codes, qubits are arranged in a two-dimensional array on a surface of nontrivial topology, and encoded quantum operations are associated with nontrivial homology cycles of the surface. We formulate protocols for error recovery, and study the efficacy of… (More)

We consider a model of quantum computation in which the set of elementary operations is limited to Clifford unitaries, the creation of the state ͉0͘, and qubit measurement in the computational basis. In addition, we allow the creation of a one-qubit ancilla in a mixed state , which should be regarded as a parameter of the model. Our goal is to determine… (More)

- Alexei Kitaev
- 2005

A spin 1/2 system on a honeycomb lattice is studied. The interactions between nearest neighbors are of XX, YY or ZZ type, depending on the direction of the link; different types of interactions may differ in strength. The model is solved exactly by a reduction to free fermions in a static Z 2 gauge field. A phase diagram in the parameter space is obtained.… (More)

- Michael H Freedman, Alexei Kitaev, Zhenghan Wang
- 2008

Quantum computers will work by evolving a high tensor power of a small (e.g. two) dimensional Hilbert space by local gates, which can be implemented by applying a local Hamiltonian H for a time t. In contrast to this quantum engineering, the most abstract reaches of theoretical physics has spawned " topological models " having a finite dimensional internal… (More)

We formulate a universal characterization of the many-particle quantum entanglement in the ground state of a topologically ordered two-dimensional medium with a mass gap. We consider a disk in the plane, with a smooth boundary of length L, large compared to the correlation length. In the ground state, by tracing out all degrees of freedom in the exterior of… (More)

- Alexei Kitaev
- 2009

Gapped phases of noninteracting fermions, with and without charge conservation and time-reversal symmetry, are classified using Bott periodicity. The symmetry and spatial dimension determines a general universality class, which corresponds to one of the 2 types of complex and 8 types of real Clifford algebras. The phases within a given class are further… (More)

- Jiannis K Pachos, bullet G K Brennen, J K Pachos, bullet M H Freedman, A Kitaev, M J Larsen +2 others
- 2010

* Copyright (C) 2010: Permission is granted to everyone to make verbatim copies of this document provided that the copyright notice and this permission notice are preserved. Synopsis • Introduction to anyons and topological models Anyons, their properties and their relation to topological quantum computation. • Quantum double models Quantum double models… (More)

- Itai Arad, Alexei Kitaev, Zeph Landau, Umesh Vazirani
- 2013

We give a new proof for the area law for general 1D gapped systems, which exponentially improves Hastings' famous result [1]. Specifically, we show that for a chain of d-dimensional spins, governed by a 1D local Hamiltonian with a spectral gap > 0, the entanglement en-tropy of the ground state with respect to any cut in the chain is upper bounded by O(log 3… (More)