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Fault tolerant quantum computation by anyons
A two-dimensional quantum system with anyonic excitations can be considered as a quantum computer. Unitary transformations can be performed by moving the excitations around each other. MeasurementsExpand
Anyons in an exactly solved model and beyond
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 mayExpand
Classical and Quantum Computation
TLDR
Introduction Classical computation Quantum computation Solutions Elementary number theory Bibliography Index. Expand
Topological quantum memory
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, andExpand
Unpaired Majorana fermions in quantum wires
Certain one-dimensional Fermi systems have an energy gap in the bulk spectrum while boundary states are described by one Majorana operator per boundary point. A finite system of length L possessesExpand
Universal quantum computation with ideal Clifford gates and noisy ancillas (14 pages)
We consider a model of quantum computation in which the set of elementary operations is limited to Clifford unitaries, the creation of the state |0>, and qubit measurement in the computational basis.Expand
Periodic table for topological insulators and superconductors
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 aExpand
Encoding a qubit in an oscillator
Quantum error-correcting codes are constructed that embed a finite-dimensional code space in the infinite-dimensional Hilbert space of a system described by continuous quantum variables. These codesExpand
Topological entanglement entropy.
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 theExpand
Quantum measurements and the Abelian Stabilizer Problem
  • A. Kitaev
  • Mathematics, Computer Science
  • Electron. Colloquium Comput. Complex.
  • 20 November 1995
TLDR
We present a polynomial quantum algorithm for the Abelian stabilizer problem which includes both factoring and the discrete logarithm. Expand
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