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- 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
- 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)

- 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)

- 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)

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 codes exploit the noncommutative geometry of phase space to protect against errors that shift the values of the canonical variables q and p. In the setting of quantum… (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)

We show that superselection rules do not enhance the information-theoretic security of quantum cryptographic protocols. Our analysis employs two quite different methods. The first method uses the concept of a reference system—in a world subject to a superselection rule, unrestricted operations can be simulated by parties who share access to a reference… (More)

We prove a new version of the quantum accuracy threshold theorem that applies to non-Markovian noise with algebraically decaying spatial correlations. We consider noise in a quantum computer arising from a perturbation that acts collectively on pairs of qubits and on the environment, and we show that an arbitrarily long quantum computation can be executed… (More)

- V, John Preskill, Peter Brooks, Alexei Kitaev
- 2012

We analyze the accuracy of quantum phase gates acting on " 0-π qubits " in superconducting circuits, where the gates are protected against thermal and Hamiltonian noise by continuous-variable quantum error-correcting codes. The gates are executed by turning on and off a tunable Josephson coupling between an LC oscillator and a qubit or pair of qubits;… (More)