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- Dorit Aharonov, Alexei Y. Kitaev, Noam Nisan
- STOC
- 1998

Current formal models for quantum computation deal only with unitary gates operating on " pure quantum states ". In these models it is difficult or impossible to deal formally with several central issues: measurements in the middle of the computation; decoherence and noise, using probabilistic subroutines, and more. It turns out, that the restriction to… (More)

- Julia Kempe, Alexei Y. Kitaev, Oded Regev
- FSTTCS
- 2004

The k-LOCAL HAMILTONIAN problem is a natural complete problem for the complexity class QMA, the quantum analog of NP. It is similar in spirit to MAX-k-SAT, which is NP-complete for k ≥ 2. It was known that the problem is QMA-complete for any k ≥ 3. On the other hand 1-LOCAL HAMILTONIAN is in P, and hence not believed to be QMA-complete. The complexity of… (More)

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)

- Alexei Y. Kitaev
- Electronic Colloquium on Computational Complexity
- 1996

We present a polynomial quantum algorithm for the Abelian stabilizer problem which includes both factoring and the discrete logarithm. Thus we extend famous Shor's results 7]. Our method is based on a procedure for measuring an eigenvalue of a unitary operator. Another application of this procedure is a polynomial quantum Fourier transform algorithm for an… (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 Y. Kitaev, John Watrous
- STOC
- 2000

In this paper we consider quantum interactive proof systems, which are interactive proof systems in which the prover and verifier may perform quantum computations and exchange quantum information. We prove that any polynomial-round quantum interactive proof system with two-sided bounded error can be parallelized to a quantum interactive proof system with… (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)

- G Vidal, J I Latorre, E Rico, A Kitaev
- Physical review letters
- 2003

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)

- 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)

- Alexei Kitaev, John Preskill
- Physical review letters
- 2006

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)