Topology driven quantum phase transitions in time-reversal invariant anyonic quantum liquids (2009)
Gils, Charlotte, Trebst, Simon, Kitaev, Alexei, Ludwig, Andreas W. W., Troyer, Matthias, Wang, Zhenghan
Indistinguishable particles in two dimensions can be characterized by anyonic quantum statistics more general than those of bosons or fermions. Such anyons emerge as quasiparticles in fractional...
Topological phases and quantum computation (2009)
Kitaev, Alexei, Laumann, Chris
This is a collection of lecture notes from three lectures given by Alexei Kitaev at the 2008 Les Houches summer school "Exact methods in low-dimensional physics and quantum computing." They provide a...
The effects of interactions on the topological classification of free fermion systems (2009)
Fidkowski, Lukasz, Kitaev, Alexei
We describe in detail a counterexample to the topological classification of free fermion systems. We deal with a one dimensional chain of Majorana fermions with an unusual T symmetry. The topological...
Periodic table for topological insulators and superconductors (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...
Quasiparticle Poisoning and Josephson Current Fluctuations Induced by Kondo Impurities (2008)
Faoro, Lara, Kitaev, Alexei, Ioffe, Lev B.
We introduce a toy model that allows us to study the physical properties of a spin impurity coupled to the electrons in the superconducting island. We show that, when the coupling of the spin is of...
Quasiparticle poisoning and Josephson current fluctuations induced by Kondo impurities (2008)
Faoro, Lara, Kitaev, Alexei, Ioffe, Lev B.
We introduce a toy model that allows us to study the physical properties of a spin impurity coupled to the electrons in the superconducting island. We show that when the coupling of the spin is of...
Wavefunction preparation using a quantum computer (2008)
Kitaev, Alexei, Webb, William A.
In this paper we describe a set of algorithms for preparing certain quantum states (representing continuous functions) on qubit ensembles. This research is part of a broader effort to develop...
Shot noise in an anyonic Mach-Zehnder interferometer (2007)
Feldman, D. E., Gefen, Yuval, Kitaev, Alexei, Law, K. T., Stern, Ady
We show how shot noise in an electronic Mach-Zehnder interferometer in the fractional quantum Hall regime probes the charge and statistics of quantum Hall quasiparticles. The dependence of the noise...
Noncommuting Flux Sectors in a Tabletop Experiment (2007)
Kitaev, Alexei, Moore, Gregory W., Walker, Kevin
We show how one can use superconductors and Josephson junctions to create a laboratory system which can explore the groundstates of the free electromagnetic field in a 3-manifold with torsion in its...
Interacting Anyons in Topological Quantum Liquids: The Golden Chain (2007)
Feiguin, Adrian, Trebst, Simon, Ludwig, Andreas W. W., Troyer, Matthis, Kitaev, Alexei, Wang, Zhenghan, ...
We discuss generalizations of quantum spin Hamiltonians using anyonic degrees of freedom. The simplest model for interacting anyons energetically favors neighboring anyons to fuse into the trivial...
Shot Noise in Anyonic Mach-Zehnder Interferometer (2006)
Feldman, D. E., Gefen, Yuval, Kitaev, Alexei, Law, K. T., Stern, Ady
We show how shot noise in an electronic Mach-Zehnder interferometer in the fractional quantum Hall regime probes the charge and statistics of quantum Hall quasiparticles. The dependence of the noise...
Interacting anyons in topological quantum liquids: The golden chain (2006)
Feiguin, Adrian, Trebst, Simon, Ludwig, Andreas W. W., Troyer, Matthias, Kitaev, Alexei, Wang, Zhenghan, ...
We discuss generalizations of quantum spin Hamiltonians using anyonic degrees of freedom. The simplest model for interacting anyons energetically favors neighboring anyons to fuse into the trivial...
Detecting Non-Abelian Statistics with an Electronic Mach-Zehnder Interferometer (2006)
Feldman, D. E., Kitaev, Alexei
Fractionally charged quasiparticles in the quantum Hall state with a filling factor nu=5/2 are expected to obey non-Abelian statistics. We demonstrate that their statistics can be probed by transport...
Protected qubit based on a superconducting current mirror (2006)
We propose a qubit implementation based on exciton condensation in capacitively coupled Josephson junction chains. The qubit is protected in the sense that all unwanted terms in its effective...
Detecting non-Abelian Statistics with Electronic Mach-Zehnder Interferometer (2006)
Feldman, D. E., Kitaev, Alexei
Fractionally charged quasiparticles in the quantum Hall state with filling factor $\nu=5/2$ are expected to obey non-Abelian statistics. We demonstrate that their statistics can be probed by...
Topological Entanglement Entropy (2006)
Kitaev, Alexei, Preskill, John
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...
The Complexity of the Local Hamiltonian Problem (2006)
Kempe, Julia, Kitaev, Alexei, Regev, Oded
The k-LOCAL Hamiltonian problem is a natural complete problem for the complexity class QMA, the quantum analogue of NP. It is similar in spirit to MAX-k-SAT, which is NP-complete for k >= 2. It was...
Fault-Tolerant Quantum Computation with Long-Range Correlated Noise (2006)
Aharonov, Dorit, Kitaev, Alexei, Preskill, John
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...
Detecting Non-Abelian Statistics in the nu=5/2 Fractional Quantum Hall State (2006)
Bonderson, Parsa, Kitaev, Alexei, Shtengel, Kirill
In this Letter we propose an interferometric experiment to detect non-Abelian quasiparticle statistics—one of the hallmark characteristics of the Moore-Read state expected to describe the observed...
Anyons in an exactly solved model and beyond (2006)
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...
Universal manifold pairings and positivity (2005)
Freedman, Michael H., Kitaev, Alexei, Nayak, Chetan, Slingerland, Johannes K., Walker, Kevin, Wang, Zhenghan
Gluing two manifolds M_1 and M_2 with a common boundary S yields a closed manifold M. Extending to formal linear combinations x=Sum_i(a_i M_i) yields a sesquilinear pairing p= with values in (formal...
Fault-tolerant quantum computation with long-range correlated noise (2005)
Aharonov, Dorit, Kitaev, Alexei, Preskill, John
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...
Topological entanglement entropy (2005)
Kitaev, Alexei, Preskill, John
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...
Detecting Non-Abelian Statistics in the nu=5/2 Fractional Quantum Hall State (2005)
Bonderson, Parsa, Kitaev, Alexei, Shtengel, Kirill
In this letter we propose an interferometric experiment to detect non-Abelian quasiparticle statistics -- one of the hallmark characteristics of the Moore-Read state expected to describe the observed...
Anyons in an exactly solved model and beyond (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...
Universal manifold pairings and positivity (2005)
Freedman, Michael H, Kitaev, Alexei, Nayak, Chetan, Slingerland, Johannes K, Walker, Kevin, Wang, Zhenghan
Gluing two manifolds M_1 and M_2 with a common boundary S yields a closed manifold M. Extending to formal linear combinations x=Sum_i(a_i M_i) yields a sesquilinear pairing p= with values in (formal...
Universal quantum computation with ideal Clifford gates and noisy ancillas (2005)
Bravyi, Sergey, Kitaev, Alexei
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....
Anyons in an exactly solved model and beyond (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...
The Complexity of the Local Hamiltonian Problem (2004)
Kempe, Julia, Kitaev, Alexei, Regev, Oded
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
Superselection rules and quantum protocols (2004)
Kitaev, Alexei, Mayers, Dominic, Preskill, John
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...
Universal Quantum Computation with ideal Clifford gates and noisy ancillas (2004)
Bravyi, Sergei, Kitaev, Alexei
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...
The complexity of the local Hamiltonian problem (2004)
Julia Kempe, Alexei Kitaev, Oded Regev
Abstract. The k-local Hamiltonian problem is a natural complete problem for the complexity class QMA, the quantum analogue of NP. It is similar in spirit to MAX-k-SAT, which is NP-complete for k ≥...
Superselection rules and quantum protocols (2003)
Kitaev, Alexei, Mayers, Dominic, Preskill, John
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...
Diameters of Homogeneous Spaces (2002)
Freedman, Michael, Kitaev, Alexei, Lurie, Jacob
Let G be a compact connected Lie group with trivial center. Using the action of G on its Lie algebra, we define an operator norm | |_{G} which induces a bi-invariant metric d_G(x,y)=|Ad(yx^{-1})|_{G}...
Topological quantum memory (2002)
Dennis, Eric, Kitaev, Alexei, Landahl, Andrew, Preskill, John
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...
Topological quantum memory (2002)
Dennis, Eric, Kitaev, Alexei, Landahl, Andrew, Preskill, John
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...
Measurability of Wilson loop operators (2002)
Beckman, David, Gottesman, Daniel, Kitaev, Alexei, Preskill, John
We show that the nondemolition measurement of a spacelike Wilson loop operator W(C) is impossible in a relativistic non-Abelian gauge theory. In particular, if two spacelike-separated magnetic flux...
Classical and Quantum Computation (2002)
Michael H. Freedman, Alexei Kitaev, Michael J. Larsen, Zhenghan Wang
Abstract. 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...
Topological quantum memory (2001)
Dennis, Eric, Kitaev, Alexei, Landahl, Andrew, Preskill, John
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...
Measurability of Wilson loop operators (2001)
Beckman, David, Gottesman, Daniel, Kitaev, Alexei, Preskill, John
We show that the nondemolition measurement of a spacelike Wilson loop operator W(C) is impossible in a relativistic non-Abelian gauge theory. In particular, if two spacelike-separated magnetic flux...
Encoding a qubit in an oscillator (2001)
Gottesman, Daniel, Kitaev, Alexei, Preskill, John
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...
Topological Quantum Computation (2001)
Freedman, Michael H., Kitaev, Alexei, Larsen, Michael J., Wang, Zhenghan
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...
Michael H. Freedman, Alexei Kitaev, Zhenghan Wang
Abstract: 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...
Unpaired Majorana fermions in quantum wires (2000)
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 $L$ possesses...
Encoding a qubit in an oscillator (2000)
Gottesman, Daniel, Kitaev, Alexei, Preskill, John
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...
Fermionic quantum computation (2000)
Bravyi, Sergey, Kitaev, Alexei
We define a model of quantum computation with local fermionic modes (LFMs) -- sites which can be either empty or occupied by a fermion. With the standard correspondence between the Foch space of $m$...
Simulation of topological field theories by quantum computers (2000)
Freedman, Michael H., Kitaev, Alexei, Wang, Zhenghan
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...
In this paper we consider quantum interactive proof systems, which are interactive proof systems in which the prover and verier may perform quantum computations and exchange quantum information. We...
Quantum Circuits with Mixed States (1998)
Aharonov, Dorit, Kitaev, Alexei, Nisan, Noam
We define the model of quantum circuits with density matrices, where non-unitary gates are allowed. Measurements in the middle of the computation, noise and decoherence are implemented in a natural...
Quantum circuits with mixed states (1998)
Dorit Aharonov, Alexei Kitaev, Noam Nisan
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...