Josephson-coupled Moore-Read states

We study a quantum Hall bilayer system of bosons at total filling factor ν = 1, and study the phase that results from short ranged pair-tunneling combined with short ranged interlayer interactions. We introduce two exactly solvable model Hamiltonians which both yield the coupled Moore-Read state [Phys. Rev. Lett. 108, 256809 (2012)] as a ground state, when projected onto fixed particle numbers in each layer. One of these Hamiltonians describes a gapped topological phase while the other is gapless. However, on introduction of a pair tunneling term, the second system becomes gapped and develops the same topological order as the gapped Hamiltonian. Supported by the exact solution of the full zero-energy quasihole spectrum and a conformal field theory approach, we develop an intuitive picture of this system as two coupled composite fermion superconductors. In this language, pair tunneling provides a Josephson coupling of the superconducting phases of the two layers, and gaps out the Goldstone mode associated with particle transport between the layers. In particular, this implies that quasiparticles are confined between the layers. In the bulk, the resulting phase has the topological order of the Halperin 220 phase with U(1)_2 x U(1)_2 topological order, but it is realized in the symmetric/antisymmetric-basis of the layer index. Consequently, the edge spectrum at a fixed particle number reveals an unexpected U(1)_4 x U(1) structure.The authors would like to thank Nordita and the Aspen Center for Physics their hospitality, and acknowledge support from the Leverhulme Trust under grant ECF-2011-565, the Newton Trust of the University of Cambridge and by the Royal Society under grant UF120157 (G.M.), the European Union under Marie Curie award 299890 QETPM (L.H.), Science Foundation Ireland principal investigator awards 08/IN.1/I1961 and 12/IA/1697 (J.K.S.) and EPSRC grant EP/I032487/1 (S.H.S.).This is the author accepted version of the manuscript which has been published at http://dx.doi.org/10.1103/PhysRevB.90.23510

Fractional Quantum Hall Effect of Lattice Bosons Near Commensurate Flux

We study interacting bosons on a lattice in a magnetic field. When the number of flux quanta per plaquette is close to a rational fraction, the low energy physics is mapped to a multi-species continuum model: bosons in the lowest Landau level where each boson is given an internal degree of freedom, or \emph{pseudospin}. We find that the interaction potential between the bosons involves terms that do not conserve pseudospin, corresponding to umklapp processes, which in some cases can also be seen as BCS-type pairing terms. We argue that in experimentally realistic regimes for bosonic atoms in optical lattices with synthetic magnetic fields, these terms are crucial for determining the nature of allowed ground states. In particular, we show numerically that certain paired wave functions related to the Moore-Read Pfaffian state are stabilized by these terms, whereas certain other wave functions can be destabilized when umklapp processes become strong

Topological Quantum Computing with Only One Mobile Quasiparticle

In a topological quantum computer, universal quantum computation is performed by dragging quasiparticle excitations of certain two dimensional systems around each other to form braids of their world lines in 2+1 dimensional space-time. In this paper we show that any such quantum computation that can be done by braiding $n$ identical quasiparticles can also be done by moving a single quasiparticle around n-1 other identical quasiparticles whose positions remain fixed.Comment: 4 pages, 5 figure

Braid Topologies for Quantum Computation

In topological quantum computation, quantum information is stored in states which are intrinsically protected from decoherence, and quantum gates are carried out by dragging particle-like excitations (quasiparticles) around one another in two space dimensions. The resulting quasiparticle trajectories define world-lines in three dimensional space-time, and the corresponding quantum gates depend only on the topology of the braids formed by these world-lines. We show how to find braids that yield a universal set of quantum gates for qubits encoded using a specific kind of quasiparticle which is particularly promising for experimental realization.Comment: 4 pages, 4 figures, minor revision

Topological Quantum Compiling

A method for compiling quantum algorithms into specific braiding patterns for non-Abelian quasiparticles described by the so-called Fibonacci anyon model is developed. The method is based on the observation that a universal set of quantum gates acting on qubits encoded using triplets of these quasiparticles can be built entirely out of three-stranded braids (three-braids). These three-braids can then be efficiently compiled and improved to any required accuracy using the Solovay-Kitaev algorithm.Comment: 20 pages, 20 figures, published versio

The Farsi version of the Hypomania Check-List 32 (HCL-32): Applicability and indication of a four-factorial solution

Background: Data from the Iranian population for hypomania core symptom clusters are lacking. The aim of the present study was therefore to apply the Farsi version of the Hypomania-Check-List 32 (HCL-32), and to explore its factorial structure.Methods: A total of 163 Iranian out-patients took part in the study; 61 suffered from Major Depressive Disorder (MDD), and 102 suffered from Bipolar Disorders (BP). Participants completed the Mood Disorder Questionnaire (MDQ) and the Hypomania Checklist (HCL-32). Exploratory factor analyses were used to examine the properties of the HCL-32. A ROC-curve analysis was performed to calculate sensitivity and specificity.Results: The HCL-32 differentiated between patients with MDD and with BP. Psychometric properties were satisfactory: sensitivity: 73; specificity: 91. MDQ and HCL-32 did correlate highly. No differences were found between patients suffering from BP I and BP II.Discussion: Instead of the two-factorial structure of the HCL-32 reported previously, the present pattern of factorial results suggest a distinction between four factors: two broadly positive dimensions of hypomania ("physically and mentally active"; "positive social interactions") and two rather negative dimensions ("risky behavior and substance use"; "difficulties in social interaction and impatience").Conclusion: The Farsi version of the HCL-32 proved to be applicable, and therefore easy to introduce within a clinical context. The pattern of results suggests a four factorial solution. © 2011 Haghighi et al; licensee BioMed Central Ltd

Topological quantum computing with Read-Rezayi states.

Read-Rezayi fractional quantum Hall states are among the prime candidates for realizing non-Abelian anyons which, in principle, can be used for topological quantum computation. We present a prescription for efficiently finding braids which can be used to carry out a universal set of quantum gates on encoded qubits based on anyons of the Read-Rezayi states with k>2, k not equal 4. This work extends previous results which only applied to the case k=3 (Fibonacci) and clarifies why, in that case, gate constructions are simpler than for a generic Read-Rezayi state