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Rapidly rotating atomic gases
 Advances in Physics, 57:539–616
, 2008
"... This article reviews developments in the theory of rapidly rotating degenerate atomic gases. The main focus is on the equilibrium properties of a single component atomic Bose gas, which (at least at rest) forms a BoseEinstein condensate. Rotation leads to the formation of quantized vortices which o ..."
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This article reviews developments in the theory of rapidly rotating degenerate atomic gases. The main focus is on the equilibrium properties of a single component atomic Bose gas, which (at least at rest) forms a BoseEinstein condensate. Rotation leads to the formation of quantized vortices which order into a vortex array, in close analogy with the behaviour of superfluid helium. Under conditions of rapid rotation, when the vortex density becomes large, atomic Bose gases offer the possibility to explore the physics of quantized vortices in novel parameter regimes. First, there is an interesting regime in which the vortices become sufficiently dense that their cores – as set by the healing length – start to overlap. In this regime, the theoretical description simplifies, allowing a reduction to single particle states in the lowest Landau level. Second, one can envisage entering a regime of very high vortex density, when the number of vortices becomes comparable to the number of particles in the gas. In this regime, theory predicts the appearance of a series of strongly correlated phases, which can be viewed as bosonic versions of fractional quantum Hall states. This article describes the
DFF 450/07/2009 Chiral Partition Functions
, 909
"... Chiral partition functions of conformal field theory describe the edge excitations of isolated Hall droplets. They are characterized by an index specifying the quasiparticle sector and transform among themselves by a finitedimensional representation of the modular group. The partition functions are ..."
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Chiral partition functions of conformal field theory describe the edge excitations of isolated Hall droplets. They are characterized by an index specifying the quasiparticle sector and transform among themselves by a finitedimensional representation of the modular group. The partition functions are derived and used to describe electron transitions leading to Coulomb blockade conductance peaks. We find the peak patterns for Abelian hierarchical states and nonAbelian ReadRezayi states, and compare them. Experimental observation of these features can check the qualitative properties of the conformal field theory description, such as the decomposition of the Hilbert space into sectors, 1.1 Disk partition functions Within the conformal field theory description of edge excitations [1][2], the advanced methods of rational conformal field theories (RCFT) [3] have been recently applied to discuss the interference of nonAbelian anyons [4][5] and to determine the bipartite
Braided Categorical Quantum Mechanics I
, 909
"... This is the first paper in a series where we generalize the Categorical Quantum Mechanics program (due to Abramsky, Coecke, et al [AC08]) to braided systems. In our view a uniform description of quantum information for braided systems has not yet emerged. The picture is complicated by a diversity of ..."
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This is the first paper in a series where we generalize the Categorical Quantum Mechanics program (due to Abramsky, Coecke, et al [AC08]) to braided systems. In our view a uniform description of quantum information for braided systems has not yet emerged. The picture is complicated by a diversity of examples that lacks a unifying framework for proving theorems and discovering new protocols. We use category theory to construct a highlevel language that abstracts the quantum mechanical properties of braided systems. We exploit this framework to propose an axiomatic description of braided quantum information intended for topological quantum computation. In this installment we first generalize the primordial AbramskyCoecke “quantum information flow ” paradigm from compact closed categories to rightrigid strict monoidal categories. We then study dagger structures for rigid and/or braided categories and formulate
The idiots guide to Quantum Error Correction.
, 2009
"... Contents Quantum Error Correction and faulttolerant quantum computation represent arguably the most vital theoretical aspect of quantum information processing. It was well known from the early developments of this exciting field that the fragility of coherent quantum systems would be a catastrophic ..."
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Contents Quantum Error Correction and faulttolerant quantum computation represent arguably the most vital theoretical aspect of quantum information processing. It was well known from the early developments of this exciting field that the fragility of coherent quantum systems would be a catastrophic obstacle to the development of large scale quantum computers. The introduction of
Fractional quantum Hall effect in the absence of Landau levels
"... It is well known that the topological phenomena with fractional excitations, the fractional quantum Hall effect, will emerge when electrons move in Landau levels. Here we show the theoretical discovery of the fractional quantum Hall effect in the absence of Landau levels in an interacting fermion mo ..."
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It is well known that the topological phenomena with fractional excitations, the fractional quantum Hall effect, will emerge when electrons move in Landau levels. Here we show the theoretical discovery of the fractional quantum Hall effect in the absence of Landau levels in an interacting fermion model. The noninteracting part of our Hamiltonian is the recently proposed topologically nontrivial flatband model on a checkerboard lattice. In the presence of nearestneighbouring repulsion, we find that at 1/3 filling, the Fermiliquid state is unstable towards the fractional quantum Hall effect. At 1/5 filling, however, a nextnearestneighbouring repulsion is needed for the occurrence of the 1/5 fractional quantum Hall effect when nearestneighbouring repulsion is not too strong. We demonstrate the characteristic features of these novel states and determine the corresponding phase diagram. 1
et INSTITUT DE PHYSIQUE THÉORIQUE CEA/SACLAY Thèse de doctorat
, 2013
"... Sujet de la thèse: Edge states and supersymmetric sigma models présentée par Roberto BONDESAN pour obtenir le grade de Docteur de l’Université Paris 6 Soutenue le 14 Septembre 2012 devant le jury composé de: ..."
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Sujet de la thèse: Edge states and supersymmetric sigma models présentée par Roberto BONDESAN pour obtenir le grade de Docteur de l’Université Paris 6 Soutenue le 14 Septembre 2012 devant le jury composé de:
Quantum computation beyond . . .
, 2008
"... The quantum circuit model is the most widely used model of quantum computation. It provides both a framework for formulating quantum algorithms and an architecture for the physical construction of quantum computers. However, several other models of quantum computation exist which provide useful alte ..."
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The quantum circuit model is the most widely used model of quantum computation. It provides both a framework for formulating quantum algorithms and an architecture for the physical construction of quantum computers. However, several other models of quantum computation exist which provide useful alternative frameworks for both discovering new quantum algorithms and devising new physical implementations of quantum computers. In this thesis, I first present necessary background material for a general physics audience and discuss existing models of quantum computation. Then, I present three new results relating to various models of quantum computation: a scheme for improving the intrinsic fault tolerance of adiabatic quantum computers using quantum error detecting codes, a proof that a certain problem of estimating Jones polynomials is complete for the one clean qubit complexity class, and a generalization of perturbative gadgets which allows kbody interactions to be directly simulated using 2body interactions. Lastly, I discuss general principles regarding quantum computation that I learned in the course of my research, and using these principles I propose directions for future research.