5,669 research outputs found
CFT Duals for Extreme Black Holes
It is argued that the general four-dimensional extremal Kerr-Newman-AdS-dS
black hole is holographically dual to a (chiral half of a) two-dimensional CFT,
generalizing an argument given recently for the special case of extremal Kerr.
Specifically, the asymptotic symmetries of the near-horizon region of the
general extremal black hole are shown to be generated by a Virasoro algebra.
Semiclassical formulae are derived for the central charge and temperature of
the dual CFT as functions of the cosmological constant, Newton's constant and
the black hole charges and spin. We then show, assuming the Cardy formula, that
the microscopic entropy of the dual CFT precisely reproduces the macroscopic
Bekenstein-Hawking area law. This CFT description becomes singular in the
extreme Reissner-Nordstrom limit where the black hole has no spin. At this
point a second dual CFT description is proposed in which the global part of the
U(1) gauge symmetry is promoted to a Virasoro algebra. This second description
is also found to reproduce the area law. Various further generalizations
including higher dimensions are discussed.Comment: 18 pages; v2 minor change
Parafermions in a Kagome lattice of qubits for topological quantum computation
Engineering complex non-Abelian anyon models with simple physical systems is
crucial for topological quantum computation. Unfortunately, the simplest
systems are typically restricted to Majorana zero modes (Ising anyons). Here we
go beyond this barrier, showing that the parafermion model of
non-Abelian anyons can be realized on a qubit lattice. Our system additionally
contains the Abelian anyons as low-energetic excitations. We
show that braiding of these parafermions with each other and with the
anyons allows the entire Clifford group to be
generated. The error correction problem for our model is also studied in
detail, guaranteeing fault-tolerance of the topological operations. Crucially,
since the non-Abelian anyons are engineered through defect lines rather than as
excitations, non-Abelian error correction is not required. Instead the error
correction problem is performed on the underlying Abelian model, allowing high
noise thresholds to be realized.Comment: 11+10 pages, 14 figures; v2: accepted for publication in Phys. Rev.
X; 4 new figures, performance of phase-gate explained in more detai
MDL Convergence Speed for Bernoulli Sequences
The Minimum Description Length principle for online sequence
estimation/prediction in a proper learning setup is studied. If the underlying
model class is discrete, then the total expected square loss is a particularly
interesting performance measure: (a) this quantity is finitely bounded,
implying convergence with probability one, and (b) it additionally specifies
the convergence speed. For MDL, in general one can only have loss bounds which
are finite but exponentially larger than those for Bayes mixtures. We show that
this is even the case if the model class contains only Bernoulli distributions.
We derive a new upper bound on the prediction error for countable Bernoulli
classes. This implies a small bound (comparable to the one for Bayes mixtures)
for certain important model classes. We discuss the application to Machine
Learning tasks such as classification and hypothesis testing, and
generalization to countable classes of i.i.d. models.Comment: 28 page
Solomonoff Induction Violates Nicod's Criterion
Nicod's criterion states that observing a black raven is evidence for the
hypothesis H that all ravens are black. We show that Solomonoff induction does
not satisfy Nicod's criterion: there are time steps in which observing black
ravens decreases the belief in H. Moreover, while observing any computable
infinite string compatible with H, the belief in H decreases infinitely often
when using the unnormalized Solomonoff prior, but only finitely often when
using the normalized Solomonoff prior. We argue that the fault is not with
Solomonoff induction; instead we should reject Nicod's criterion.Comment: ALT 201
Enhanced thermal stability of the toric code through coupling to a bosonic bath
We propose and study a model of a quantum memory that features
self-correcting properties and a lifetime growing arbitrarily with system size
at non-zero temperature. This is achieved by locally coupling a 2D L x L toric
code to a 3D bath of bosons hopping on a cubic lattice. When the stabilizer
operators of the toric code are coupled to the displacement operator of the
bosons, we solve the model exactly via a polaron transformation and show that
the energy penalty to create anyons grows linearly with L. When the stabilizer
operators of the toric code are coupled to the bosonic density operator, we use
perturbation theory to show that the energy penalty for anyons scales with
ln(L). For a given error model, these energy penalties lead to a lifetime of
the stored quantum information growing respectively exponentially and
polynomially with L. Furthermore, we show how to choose an appropriate coupling
scheme in order to hinder the hopping of anyons (and not only their creation)
with energy barriers that are of the same order as the anyon creation gaps. We
argue that a toric code coupled to a 3D Heisenberg ferromagnet realizes our
model in its low-energy sector. Finally, we discuss the delicate issue of the
stability of topological order in the presence of perturbations. While we do
not derive a rigorous proof of topological order, we present heuristic
arguments suggesting that topological order remains intact when perturbative
operators acting on the toric code spins are coupled to the bosonic
environment.Comment: This manuscript has some overlap with arXiv:1209.5289. However, a
different model is the focus of the current work. Since this model is exactly
solvable, it allows a clearer demonstration of the principle behind our
quantum memory proposal. v2: minor changes and additional referenc
Milieu-adopted in vitro and in vivo differentiation of mesenchymal tissues derived from different adult human CD34-negative progenitor cell clones
Adult mesenchymal stem cells with multilineage differentiation potentially exist in the bone marrow, but have also been isolated from the peripheral blood. The differentiation of stem cells after leaving their niches depends predominately on the local milieu and its new microenvironment, and is facilitated by soluble factors but also by the close cell-cell interaction in a three-dimensional tissue or organ system. We have isolated CD34-negative, mesenchymal stem cell lines from human bone marrow and peripheral blood and generated monoclonal cell populations after immortalization with the SV40 large T-antigen. The cultivation of those adult stem cell clones in an especially designed in vitro environment, including self-constructed glass capillaries with defined growth conditions, leads to the spontaneous establishment of pleomorphic three-dimensional cell aggregates ( spheroids) from the monoclonal cell population, which consist of cells with an osteoblast phenotype and areas of mineralization along with well-vascularized tissue areas. Modifications of the culture conditions favored areas of bone-like calcifications. After the transplantation of the at least partly mineralized human spheroids into different murine soft tissue sites but also a dorsal skinfold chamber, no further bone formation could be observed, but angiogenesis and neovessel formation prevailed instead, enabling the transplanted cells and cell aggregates to survive. This study provides evidence that even monoclonal adult human CD34-negative stem cells from the bone marrow as well as peripheral blood can potentially differentiate into different mesenchymal tissues depending on the local milieu and responding to the needs within the microenvironment. Copyright (C) 2005 S. Karger AG, Basel
Effective quantum memory Hamiltonian from local two-body interactions
In [Phys. Rev. A 88, 062313 (2013)] we proposed and studied a model for a
self-correcting quantum memory in which the energetic cost for introducing a
defect in the memory grows without bounds as a function of system size. This
positive behavior is due to attractive long-range interactions mediated by a
bosonic field to which the memory is coupled. The crucial ingredients for the
implementation of such a memory are the physical realization of the bosonic
field as well as local five-body interactions between the stabilizer operators
of the memory and the bosonic field. Here, we show that both of these
ingredients appear in a low-energy effective theory of a Hamiltonian that
involves only two-body interactions between neighboring spins. In particular,
we consider the low-energy, long-wavelength excitations of an ordered
Heisenberg ferromagnet (magnons) as a realization of the bosonic field.
Furthermore, we present perturbative gadgets for generating the required
five-spin operators. Our Hamiltonian involving only local two-body interactions
is thus expected to exhibit self-correcting properties as long as the noise
affecting it is in the regime where the effective low-energy description
remains valid.Comment: 14 pages, 3 figure
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