288 research outputs found
Quantum Reed-Solomon Codes
After a brief introduction to both quantum computation and quantum error
correction, we show how to construct quantum error-correcting codes based on
classical BCH codes. With these codes, decoding can exploit additional
information about the position of errors. This error model - the quantum
erasure channel - is discussed. Finally, parameters of quantum BCH codes are
provided.Comment: Summary only (2 pages), for the full version see: Proceedings Applied
Algebra, Algebraic Algorithms and Error-Correcting Codes (AAECC-13), Lecture
Notes in Computer Science 1719, Springer, 199
Ischaemic colitis: Practical challenges and evidence-based recommendations for management
Ischaemic colitis (IC) is a common condition with rising incidence, and in severe cases a high mortality rate. Its presentation, severity and disease behaviour can vary widely, and there exists significant heterogeneity in treatment strategies and resultant outcomes. In this article we explore practical challenges in the management of IC, and where available make evidence-based recommendations for its management based on a comprehensive review of available literature. An optimal approach to initial management requires early recognition of the diagnosis followed by prompt and appropriate investigation. Ideally, this should involve the input of both gastroenterology and surgery. CT with intravenous contrast is the imaging modality of choice. It can support clinical diagnosis, define the severity and distribution of ischaemia, and has prognostic value. In all but fulminant cases, this should be followed (within 48 hours) by lower gastrointestinal endoscopy to reach the distal-most extent of the disease, providing endoscopic (and histological) confirmation. The mainstay of medical management is conservative/supportive treatment, with bowel rest, fluid resuscitation and antibiotics. Specific laboratory, radiological and endoscopic features are recognised to correlate with more severe disease, higher rates of surgical intervention and ultimately worse outcomes. These factors should be carefully considered when deciding on the need for and timing of surgical intervention
Experimental quantum coding against photon loss error
A significant obstacle for practical quantum computation is the loss of
physical qubits in quantum computers, a decoherence mechanism most notably in
optical systems. Here we experimentally demonstrate, both in the quantum
circuit model and in the one-way quantum computer model, the smallest
non-trivial quantum codes to tackle this problem. In the experiment, we encode
single-qubit input states into highly-entangled multiparticle codewords, and we
test their ability to protect encoded quantum information from detected
one-qubit loss error. Our results prove the in-principle feasibility of
overcoming the qubit loss error by quantum codes.Comment: "Quantum Computing even when Photons Go AWOL". published versio
Einstein metrics in projective geometry
It is well known that pseudo-Riemannian metrics in the projective class of a
given torsion free affine connection can be obtained from (and are equivalent
to) the solutions of a certain overdetermined projectively invariant
differential equation. This equation is a special case of a so-called first BGG
equation. The general theory of such equations singles out a subclass of
so-called normal solutions. We prove that non-degerate normal solutions are
equivalent to pseudo-Riemannian Einstein metrics in the projective class and
observe that this connects to natural projective extensions of the Einstein
condition.Comment: 10 pages. Adapted to published version. In addition corrected a minor
sign erro
MUBs inequivalence and affine planes
There are fairly large families of unitarily inequivalent complete sets of
N+1 mutually unbiased bases (MUBs) in C^N for various prime powers N. The
number of such sets is not bounded above by any polynomial as a function of N.
While it is standard that there is a superficial similarity between complete
sets of MUBs and finite affine planes, there is an intimate relationship
between these large families and affine planes. This note briefly summarizes
"old" results that do not appear to be well-known concerning known families of
complete sets of MUBs and their associated planes.Comment: This is the version of this paper appearing in J. Mathematical
Physics 53, 032204 (2012) except for format changes due to the journal's
style policie
Basic concepts in quantum computation
Section headings: 1 Qubits, gates and networks 2 Quantum arithmetic and
function evaluations 3 Algorithms and their complexity 4 From interferometers
to computers 5 The first quantum algorithms 6 Quantum search 7 Optimal phase
estimation 8 Periodicity and quantum factoring 9 Cryptography 10 Conditional
quantum dynamics 11 Decoherence and recoherence 12 Concluding remarksComment: 37 pages, lectures given at les Houches Summer School on "Coherent
Matter Waves", July-August 199
Indeterminate-length quantum coding
The quantum analogues of classical variable-length codes are
indeterminate-length quantum codes, in which codewords may exist in
superpositions of different lengths. This paper explores some of their
properties. The length observable for such codes is governed by a quantum
version of the Kraft-McMillan inequality. Indeterminate-length quantum codes
also provide an alternate approach to quantum data compression.Comment: 32 page
A construction of G_2 holonomy spaces with torus symmetry
In the present work the Calderbank-Pedersen description of four dimensional
manifolds with self-dual Weyl tensor is used to obtain examples of
quaternionic-kahler metrics with two commuting isometries. The eigenfunctions
of the hyperbolic laplacian are found by use of Backglund transformations
acting over solutions of the Ward monopole equation. The Bryant-Salamon
construction of holonomy metrics arising as bundles over
quaternionic-kahler base spaces is applied to this examples to find internal
spaces of the M-theory that leads to an N=1 supersymmetry in four dimensions.
Type IIA solutions will be obtained too by reduction along one of the
isometries. The torus symmetry of the base spaces is extended to the total
ones.Comment: Version with 23 pages, no figures, the one form corresponding to the
3 pole solution are expressed in another wa
Topological quantum memory
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 these protocols. An
order-disorder phase transition occurs in this system at a nonzero critical
value of the error rate; if the error rate is below the critical value (the
accuracy threshold), encoded information can be protected arbitrarily well in
the limit of a large code block. This phase transition can be accurately
modeled by a three-dimensional Z_2 lattice gauge theory with quenched disorder.
We estimate the accuracy threshold, assuming that all quantum gates are local,
that qubits can be measured rapidly, and that polynomial-size classical
computations can be executed instantaneously. We also devise a robust recovery
procedure that does not require measurement or fast classical processing;
however for this procedure the quantum gates are local only if the qubits are
arranged in four or more spatial dimensions. We discuss procedures for
encoding, measurement, and performing fault-tolerant universal quantum
computation with surface codes, and argue that these codes provide a promising
framework for quantum computing architectures.Comment: 39 pages, 21 figures, REVTe
Encoding a qubit in an oscillator
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 exploit the
noncommutative geometry of phase space to protect against errors that shift the
values of the canonical variables q and p. In the setting of quantum optics,
fault-tolerant universal quantum computation can be executed on the protected
code subspace using linear optical operations, squeezing, homodyne detection,
and photon counting; however, nonlinear mode coupling is required for the
preparation of the encoded states. Finite-dimensional versions of these codes
can be constructed that protect encoded quantum information against shifts in
the amplitude or phase of a d-state system. Continuous-variable codes can be
invoked to establish lower bounds on the quantum capacity of Gaussian quantum
channels.Comment: 22 pages, 8 figures, REVTeX, title change (qudit -> qubit) requested
by Phys. Rev. A, minor correction
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