6,478 research outputs found
Pinwheel Scheduling for Fault-tolerant Broadcast Disks in Real-time Database Systems
The design of programs for broadcast disks which incorporate real-time and fault-tolerance requirements is considered. A generalized model for real-time fault-tolerant broadcast disks is defined. It is shown that designing programs for broadcast disks specified in this model is closely related to the scheduling of pinwheel task systems. Some new results in pinwheel scheduling theory are derived, which facilitate the efficient generation of real-time fault-tolerant broadcast disk programs.National Science Foundation (CCR-9308344, CCR-9596282
Unitary reflection groups for quantum fault tolerance
This paper explores the representation of quantum computing in terms of
unitary reflections (unitary transformations that leave invariant a hyperplane
of a vector space). The symmetries of qubit systems are found to be supported
by Euclidean real reflections (i.e., Coxeter groups) or by specific imprimitive
reflection groups, introduced (but not named) in a recent paper [Planat M and
Jorrand Ph 2008, {\it J Phys A: Math Theor} {\bf 41}, 182001]. The
automorphisms of multiple qubit systems are found to relate to some Clifford
operations once the corresponding group of reflections is identified. For a
short list, one may point out the Coxeter systems of type and (for
single qubits), and (for two qubits), and (for three
qubits), the complex reflection groups and groups No 9 and 31 in
the Shephard-Todd list. The relevant fault tolerant subsets of the Clifford
groups (the Bell groups) are generated by the Hadamard gate, the phase
gate and an entangling (braid) gate [Kauffman L H and Lomonaco S J 2004 {\it
New J. of Phys.} {\bf 6}, 134]. Links to the topological view of quantum
computing, the lattice approach and the geometry of smooth cubic surfaces are
discussed.Comment: new version for the Journal of Computational and Theoretical
Nanoscience, focused on "Technology Trends and Theory of Nanoscale Devices
for Quantum Applications
Exploiting Data Representation for Fault Tolerance
We explore the link between data representation and soft errors in dot
products. We present an analytic model for the absolute error introduced should
a soft error corrupt a bit in an IEEE-754 floating-point number. We show how
this finding relates to the fundamental linear algebra concepts of
normalization and matrix equilibration. We present a case study illustrating
that the probability of experiencing a large error in a dot product is
minimized when both vectors are normalized. Furthermore, when data is
normalized we show that the absolute error is less than one or very large,
which allows us to detect large errors. We demonstrate how this finding can be
used by instrumenting the GMRES iterative solver. We count all possible errors
that can be introduced through faults in arithmetic in the computationally
intensive orthogonalization phase, and show that when scaling is used the
absolute error can be bounded above by one
SU(2) and SU(1,1) Approaches to Phase Operators and Temporally Stable Phase States: Applications to Mutually Unbiased Bases and Discrete Fourier Transforms
We propose a group-theoretical approach to the generalized oscillator algebra
Ak recently investigated in J. Phys. A: Math. Theor. 43 (2010) 115303. The case
k > or 0 corresponds to the noncompact group SU(1,1) (as for the harmonic
oscillator and the Poeschl-Teller systems) while the case k < 0 is described by
the compact group SU(2) (as for the Morse system). We construct the phase
operators and the corresponding temporally stable phase eigenstates for Ak in
this group-theoretical context. The SU(2) case is exploited for deriving
families of mutually unbiased bases used in quantum information. Along this
vein, we examine some characteristics of a quadratic discrete Fourier transform
in connection with generalized quadratic Gauss sums and generalized Hadamard
matrices
Holonomic quantum computation in decoherence-free subspaces
We show how to realize, by means of non-abelian quantum holonomies, a set of
universal quantum gates acting on decoherence-free subspaces and subsystems. In
this manner we bring together the quantum coherence stabilization virtues of
decoherence-free subspaces and the fault-tolerance of all-geometric holonomic
control. We discuss the implementation of this scheme in the context of quantum
information processing using trapped ions and quantum dots.Comment: 4 pages, no figures. v2: minor changes. To appear in PR
Correcting soft errors online in fast fourier transform
While many algorithm-based fault tolerance (ABFT) schemes have been proposed to detect soft errors offline in the fast Fourier transform (FFT) after computation finishes, none of the existing ABFT schemes detect soft errors online before the computation finishes. This paper presents an online ABFT scheme for FFT so that soft errors can be detected online and the corrupted computation can be terminated in a much more timely manner. We also extend our scheme to tolerate both arithmetic errors and memory errors, develop strategies to reduce its fault tolerance overhead and improve its numerical stability and fault coverage, and finally incorporate it into the widely used FFTW library - one of the today's fastest FFT software implementations. Experimental results demonstrate that: (1) the proposed online ABFT scheme introduces much lower overhead than the existing offline ABFT schemes; (2) it detects errors in a much more timely manner; and (3) it also has higher numerical stability and better fault coverage
Generalized Cluster States Based on Finite Groups
We define generalized cluster states based on finite group algebras in
analogy to the generalization of the toric code to the Kitaev quantum double
models. We do this by showing a general correspondence between systems with CSS
structure and finite group algebras, and applying this to the cluster states to
derive their generalization. We then investigate properties of these states
including their PEPS representations, global symmetries, and relationship to
the Kitaev quantum double models. We also discuss possible applications of
these states.Comment: 23 pages, 4 figure
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