7,070 research outputs found
CSP methods for identifying atomic actions in the design of fault tolerant concurrent systems
Limiting the extent of error propagation when faults occur and localizing the subsequent error recovery are common concerns in the design of fault tolerant parallel processing systems, Both activities are made easier if the designer associates fault tolerance mechanisms with the underlying atomic actions of the system, With this in mind, this paper has investigated two methods for the identification of atomic actions in parallel processing systems described using CSP, Explicit trace evaluation forms the basis of the first algorithm, which enables a designer to analyze interprocess communications and thereby locate atomic action boundaries in a hierarchical fashion, The second method takes CSP descriptions of the parallel processes and uses structural arguments to infer the atomic action boundaries. This method avoids the difficulties involved with producing full trace sets, but does incur the penalty of a more complex algorithm
Quantum information and statistical mechanics: an introduction to frontier
This is a short review on an interdisciplinary field of quantum information
science and statistical mechanics. We first give a pedagogical introduction to
the stabilizer formalism, which is an efficient way to describe an important
class of quantum states, the so-called stabilizer states, and quantum
operations on them. Furthermore, graph states, which are a class of stabilizer
states associated with graphs, and their applications for measurement-based
quantum computation are also mentioned. Based on the stabilizer formalism, we
review two interdisciplinary topics. One is the relation between quantum error
correction codes and spin glass models, which allows us to analyze the
performances of quantum error correction codes by using the knowledge about
phases in statistical models. The other is the relation between the stabilizer
formalism and partition functions of classical spin models, which provides new
quantum and classical algorithms to evaluate partition functions of classical
spin models.Comment: 15pages, 4 figures, to appear in Proceedings of 4th YSM-SPIP (Sendai,
14-16 December 2012
Design for validation: An approach to systems validation
Every complex system built is validated in some manner. Computer validation begins with review of the system design. As systems became too complicated for one person to review, validation began to rely on the application of adhoc methods by many individuals. As the cost of the changes mounted and the expense of failure increased, more organized procedures became essential. Attempts at devising and carrying out those procedures showed that validation is indeed a difficult technical problem. The successful transformation of the validation process into a systematic series of formally sound, integrated steps is necessary if the liability inherent in the future digita-system-based avionic and space systems is to be minimized. A suggested framework and timetable for the transformtion are presented. Basic working definitions of two pivotal ideas (validation and system life-cyle) are provided and show how the two concepts interact. Many examples are given of past and present validation activities by NASA and others. A conceptual framework is presented for the validation process. Finally, important areas are listed for ongoing development of the validation process at NASA Langley Research Center
Topological fault-tolerance in cluster state quantum computation
We describe a fault-tolerant version of the one-way quantum computer using a
cluster state in three spatial dimensions. Topologically protected quantum
gates are realized by choosing appropriate boundary conditions on the cluster.
We provide equivalence transformations for these boundary conditions that can
be used to simplify fault-tolerant circuits and to derive circuit identities in
a topological manner. The spatial dimensionality of the scheme can be reduced
to two by converting one spatial axis of the cluster into time. The error
threshold is 0.75% for each source in an error model with preparation, gate,
storage and measurement errors. The operational overhead is poly-logarithmic in
the circuit size.Comment: 20 pages, 12 figure
Numerical and analytical bounds on threshold error rates for hypergraph-product codes
We study analytically and numerically decoding properties of finite rate
hypergraph-product quantum LDPC codes obtained from random (3,4)-regular
Gallager codes, with a simple model of independent X and Z errors. Several
non-trival lower and upper bounds for the decodable region are constructed
analytically by analyzing the properties of the homological difference, equal
minus the logarithm of the maximum-likelihood decoding probability for a given
syndrome. Numerical results include an upper bound for the decodable region
from specific heat calculations in associated Ising models, and a minimum
weight decoding threshold of approximately 7%.Comment: 14 pages, 5 figure
On group theory for quantum gates and quantum coherence
Finite group extensions offer a natural language to quantum computing. In a
nutshell, one roughly describes the action of a quantum computer as consisting
of two finite groups of gates: error gates from the general Pauli group P and
stabilizing gates within an extension group C. In this paper one explores the
nice adequacy between group theoretical concepts such as commutators, normal
subgroups, group of automorphisms, short exact sequences, wreath products...
and the coherent quantum computational primitives. The structure of the single
qubit and two-qubit Clifford groups is analyzed in detail. As a byproduct, one
discovers that M20, the smallest perfect group for which the commutator
subgroup departs from the set of commutators, underlies quantum coherence of
the two-qubit system. One recovers similar results by looking at the
automorphisms of a complete set of mutually unbiased bases.Comment: 10 pages, to appear in J Phys A: Math and Theo (Fast Track
Communication
On a New Notion of Partial Refinement
Formal specification techniques allow expressing idealized specifications,
which abstract from restrictions that may arise in implementations. However,
partial implementations are universal in software development due to practical
limitations. Our goal is to contribute to a method of program refinement that
allows for partial implementations. For programs with a normal and an
exceptional exit, we propose a new notion of partial refinement which allows an
implementation to terminate exceptionally if the desired results cannot be
achieved, provided the initial state is maintained. Partial refinement leads to
a systematic method of developing programs with exception handling.Comment: In Proceedings Refine 2013, arXiv:1305.563
Symmetry and Topological Order
We prove sufficient conditions for Topological Quantum Order at both zero and
finite temperatures. The crux of the proof hinges on the existence of
low-dimensional Gauge-Like Symmetries (that notably extend and differ from
standard local gauge symmetries) and their associated defects, thus providing a
unifying framework based on a symmetry principle. These symmetries may be
actual invariances of the system, or may emerge in the low-energy sector.
Prominent examples of Topological Quantum Order display Gauge-Like Symmetries.
New systems exhibiting such symmetries include Hamiltonians depicting
orbital-dependent spin exchange and Jahn-Teller effects in transition metal
orbital compounds, short-range frustrated Klein spin models, and p+ip
superconducting arrays. We analyze the physical consequences of Gauge-Like
Symmetries (including topological terms and charges), discuss associated
braiding, and show the insufficiency of the energy spectrum, topological
entanglement entropy, maximal string correlators, and fractionalization in
establishing Topological Quantum Order. General symmetry considerations
illustrate that not withstanding spectral gaps, thermal fluctuations may impose
restrictions on certain suggested quantum computing schemes and lead to
"thermal fragility". Our results allow us to go beyond standard topological
field theories and engineer systems with Topological Quantum Order.Comment: 10 pages, 2 figures. Minimal changes relative to published version-
most notably the above shortened title (which was too late to change upon
request in the galley proofs). An elaborate description of all of the results
in this article appeared in subsequent works, principally in
arXiv:cond-mat/0702377 which was published in the Annals of Physics 324, 977-
1057 (2009
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