30,209 research outputs found
Codeword Stabilized Quantum Codes
We present a unifying approach to quantum error correcting code design that
encompasses additive (stabilizer) codes, as well as all known examples of
nonadditive codes with good parameters. We use this framework to generate new
codes with superior parameters to any previously known. In particular, we find
((10,18,3)) and ((10,20,3)) codes. We also show how to construct encoding
circuits for all codes within our framework.Comment: 5 pages, 1 eps figure, ((11,48,3)) code removed, encoding circuits
added, typos corrected in codewords and elsewher
Quantum Computing: Pro and Con
I assess the potential of quantum computation. Broad and important
applications must be found to justify construction of a quantum computer; I
review some of the known quantum algorithms and consider the prospects for
finding new ones. Quantum computers are notoriously susceptible to making
errors; I discuss recently developed fault-tolerant procedures that enable a
quantum computer with noisy gates to perform reliably. Quantum computing
hardware is still in its infancy; I comment on the specifications that should
be met by future hardware. Over the past few years, work on quantum computation
has erected a new classification of computational complexity, has generated
profound insights into the nature of decoherence, and has stimulated the
formulation of new techniques in high-precision experimental physics. A broad
interdisciplinary effort will be needed if quantum computers are to fulfill
their destiny as the world's fastest computing devices. (This paper is an
expanded version of remarks that were prepared for a panel discussion at the
ITP Conference on Quantum Coherence and Decoherence, 17 December 1996.)Comment: 17 pages, LaTeX, submitted to Proc. Roy. Soc. Lond. A, minor
correction
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
Quantum computing and the entanglement frontier - Rapporteur talk at the 25th Solvay Conference
Quantum information science explores the frontier of highly complex quantum states,
the "entanglement frontier". This study is motivated by the observation (widely believed
but unproven) that classical systems cannot simulate highly entangled quantum systems
efficiently, and we hope to hasten the day when well controlled quantum systems can
perform tasks surpassing what can be done in the classical world. One way to achieve
such "quantum supremacy" would be to run an algorithm on a quantum computer which
solves a problem with a super-polynomial speedup relative to classical computers, but
there may be other ways that can be achieved sooner, such as simulating exotic quantum
states of strongly correlated matter. To operate a large scale quantum computer reliably
we will need to overcome the debilitating effects of decoherence, which might be done
using "standard" quantum hardware protected by quantum error-correcting codes, or by
exploiting the nonabelian quantum statistics of anyons realized in solid state systems,
or by combining both methods. Only by challenging the entanglement frontier will we
learn whether Nature provides extravagant resources far beyond what the classical world
would allow
EVENODD: An Efficient Scheme for Tolerating Double Disk Failures in RAID Architectures
We present a novel method, that we call EVENODD, for tolerating up to two disk failures in RAID architectures. EVENODD employs the addition of only two redundant disks and consists of simple exclusive-OR computations. This redundant storage is optimal, in the sense that two failed disks cannot be retrieved with less than two redundant disks. A major advantage of EVENODD is that it only requires parity hardware, which is typically present in standard RAID-5 controllers. Hence, EVENODD can be implemented on standard RAID-5 controllers without any hardware changes. The most commonly used scheme that employes optimal redundant storage (i.e., two extra disks) is based on Reed-Solomon (RS) error-correcting codes. This scheme requires computation over finite fields and results in a more complex implementation. For example, we show that the complexity of implementing EVENODD in a disk array with 15 disks is about 50% of the one required when using the RS scheme. The new scheme is not limited to RAID architectures: it can be used in any system requiring large symbols and relatively short codes, for instance, in multitrack magnetic recording. To this end, we also present a decoding algorithm for one column (track) in error
Unordered Error-Correcting Codes and their Applications
We give efficient constructions for error correcting
unordered {ECU) codes, i.e., codes such that any
pair of codewords are at a certain minimal distance
apart and at the same time they are unordered. These
codes are used for detecting a predetermined number
of (symmetric) errors and for detecting all unidirectional
errors. We also give an application in parallel
asynchronous communications
Some new EC/AUED codes
A novel construction that differs from the traditional way of constructing systematic EC/AUED/(error-correcting/all unidirectional error-detecting) codes is presented. The usual method is to take a systematic t-error-correcting code and then append a tail so that the code can detect more than t errors when they are unidirectional. In the authors' construction, the t-error-correcting code is modified in such a way that the weight distribution of the original code is reduced. The authors then have to add a smaller tail. Frequently they have less redundancy than the best available systematic t-EC/AUED codes
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