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Search: Martin Grassl
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1.
Züchtung großer GalliumphosphatEinkristalle aus phosphorsäurereicher Lösung unter hydrothermalen Bedingungen
Title:
Züchtung großer GalliumphosphatEinkristalle aus phosphorsäurereicher Lösung unter hydrothermalen Bedingungen
Author:
Grassl, Martin
Grassl, Martin
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Publisher:
LudwigMaximiliansUniversität München
Year of Publication:
20030423
Document Type:
Dissertation ; NonPeerReviewed
Subjects:
Fakultät für Geowissenschaften
Fakultät für Geowissenschaften
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Relations:
http://edoc.ub.unimuenchen.de/1158/
URL:
http://edoc.ub.unimuenchen.de/1158/1/Grassl_Martin.pdf
http://nbnresolving.de/urn:nbn:de:bvb:1911585
http://edoc.ub.unimuenchen.de/1158/1/Grassl_Martin.pdf
http://nbnresolving.de/urn:nbn:de:bvb:1911585
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University of Munich: Digital theses
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2.
NonAdditive Quantum Codes from Goethals and Preparata Codes
Open Access
Title:
NonAdditive Quantum Codes from Goethals and Preparata Codes
Author:
Grassl, Markus
;
Roetteler, Martin
Grassl, Markus
;
Roetteler, Martin
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Description:
We extend the stabilizer formalism to a class of nonadditive quantum codes which are constructed from nonlinear classical codes. As an example, we present infinite families of nonadditive codes which are derived from Goethals and Preparata codes. ; Comment: submitted to the 2008 IEEE Information Theory Workshop (ITW 2008)
We extend the stabilizer formalism to a class of nonadditive quantum codes which are constructed from nonlinear classical codes. As an example, we present infinite families of nonadditive codes which are derived from Goethals and Preparata codes. ; Comment: submitted to the 2008 IEEE Information Theory Workshop (ITW 2008)
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Year of Publication:
20080114
Document Type:
text
Subjects:
Quantum Physics ; Computer Science  Information Theory
Quantum Physics ; Computer Science  Information Theory
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URL:
http://arxiv.org/abs/0801.2144
http://arxiv.org/abs/0801.2144
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ArXiv.org (Cornell University Library)
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3.
Quantum GoethalsPreparata Codes
Open Access
Title:
Quantum GoethalsPreparata Codes
Author:
Grassl, Markus
;
Roetteler, Martin
Grassl, Markus
;
Roetteler, Martin
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Description:
We present a family of nonadditive quantum codes based on Goethals and Preparata codes with parameters ((2^m,2^{2^m5m+1},8)). The dimension of these codes is eight times higher than the dimension of the best known additive quantum codes of equal length and minimum distance. ; Comment: Submitted to the 2008 IEEE International Symposium on Infor...
We present a family of nonadditive quantum codes based on Goethals and Preparata codes with parameters ((2^m,2^{2^m5m+1},8)). The dimension of these codes is eight times higher than the dimension of the best known additive quantum codes of equal length and minimum distance. ; Comment: Submitted to the 2008 IEEE International Symposium on Information Theory
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Year of Publication:
20080114
Document Type:
text
Subjects:
Quantum Physics ; Computer Science  Information Theory
Quantum Physics ; Computer Science  Information Theory
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URL:
http://arxiv.org/abs/0801.2150
http://arxiv.org/abs/0801.2150
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ArXiv.org (Cornell University Library)
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4.
Quantum Block and Convolutional Codes from Selforthogonal Product Codes
Open Access
Title:
Quantum Block and Convolutional Codes from Selforthogonal Product Codes
Author:
Grassl, Markus
;
Roetteler, Martin
Grassl, Markus
;
Roetteler, Martin
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Description:
We present a construction of selforthogonal codes using product codes. From the resulting codes, one can construct both block quantum errorcorrecting codes and quantum convolutional codes. We show that from the examples of convolutional codes found, we can derive ordinary quantum errorcorrecting codes using tailbiting with parameters [[42N,2...
We present a construction of selforthogonal codes using product codes. From the resulting codes, one can construct both block quantum errorcorrecting codes and quantum convolutional codes. We show that from the examples of convolutional codes found, we can derive ordinary quantum errorcorrecting codes using tailbiting with parameters [[42N,24N,3]]_2. While it is known that the product construction cannot improve the rate in the classical case, we show that this can happen for quantum codes: we show that a code [[15,7,3]]_2 is obtained by the product of a code [[5,1,3]]_2 with a suitable code. ; Comment: 5 pages, paper presented at the 2005 IEEE International Symposium on Information Theory
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Year of Publication:
20070319
Document Type:
text
Subjects:
Quantum Physics ; Computer Science  Information Theory
Quantum Physics ; Computer Science  Information Theory
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URL:
http://arxiv.org/abs/quantph/0703181
http://arxiv.org/abs/quantph/0703181
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ArXiv.org (Cornell University Library)
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5.
Constructions of Quantum Convolutional Codes
Open Access
Title:
Constructions of Quantum Convolutional Codes
Author:
Grassl, Markus
;
Roetteler, Martin
Grassl, Markus
;
Roetteler, Martin
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Description:
We address the problems of constructing quantum convolutional codes (QCCs) and of encoding them. The first construction is a CSStype construction which allows us to find QCCs of rate 2/4. The second construction yields a quantum convolutional code by applying a product code construction to an arbitrary classical convolutional code and an arbitr...
We address the problems of constructing quantum convolutional codes (QCCs) and of encoding them. The first construction is a CSStype construction which allows us to find QCCs of rate 2/4. The second construction yields a quantum convolutional code by applying a product code construction to an arbitrary classical convolutional code and an arbitrary quantum block code. We show that the resulting codes have highly structured and efficient encoders. Furthermore, we show that the resulting quantum circuits have finite depth, independent of the lengths of the input stream, and show that this depth is polynomial in the degree and frame size of the code. ; Comment: 5 pages, to appear in the Proceedings of the 2007 IEEE International Symposium on Information Theory
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Year of Publication:
20070319
Document Type:
text
Subjects:
Quantum Physics ; Computer Science  Information Theory
Quantum Physics ; Computer Science  Information Theory
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URL:
http://arxiv.org/abs/quantph/0703182
http://arxiv.org/abs/quantph/0703182
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ArXiv.org (Cornell University Library)
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6.
Leveraging Automorphisms of Quantum Codes for FaultTolerant Quantum Computation
Open Access
Title:
Leveraging Automorphisms of Quantum Codes for FaultTolerant Quantum Computation
Author:
Grassl, Markus
;
Roetteler, Martin
Grassl, Markus
;
Roetteler, Martin
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Description:
Faulttolerant quantum computation is a technique that is necessary to build a scalable quantum computer from noisy physical building blocks. Key for the implementation of faulttolerant computations is the ability to perform a universal set of quantum gates that act on the code space of an underlying quantum code. To implement such a universal ...
Faulttolerant quantum computation is a technique that is necessary to build a scalable quantum computer from noisy physical building blocks. Key for the implementation of faulttolerant computations is the ability to perform a universal set of quantum gates that act on the code space of an underlying quantum code. To implement such a universal gate set faulttolerantly is an expensive task in terms of physical operations, and any possible shortcut to save operations is potentially beneficial and might lead to a reduction in overhead for faulttolerant computations. We show how the automorphism group of a quantum code can be used to implement some operators on the encoded quantum states in a faulttolerant way by merely permuting the physical qubits. We derive conditions that a code has to satisfy in order to have a large group of operations that can be implemented transversally when combining transversal CNOT with automorphisms. We give several examples for quantum codes with large groups, including codes with parameters [[8,3,3]], [[15,7,3]], [[22,8,4]], and [[31,11,5]].
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Year of Publication:
20130205
Document Type:
text
Subjects:
Quantum Physics ; Computer Science  Information Theory
Quantum Physics ; Computer Science  Information Theory
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URL:
http://arxiv.org/abs/1302.1035
http://arxiv.org/abs/1302.1035
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ArXiv.org (Cornell University Library)
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7.
Noncatastrophic Encoders and Encoder Inverses for Quantum Convolutional Codes
Open Access
Title:
Noncatastrophic Encoders and Encoder Inverses for Quantum Convolutional Codes
Author:
Grassl, Markus
;
Roetteler, Martin
Grassl, Markus
;
Roetteler, Martin
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Description:
We present an algorithm to construct quantum circuits for encoding and inverse encoding of quantum convolutional codes. We show that any quantum convolutional code contains a subcode of finite index which has a noncatastrophic encoding circuit. Our work generalizes the conditions for noncatastrophic encoders derived in a paper by Ollivier and ...
We present an algorithm to construct quantum circuits for encoding and inverse encoding of quantum convolutional codes. We show that any quantum convolutional code contains a subcode of finite index which has a noncatastrophic encoding circuit. Our work generalizes the conditions for noncatastrophic encoders derived in a paper by Ollivier and Tillich (quantph/0401134) which are applicable only for a restricted class of quantum convolutional codes. We also show that the encoders and their inverses constructed by our method naturally can be applied online, i.e., qubits can be sent and received with constant delay. ; Comment: 6 pages, 1 figure, submitted to 2006 IEEE International Symposium on Information Theory
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Year of Publication:
20060215
Document Type:
text
Subjects:
Quantum Physics ; Computer Science  Information Theory
Quantum Physics ; Computer Science  Information Theory
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URL:
http://arxiv.org/abs/quantph/0602129
http://arxiv.org/abs/quantph/0602129
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ArXiv.org (Cornell University Library)
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8.
Quantum MDS Codes over Small Fields
Open Access
Title:
Quantum MDS Codes over Small Fields
Author:
Grassl, Markus
;
Roetteler, Martin
Grassl, Markus
;
Roetteler, Martin
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Description:
We consider quantum MDS (QMDS) codes for quantum systems of dimension $q$ with lengths up to $q^2+2$ and minimum distances up to $q+1$. We show how starting from QMDS codes of length $q^2+1$ based on cyclic and constacyclic codes, new QMDS codes can be obtained by shortening. We provide numerical evidence for our conjecture that almost all admis...
We consider quantum MDS (QMDS) codes for quantum systems of dimension $q$ with lengths up to $q^2+2$ and minimum distances up to $q+1$. We show how starting from QMDS codes of length $q^2+1$ based on cyclic and constacyclic codes, new QMDS codes can be obtained by shortening. We provide numerical evidence for our conjecture that almost all admissible lengths, from a lower bound $n_0(q,d)$ on, are achievable by shortening. Some additional codes that fill gaps in the list of achievable lengths are presented as well along with a construction of a family of QMDS codes of length $q^2+2$, where $q=2^m$, that appears to be new. ; Comment: 6 pages, 3 figures
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Year of Publication:
20150218
Document Type:
text
Subjects:
Quantum Physics ; Computer Science  Information Theory
Quantum Physics ; Computer Science  Information Theory
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URL:
http://arxiv.org/abs/1502.05267
http://arxiv.org/abs/1502.05267
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ArXiv.org (Cornell University Library)
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9.
On optimal quantum codes
Open Access
Title:
On optimal quantum codes
Author:
Grassl, Markus
;
Beth, Thomas
;
Roetteler, Martin
Grassl, Markus
;
Beth, Thomas
;
Roetteler, Martin
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Description:
We present families of quantum errorcorrecting codes which are optimal in the sense that the minimum distance is maximal. These maximum distance separable (MDS) codes are defined over qdimensional quantum systems, where q is an arbitrary prime power. It is shown that codes with parameters [[n,n2d+2,d]]_q exist for all 3 <= n <= q and 1 <= d <...
We present families of quantum errorcorrecting codes which are optimal in the sense that the minimum distance is maximal. These maximum distance separable (MDS) codes are defined over qdimensional quantum systems, where q is an arbitrary prime power. It is shown that codes with parameters [[n,n2d+2,d]]_q exist for all 3 <= n <= q and 1 <= d <= n/2+1. We also present quantum MDS codes with parameters [[q^2,q^22d+2,d]]_q for 1 <= d <= q which additionally give rise to shortened codes [[q^2s,q^22d+2s,d]]_q for some s. ; Comment: Accepted for publication in the International Journal of Quantum Information
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Year of Publication:
20031219
Document Type:
text
Subjects:
Quantum Physics
Quantum Physics
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URL:
http://arxiv.org/abs/quantph/0312164
http://arxiv.org/abs/quantph/0312164
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ArXiv.org (Cornell University Library)
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10.
Graphs, Quadratic Forms, and Quantum Codes
Open Access
Title:
Graphs, Quadratic Forms, and Quantum Codes
Author:
Grassl, Markus
;
Klappenecker, Andreas
;
Roetteler, Martin
Grassl, Markus
;
Klappenecker, Andreas
;
Roetteler, Martin
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Description:
We show that any stabilizer code over a finite field is equivalent to a graphical quantum code. Furthermore we prove that a graphical quantum code over a finite field is a stabilizer code. The technique used in the proof establishes a new connection between quantum codes and quadratic forms. We provide some simple examples to illustrate our resu...
We show that any stabilizer code over a finite field is equivalent to a graphical quantum code. Furthermore we prove that a graphical quantum code over a finite field is a stabilizer code. The technique used in the proof establishes a new connection between quantum codes and quadratic forms. We provide some simple examples to illustrate our results. ; Comment: 5 pages, 2 figures, paper presented at the 2002 IEEE International Symposium on Information Theory
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Year of Publication:
20070313
Document Type:
text
Subjects:
Quantum Physics ; Computer Science  Information Theory
Quantum Physics ; Computer Science  Information Theory
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URL:
http://arxiv.org/abs/quantph/0703112
http://arxiv.org/abs/quantph/0703112
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(12) Grassl, Markus
(12) Roetteler, Martin
(12) The Pennsylvania State University CiteSeerX...
(11) Markus Grassl
(10) Martin Rötteler
(3) Beth, Thomas
(3) Brand, Stephan
(3) Dambacher, Julia
(3) Folwaczny, Christian
(3) Folwaczny, Matthias
(3) Glas, Jürgen
(3) Grassl, Christine
(3) Griga, Thomas
(3) Göke, Burkhard
(3) Klein, Wolfram
(3) Konrad, Astrid
(3) Lohse, Peter
(3) Maier, Kerstin
(3) Mussack, Thomas
(3) MüllerMyhsok, Bertram
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(3) Schmechel, Silke
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(3) Török, HelgaPaula
(3) Wetzke, Martin
(2) Andreas Klappenecker
(2) Epplen, Jörg T.
(2) Klappenecker, Andreas
(2) Pradeep Kiran Sarvepalli
(2) Salah A. Aly
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(1) Aly, Salah A.
(1) Astrid Konrad
(1) Bertram Müllermyhsok
(1) Burkhard Göke
(1) Christian Folwaczny
(1) Christine Grassl
(1) Communicated Jozef Gruska
(1) Epplen, Jörg T
(1) Grassl, Martin
(1) Grassl, Peter
(1) Graßl, Hartmut
(1) Graßl, Martin Bernhard Anton
(1) Held, Martin
(1) Helgapaula Török
(1) Horák, Martin
(1) Jirásek, Milan
(1) Julia Dambacher
(1) Julia Seiderer
(1) Jürgen Glas
(1) Kerstin Maier
(1) Klinikum Veterinärmedizin, Klinik für...
(1) Laurian Tonenchi
(1) Let K
(1) Luhmann, HansJochen
(1) Martin R Ötteler
(1) Martin Wetzke
(1) Matthias Folwaczny
(1) Peter Lohse
(1) Sarvepalli, Pradeep Kiran
(1) Schiemann, Uwe Kurt
(1) Schindler, Jörg
(1) Schneider, Manuel
(1) Silke Schmechel
(1) Simone Pfennig
(1) Stephan Br
(1) Thomas Beth
(1) Thomas Griga
(1) Thomas Mussack
(1) Thomas Ochsenkühn
(1) Uwe Schiemann
(1) Wolfram Klein
(1) Xenos, Dimitrios
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(12) quantum physics
(9) computer science information theory
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(1) i graphical quantum codes
(1) medizin
(1) quantum circuits
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(1) research article
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(1) Agriculture [63*]
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