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Title:

Züchtung großer Galliumphosphat-Einkristalle aus phosphorsäurereicher Lösung unter hydrothermalen Bedingungen

Publisher:

Ludwig-Maximilians-Universität München

Year of Publication:

2003-04-23

Document Type:

Dissertation ; NonPeerReviewed

Subjects:

Fakultät für Geowissenschaften

Fakultät für Geowissenschaften Minimize

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http://edoc.ub.uni-muenchen.de/1158/

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Title:

Leveraging Automorphisms of Quantum Codes for Fault-Tolerant Quantum Computation

Description:

Fault-tolerant quantum computation is a technique that is necessary to build a scalable quantum computer from noisy physical building blocks. Key for the implementation of fault-tolerant 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 ...

Fault-tolerant quantum computation is a technique that is necessary to build a scalable quantum computer from noisy physical building blocks. Key for the implementation of fault-tolerant 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 fault-tolerantly 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 fault-tolerant 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 fault-tolerant 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]]. Minimize

Year of Publication:

2013-02-05

Document Type:

text

Subjects:

Quantum Physics ; Computer Science - Information Theory

Quantum Physics ; Computer Science - Information Theory Minimize

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Title:

Quantum Block and Convolutional Codes from Self-orthogonal Product Codes

Description:

We present a construction of self-orthogonal codes using product codes. From the resulting codes, one can construct both block quantum error-correcting codes and quantum convolutional codes. We show that from the examples of convolutional codes found, we can derive ordinary quantum error-correcting codes using tail-biting with parameters [[42N,2...

We present a construction of self-orthogonal codes using product codes. From the resulting codes, one can construct both block quantum error-correcting codes and quantum convolutional codes. We show that from the examples of convolutional codes found, we can derive ordinary quantum error-correcting codes using tail-biting 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 Minimize

Year of Publication:

2007-03-19

Document Type:

text

Subjects:

Quantum Physics ; Computer Science - Information Theory

Quantum Physics ; Computer Science - Information Theory Minimize

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Title:

Constructions of Quantum Convolutional Codes

Description:

We address the problems of constructing quantum convolutional codes (QCCs) and of encoding them. The first construction is a CSS-type 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 CSS-type 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 Minimize

Year of Publication:

2007-03-19

Document Type:

text

Subjects:

Quantum Physics ; Computer Science - Information Theory

Quantum Physics ; Computer Science - Information Theory Minimize

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Title:

Non-catastrophic Encoders and Encoder Inverses for Quantum Convolutional Codes

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 non-catastrophic encoding circuit. Our work generalizes the conditions for non-catastrophic 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 non-catastrophic encoding circuit. Our work generalizes the conditions for non-catastrophic encoders derived in a paper by Ollivier and Tillich (quant-ph/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 Minimize

Year of Publication:

2006-02-15

Document Type:

text

Subjects:

Quantum Physics ; Computer Science - Information Theory

Quantum Physics ; Computer Science - Information Theory Minimize

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Title:

Quantum MDS Codes over Small Fields

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 Minimize

Year of Publication:

2015-02-18

Document Type:

text

Subjects:

Quantum Physics ; Computer Science - Information Theory

Quantum Physics ; Computer Science - Information Theory Minimize

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Title:

Non-Additive Quantum Codes from Goethals and Preparata Codes

Description:

We extend the stabilizer formalism to a class of non-additive quantum codes which are constructed from non-linear classical codes. As an example, we present infinite families of non-additive 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 non-additive quantum codes which are constructed from non-linear classical codes. As an example, we present infinite families of non-additive codes which are derived from Goethals and Preparata codes. ; Comment: submitted to the 2008 IEEE Information Theory Workshop (ITW 2008) Minimize

Year of Publication:

2008-01-14

Document Type:

text

Subjects:

Quantum Physics ; Computer Science - Information Theory

Quantum Physics ; Computer Science - Information Theory Minimize

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Title:

Quantum Goethals-Preparata Codes

Description:

We present a family of non-additive quantum codes based on Goethals and Preparata codes with parameters ((2^m,2^{2^m-5m+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 non-additive quantum codes based on Goethals and Preparata codes with parameters ((2^m,2^{2^m-5m+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 Minimize

Year of Publication:

2008-01-14

Document Type:

text

Subjects:

Quantum Physics ; Computer Science - Information Theory

Quantum Physics ; Computer Science - Information Theory Minimize

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Title:

Computing Local Invariants of Qubit Systems

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Description:

We investigate means to describe the non-local properties of quantum systems and to test if two quantum systems are locally equivalent. For this we consider quantum systems that consist of several subsystems, especially multiple qubits. We compute invariant polynomials, i. e., polynomial functions of the entries of the density operator which are...

We investigate means to describe the non-local properties of quantum systems and to test if two quantum systems are locally equivalent. For this we consider quantum systems that consist of several subsystems, especially multiple qubits. We compute invariant polynomials, i. e., polynomial functions of the entries of the density operator which are invariant under local unitary operations. As an example, we consider a system of two qubits. We compute the Molien series for the corresponding representation which gives information about the number of linearly independent invariants. Furthermore, we present a set of polynomials which generate all invariants (at least) up to degree 23. Finally, the use of invariants to check whether two density operators are locally equivalent is demonstrated. ; Comment: 8 pages, RevTeX, submitted to PRA; example added to demonstrate the application of the invariants Minimize

Year of Publication:

1997-12-18

Document Type:

text

Subjects:

Quantum Physics

Quantum Physics Minimize

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Title:

Graphs, Quadratic Forms, and Quantum Codes

Author:

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 Minimize

Year of Publication:

2007-03-13

Document Type:

text

Subjects:

Quantum Physics ; Computer Science - Information Theory

Quantum Physics ; Computer Science - Information Theory Minimize

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