Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Quantum Information and Computation

Cluster states, algorithms and graphs

SchlingemannDirk

Published Jul 1, 2004• 0 citations
Publisher

Abstract

The present paper is concerned with the concept of the one-way quantum computer,beyond binary-systems, and its relation to the concept of stabilizer quantum codes.This relation is exploited to anal...
DOI
10.5555/2011827.2011831

Related papers

Cluster states, algorithms and graphs

Dirk-M. Schlingemann

The present paper is concerned with the concept of the one-way quantum computer, beyond binary-systems, and its relation to the concept of stabilizer quantum codes. This relation is exploited to analyze a particular class of quantum algorithms, called graph algorithms, which correspond in the binary case to the Clifford group part of a network and which can efficiently be implemented on a one-way quantum computer. These algorithms can ``completely be solved" in the sense that the manipulation of quantum states in each step can be computed explicitly. Graph algorithms are precisely those which implement encoding schemes for graph codes. Starting from a given initial graph, which represents the underlying resource of multipartite entanglement, each step of the algorithm is related to a explicit transformation on the graph.

arXiv:quant-ph/0305170•Quantum Information and Computation•Jul 1, 2004•34 citations

Quantum error correcting codes and one-way quantum computing: Towards a quantum memory

Dirk Schlingemann

For realizing a quantum memory we suggest to first encode quantum information via a quantum error correcting code and then concatenate combined decoding and re-encoding operations. This requires that the encoding and the decoding operation can be performed faster than the typical decoherence time of the underlying system. The computational model underlying the one-way quantum computer, which has been introduced by Hans Briegel and Robert Raussendorf, provides a suitable concept for a fast implementation of quantum error correcting codes. It is shown explicitly in this article is how encoding and decoding operations for stabilizer codes can be realized on a one-way quantum computer. This is based on the graph code representation for stabilizer codes, on the one hand, and the relation between cluster states and graph codes, on the other hand.

arXiv:quant-ph/0308022•Aug 4, 2003•2 citations

A One-Way Quantum Computer

Robert Raussendorf, Hans J. Briegel

We present a scheme of quantum computation that consists entirely of one-qubit measurements on a particular class of entangled states, the cluster states. The measurements are used to imprint a quantum logic circuit on the state, thereby destroying its entanglement at the same time. Cluster states are thus one-way quantum computers and the measurements form the program.

Physical Review Letters•May 28, 2001•4,478 citations

Stabilizer codes can be realized as graph codes

SchlingemannD.

We establish the connection between a recent new construction technique for quantum error correcting codes, based on graphs, and the so-called stabilizer codes: Each stabilizer code can be realized...

Quantum Information and Computation•Jun 1, 2002•2 citations

Error syndrome calculation for graph codes on a one-way quantum computer: Towards a quantum memory

Dirk-M. Schlingemann

For realizing a quantum memory the encoded quantum information can be protected against decoherence via repeated decoding and re-encoding operations. This requires us to perform fast encoding and decoding operations. The computational model underlying the one-way quantum computer provides a suitable concept for a fast implementation, which has been solved in a previous article for the encoding operation. In the present paper we show that the missing part, the decoding operation, can also be realized on a one-way quantum computer. This is based on the graph code representation for stabilizer codes, on the one hand, and the relation between cluster states and graph codes, on the other hand.

Journal of Mathematical Physics•Oct 23, 2004•5 citations

Stabilizer codes can be realized as graph codes

Dirk-M. Schlingemann

We establish the connection between a recent new construction technique for quantum error correcting codes, based on graphs, and the so-called stabilizer codes: Each stabilizer code can be realized as a graph code and vice versa.

arXiv:quant-ph/0111080•Quantum Information and Computation•Jun 1, 2002•136 citations
The present paper is concerned with the concept of the one-way quantum computer, beyond binary-systems, and its relation to the concept of stabilizer quantum codes. This relation is exploited to analyze a particular class of quantum algorithms, called graph algorithms, which correspond in the binary case to the Clifford group part of a network and which can efficiently be implemented on a one-way quantum computer. These algorithms can ``completely be solved" in the sense that the manipulation of quantum states in each step can be computed explicitly. Graph algorithms are precisely those which implement encoding schemes for graph codes. Starting from a given initial graph, which represents the underlying resource of multipartite entanglement, each step of the algorithm is related to a explicit transformation on the graph.
For realizing a quantum memory we suggest to first encode quantum information via a quantum error correcting code and then concatenate combined decoding and re-encoding operations. This requires that the encoding and the decoding operation can be performed faster than the typical decoherence time of the underlying system. The computational model underlying the one-way quantum computer, which has been introduced by Hans Briegel and Robert Raussendorf, provides a suitable concept for a fast implementation of quantum error correcting codes. It is shown explicitly in this article is how encoding and decoding operations for stabilizer codes can be realized on a one-way quantum computer. This is based on the graph code representation for stabilizer codes, on the one hand, and the relation between cluster states and graph codes, on the other hand.
For realizing a quantum memory the encoded quantum information can be protected against decoherence via repeated decoding and re-encoding operations. This requires us to perform fast encoding and decoding operations. The computational model underlying the one-way quantum computer provides a suitable concept for a fast implementation, which has been solved in a previous article for the encoding operation. In the present paper we show that the missing part, the decoding operation, can also be realized on a one-way quantum computer. This is based on the graph code representation for stabilizer codes, on the one hand, and the relation between cluster states and graph codes, on the other hand.