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View all- Schlingemann D(2018)Cluster states, algorithms and graphsQuantum Information & Computation10.5555/2011827.20118314:4(287-324)Online publication date: 27-Dec-2018
Logical network implementation for cluster states and graph codes
Pages 431 - 449
Abstract
In a previous paper a straight forward construction method for quantum error correcting codes, based on graphs, has been presented. These graph codes are directly related to cluster states which have been introduced by Briegel and Raussendorf. We show that the preparation of a cluster state as well as the coding operation for a graph code, can be implemented by a logical network by only using one type of two-qubit gate, e.g. CNOT or controlled Phase, and one type of one-qubit gate, e.g. the Hadamard transform. Concerning the qubit case each vertex corresponds to an Hadamard gate and each edge corresponds to a controlled not gate.
References
[1]
Schlingemann, D. and Werner R.F.: Quantum error-correcting codes associated with graphs. Phys. Rev. A, 65, 012308, (2001), quant-ph/0012111.
[2]
Cleve R. and Gottesman, D.: Efficient computations of encodings for quantum error correction. Phys. Rev. A, 56, 76-83, (1997), quant-ph/9607030.
[3]
Grassl, M.: Private communications. A table of circuits for cyclic and weakly self-dual codes can be found on the webpage: http://iaks-www.ira.uka.de/home/grassl/QECC/ Grassl, M. and Beth, T.: Cyclic quantum error-correcting codes quant-ph/9910061.
[4]
Briegel, H.J. and Raussendorf, R.: Quantum computing via measurements only, quant-ph/0010033.
[5]
Briegel, H.J. and Raussendorf, R.: A one-way quantum computer. Phys. Rev. Lett. 86, 5188 (2001).
[6]
Briegel, H.J. and Raussendorf, R.: Persistent entanglement in arrays of interacting particles. Phys. Rev. Lett. 86, 910 (2001).
[7]
Schlingemann, D.: Stabilizer codes can be realized as graph codes, Quant. Inf. Comp. 2, No 4, 307-323, (2002).
- Logical network implementation for cluster states and graph codes
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Rinton Press, Incorporated
Paramus, NJ
Publication History
Published: 01 September 2003
Revised: 02 June 2003
Received: 15 April 2002
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View all- Schlingemann D(2018)Cluster states, algorithms and graphsQuantum Information & Computation10.5555/2011827.20118314:4(287-324)Online publication date: 27-Dec-2018