Quantum error-correcting codes associated with graphs
Open accessAbstract
We present a construction for quantum error correcting codes. The basic ingredients are a graph and a finite Abelian group, from which the code can explicitly be obtained. We prove necessary and sufficient conditions for the graph such that the resulting code corrects a certain number of errors. This allows a simple verification of the one-error correcting property of codes of length 5 in any dimension. As examples, we construct a large class of maximum distance separable codes, i.e. codes saturating the Singleton bound, as well as a code of length 10 detecting three errors.
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The computational model that emerges for the QC_C makes no reference to the concept of unitary evolution.
“However, the computational model that emerges for the QC C [7] makes no reference to the concept of unitary evolution”
From Measurement-based quantum computation on cluster states (2003) · cites this paper as [7]
In [7] it has been shown that the required classical processing increases the computation time only marginally (logarithmically in the number n of logical qubits) and thus there is no exponential overhead in either classical or quantum resources.
“In [7] it has been shown, as stated in Section III A, that the required classical processing increases the computation time only marginally (logarithmically in the number n of logical qubits) and thus there is no exponential overhead in either classical or quantum resources.”
From Measurement-based quantum computation on cluster states (2003) · cites this paper as [7]
Instead of describing a quantum algorithm as a network of gates applied to a fiducial input state, a quantum algorithm may be characterized by a graph specifying the quantum resource and the structure for processing the measurement outcomes.
“In conclusion, instead of describing a quantum algorithm as a network of gates applied to some fiducial input state, a quantum algorithm may (arguably more effectively) be characterized by a graph specifying the quantum resource and the structure [7] for the processing of the measurement outcomes.”
From Measurement-based quantum computation on cluster states (2003) · cites this paper as [7]
The classical processing of measurement outcomes in a QC_C-computation increases the total time of computation only marginally.
“Concerning the resources for the classical processing of the measurement outcomes in a QC C -computation, we point out that this processing increases the total time of computation only marginally [7].”
From Measurement-based quantum computation on cluster states (2003) · cites this paper as [7]
As shown in [7], there is no difference in the way measurements of cluster qubits in I, O or M contribute to the final result of the computation.
“As shown in [7], it turns out that there is none.”
From Measurement-based quantum computation on cluster states (2003) · cites this paper as [7]
For an n-qubit network algorithm, the classical data that the QC_C has to keep track of is entirely contained in a 2n-component binary-valued information flow vector I(t).
“If the network algorithm runs on n qubits then the classical data that the QC C has to keep track of is entirely contained in a 2ncomponent binary valued vector, which we have called the information flow vector I(t) [7].”
From Measurement-based quantum computation on cluster states (2003) · cites this paper as [7]
The QC C has no quantum register.
“However, as we have explained in [7] and also briefly sketched in Section III A, the QC C has no quantum register.”
From Measurement-based quantum computation on cluster states (2003) · cites this paper as [7]
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Cites
A single quantum cannot be cloned
Wootters, W. K., & Zurek, W. H. (1982) · Nature · doi:10.1038/299802a0 · Cited by 5,406 · cited 1× · see citing works
“On the other hand, the no-cloning theorem [1] seemed to forbid at least the most naive approach to classical error correction for noisy channels, e.”
BackgroundMixed-state entanglement and quantum error correction
Bennett, C. H., DiVincenzo, D. P., Smolin, J. A., & Wootters, W. K. (1996) · Physical Review A · doi:10.1103/physreva.54.3824 · Cited by 5,272 · see citing works
Good quantum error-correcting codes exist
Calderbank, A. R., & Shor, P. W. (1996) · Physical Review A · doi:10.1103/physreva.54.1098 · Cited by 2,516 · see citing works
Quantum error correction via codes over GF(4)
Calderbank, A. R., Rains, E. M., Shor, P. W., & Sloane, N. J. A. (1998) · IEEE Transactions on Information Theory · doi:10.1109/18.681315 · Cited by 1,735 · see citing works
Theory of quantum error-correcting codes
Knill, E., & Laflamme, R. (1997) · Physical Review A · doi:10.1103/physreva.55.900 · Cited by 1,593 · see citing works
Class of quantum error-correcting codes saturating the quantum Hamming bound
Gottesman, D. (1996) · Physical Review A · doi:10.1103/physreva.54.1862 · Cited by 1,227 · cited 1× · see citing works
“There are various efficient methods for constructing stabilizer codes [3,4,12–16].”
MethodJacobson, N. S. (1964) · Graduate texts in mathematics · doi:10.1007/978-1-4612-9872-4 · Cited by 1,051 · see citing works
Perfect Quantum Error Correcting Code
Laflamme, R., Miquel, C., Paz, J. P., & Zurek, W. H. (1996) · Physical Review Letters · doi:10.1103/physrevlett.77.198 · Cited by 966 · see citing works
Quantum Error Correction and Orthogonal Geometry
Calderbank, A. R., Rains, E. M., Shor, P. W., & Sloane, N. J. A. (1997) · Physical Review Letters · doi:10.1103/physrevlett.78.405 · Cited by 811 · see citing works
Stabilizer Codes and Quantum Error Correction
Gottesman, D. (1997) · arXiv · doi:10.48550/arxiv.quant-ph/9705052 · Cited by 753 · see citing works
Nonbinary quantum stabilizer codes
Ashikhmin, A., & Knill, E. H. (2001) · IEEE Transactions on Information Theory · doi:10.1109/18.959288 · Cited by 614 · see citing works
Non-binary unitary error bases and quantum codes
Lab., N. (. S. L. A. N., Knill, E., & USDOE, W. (1996) · doi:10.2172/373768 · Cited by 138 · see citing works
Polynomial invariants of quantum codes
Rains, E. M. (2000) · IEEE Transactions on Information Theory · doi:10.1109/18.817508 · Cited by 95 · see citing works
Quantum codes of minimum distance two
Rains, E. M. (1999) · IEEE Transactions on Information Theory · doi:10.1109/18.746807 · Cited by 78 · see citing works
Quantum Reed-Solomon CodesPreprint
Grassl, M., Geiselmann, W., Beth, T., & Karlsruhe, U. (1999) · Cited by 75 · see citing works
Cyclic Quantum Error-Correcting Codes and Quantum Shift RegistersPreprint
Grassl, M., & Beth, T. (1999) · Cited by 36 · see citing works
Matsumoto, R., & Uyematsu, T. (2000) · Institutional Repositories DataBase (IRDB) · Cited by 31 · see citing works
A Note on Non-Additive Quantum CodesPreprint
Grassl, M., & Beth, T. (1997) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/9703016 · Cited by 17 · see citing works
Polynomial invariants of quantum codesPreprint
Rains, E. M. (1997) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/9704042 · Cited by 12 · see citing works
Nonbinary Quantum Stabilizer CodesPreprint
Ashikhmin, A., & Knill, E. H. (2000) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/0005008 · Cited by 3 · see citing works
Pauli exchange and quantum error correction
Ruskai, M. B. (2002) · Contemporary mathematics - American Mathematical Society · doi:10.1090/conm/305/05224 · Cited by 1 · see citing works
Flagged first, then by citations
Research works printed but not linked: 1
- [14]Grassl, M. and Beth, T.: Quantum BCH codes Proceedings X. International Symposium on Theoretical Electrical Engineering, Magdeburg 1999
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<i>Colloquium</i> : Area laws for the entanglement entropy
Eisert, J., Cramer, M., & Plenio, M. B. (2010) · Reviews of Modern Physics · doi:10.1103/revmodphys.82.277 · Cited by 2,873 · see citing works
Measurement-based quantum computation on cluster states
Raussendorf, R., Browne, D. E., & Briegel, H. J. (2003) · Physical Review A · doi:10.1103/physreva.68.022312 · Cited by 1,655 · see citing works
Multiparty entanglement in graph states
Hein, M., Eisert, J., & Briegel, H. J. (2004) · Physical Review A · doi:10.1103/physreva.69.062311 · Cited by 1,035 · see citing works
Experimental entanglement of six photons in graph states
Lu, C.-Y., Zhou, X.-Q., Gühne, O., Gao, W.-B., Zhang, J., Yuan, Z.-S., Goebel, A., Yang, T., & Pan, J.-W. (2007) · Nature Physics · doi:10.1038/nphys507 · Cited by 683 · see citing works
Nonbinary Stabilizer Codes Over Finite Fields
Ketkar, A. U., Klappenecker, A., Kumar, S., & Sarvepalli, P. K. (2006) · IEEE Transactions on Information Theory · doi:10.1109/tit.2006.883612 · Cited by 618 · see citing works
Graph states for quantum secret sharing
Markham, D., & Sanders, B. C. (2008) · Physical Review A · doi:10.1103/physreva.78.042309 · Cited by 445 · see citing works
Scott, A. J. (2004) · Physical Review A · doi:10.1103/physreva.69.052330 · Cited by 353 · see citing works
Valence-bond states for quantum computation
Verstraete, F., & Cirac, J. I. (2004) · Physical Review A · doi:10.1103/physreva.70.060302 · Cited by 333 · see citing works
Entanglement purification and quantum error correction
Dür, W., & Briegel, H. J. (2007) · Reports on Progress in Physics · doi:10.1088/0034-4885/70/8/r03 · Cited by 327 · see citing works
Stability of Macroscopic Entanglement under Decoherence
Dür, W., & Briegel, H. J. (2004) · Physical Review Letters · doi:10.1103/physrevlett.92.180403 · Cited by 319 · see citing works
Fundamentals of quantum information theory
Keyl, M. (2002) · Physics Reports · doi:10.1016/s0370-1573(02)00266-1 · Cited by 302 · see citing works
Open-system dynamics of entanglement:a key issues review
Aolita, L., de Melo, F., & Davidovich, L. (2015) · Reports on Progress in Physics · doi:10.1088/0034-4885/78/4/042001 · Cited by 310 · see citing works
Experimental Analysis of a Four-Qubit Photon Cluster State
Kiesel, N., Schmid, C., Weber, U., Tóth, G., Gühne, O., Ursin, R., & Weinfurter, H. (2005) · Physical Review Letters · doi:10.1103/physrevlett.95.210502 · Cited by 284 · see citing works
Most Quantum States Are Too Entangled To Be Useful As Computational Resources
Gross, D., Flammia, S. T., & Eisert, J. (2009) · Physical Review Letters · doi:10.1103/physrevlett.102.190501 · Cited by 279 · see citing works
Open-system dynamics of entanglement:a key issues review
Aolita, L., de Melo, F., & Davidovich, L. (2015) · Refubium (Universitätsbibliothek der Freien Universität Berlin) · doi:10.17169/refubium-20820 · Cited by 258 · see citing works
Novel Schemes for Measurement-Based Quantum Computation
Gross, D., & Eisert, J. (2007) · Physical Review Letters · doi:10.1103/physrevlett.98.220503 · Cited by 255 · see citing works
Contextuality in measurement-based quantum computation
Raussendorf, R. (2013) · Physical Review A · doi:10.1103/physreva.88.022322 · Cited by 248 · see citing works
Measurement-based quantum computation beyond the one-way model
Gross, D., Eisert, J., Schuch, N., & Perez-Garcia, D. (2007) · Physical Review A · doi:10.1103/physreva.76.052315 · Cited by 236 · see citing works
Bell Inequalities for Graph States
Gühne, O., Tóth, G., Hyllus, P., & Briegel, H. J. (2005) · Physical Review Letters · doi:10.1103/physrevlett.95.120405 · Cited by 221 · see citing works
Multiparticle Entanglement Purification for Graph States
Dür, W., Aschauer, H. N., & Briegel, H. J. (2003) · Physical Review Letters · doi:10.1103/physrevlett.91.107903 · Cited by 216 · see citing works
Quantitative entanglement witnesses
Eisert, J., Brandão, F. G. S. L., & Audenaert, K. M. R. (2007) · New Journal of Physics · doi:10.1088/1367-2630/9/3/046 · Cited by 209 · see citing works
Experimental demonstration of topological error correction
Yao, X.-C., Wang, T., Chen, H.-Z., Gao, W., Fowler, A. G., Raussendorf, R., Chen, Z., Liu, N.-L., Lu, C., Deng, Y., et al. (2012) · Nature · doi:10.1038/nature10770 · Cited by 204 · see citing works
Experimental Realization of One-Way Quantum Computing with Two-Photon Four-Qubit Cluster States
Chen, K., Li, C.-M., Zhang, Q., Chen, Y.-A., Goebel, A., Chen, S., Mair, A., & Pan, J.-W. (2007) · Physical Review Letters · doi:10.1103/physrevlett.99.120503 · Cited by 204 · see citing works
Quantum-information splitting using multipartite cluster states
Muralidharan, S., & Panigrahi, P. K. (2008) · Physical Review A · doi:10.1103/physreva.78.062333 · Cited by 202 · see citing works
Nonlocality of cluster states of qubits
Scarani, V., Acín, A., Schenck, E., & Aspelmeyer, M. (2005) · Physical Review A · doi:10.1103/physreva.71.042325 · Cited by 195 · see citing works
Entanglement properties of multipartite entangled states under the influence of decoherence
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Popescu-Rohrlich Correlations as a Unit of Nonlocality
Barrett, J., & Pironio, S. (2005) · Physical Review Letters · doi:10.1103/physrevlett.95.140401 · Cited by 177 · see citing works
Rossi, M. A. C., Huber, M., Bruß, D., & Macchiavello, C. (2013) · New Journal of Physics · doi:10.1088/1367-2630/15/11/113022 · Cited by 175 · see citing works
Experimental demonstration of graph-state quantum secret sharing
Bell, B. A., Markham, D., Herrera-Martí, D. A., Marin, A., Wadsworth, W. J., Rarity, J., & Tame, M. (2014) · Nature Communications · doi:10.1038/ncomms6480 · Cited by 165 · see citing works
Fast simulation of stabilizer circuits using a graph-state representation
Anders, S., & Briegel, H. J. (2006) · Physical Review A · doi:10.1103/physreva.73.022334 · Cited by 163 · see citing works
Genuinely multipartite entangled states and orthogonal arrays
Goyeneche, D., & Życzkowski, K. (2014) · Physical Review A · doi:10.1103/physreva.90.022316 · Cited by 157 · see citing works
Index Theory of One Dimensional Quantum Walks and Cellular Automata
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Self-citationAll maximally entangled four-qubit states
Gour, G., & Wallach, N. R. (2010) · Journal of Mathematical Physics · doi:10.1063/1.3511477 · Cited by 137 · see citing works
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Hostens, E., Dehaene, J., & Moor, B. D. (2005) · Physical Review A · doi:10.1103/physreva.71.042315 · Cited by 137 · see citing works
Unified derivations of measurement-based schemes for quantum computation
Childs, A. M., Leung, D., & Nielsen, M. A. (2005) · Physical Review A · doi:10.1103/physreva.71.032318 · Cited by 135 · see citing works
Stabilizer codes can be realized as graph codes
Schlingemann, D.-M. (2002) · Quantum Information and Computation · doi:10.26421/qic2.4-4 · Cited by 143 · see citing works
Self-citationMultiparticle entanglement purification for two-colorable graph states
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Realization and Characterization of a Two-Photon Four-Qubit Linear Cluster State
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Vigliar, C., Paesani, S., Ding, Y., Adcock, J. C., Wang, J., Morley-Short, S., Bacco, D., Oxenløwe, L. K., Thompson, M. G., Rarity, J. G., et al. (2021) · Nature Physics · doi:10.1038/s41567-021-01333-w · Cited by 118 · see citing works
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Looi, S. Y., Yu, L. Z., Gheorghiu, V., & Griffiths, R. B. (2008) · Physical Review A · doi:10.1103/physreva.78.042303 · Cited by 111 · see citing works
Prospects for measurement‐based quantum computing with solid state spins
Benjamin, S. C., Lovett, B. W., & Smith, J. M. (2009) · Laser & Photonics Review · doi:10.1002/lpor.200810051 · Cited by 108 · see citing works
Nie, Y.-Y., Li, Y., Liu, J., & Sang, M.-H. (2010) · Quantum Information Processing · doi:10.1007/s11128-010-0196-8 · Cited by 97 · see citing works
<i>Tema con variazioni</i>: quantum channel capacity
Kretschmann, D., & Werner, R. F. (2004) · New Journal of Physics · doi:10.1088/1367-2630/6/1/026 · Cited by 123 · see citing works
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Sun, Z., Du, R., & Long, D. (2012) · International Journal of Theoretical Physics · doi:10.1007/s10773-011-1072-8 · Cited by 92 · see citing works
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Vallone, G., Donati, G., Ceccarelli, R., & Mataloni, P. (2010) · Physical Review A · doi:10.1103/physreva.81.052301 · Cited by 50 · see citing works
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Epping, M., Kampermann, H., & Bruß, D. (2016) · New Journal of Physics · doi:10.1088/1367-2630/18/10/103052 · Cited by 46 · see citing works
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Glancy, S., Knill, E. H., & Vasconcelos, H. M. (2006) · Physical Review A · doi:10.1103/physreva.74.032319 · Cited by 45 · see citing works
Multiphoton Graph States from a Solid-State Single-Photon Source
Li, J., Qin, J., Chen, A., Duan, Z.-C., Yu, Y., Huo, Y.-H., Höfling, S., Lu, C., Chen, K., & Pan, J.-W. (2020) · ACS Photonics · doi:10.1021/acsphotonics.0c00192 · Cited by 44 · see citing works
Optimal verification of stabilizer states
Dangniam, N., Han, Y.-G., & Zhu, H. (2020) · Physical Review Research · doi:10.1103/physrevresearch.2.043323 · Cited by 43 · see citing works
MEASUREMENT-BASED QUANTUM COMPUTATION WITH CLUSTER STATES
Raussendorf, R. (2009) · International Journal of Quantum Information · doi:10.1142/s0219749909005699 · Cited by 46 · see citing works
A Simple Protocol for Certifying Graph States and Applications in Quantum Networks
Markham, D., & Krause, A. (2020) · Cryptography · doi:10.3390/cryptography4010003 · Cited by 41 · see citing works
Optimal quantum-state reconstruction for cold trapped ions
Klimov, A. B., Muñoz, C., Fernández, A., & Saavedra, C. (2008) · Physical Review A · doi:10.1103/physreva.77.060303 · Cited by 41 · see citing works
Optimal preparation of graph states
Cabello, A., Danielsen, L. E., López-Tarrida, A. J., & Portillo, J. R. (2011) · Physical Review A · doi:10.1103/physreva.83.042314 · Cited by 41 · see citing works
Noisy evolution of graph-state entanglement
Aolita, L., Cavalcanti, D., Chaves, R., Dhara, C., Davidovich, L., & Acín, A. (2010) · Physical Review A · doi:10.1103/physreva.82.032317 · Cited by 41 · see citing works
Photonic resource state generation from a minimal number of quantum emitters
Li, B., Economou, S. E., & Barnes, E. (2022) · npj Quantum Information · doi:10.1038/s41534-022-00522-6 · Cited by 40 · see citing works
Greenberger-Horne-Zeilinger Paradoxes from Qudit Graph States
Tang, W., Yu, S., & Oh, C. H. (2013) · Physical Review Letters · doi:10.1103/physrevlett.110.100403 · Cited by 40 · see citing works
Photonic graph state generation from quantum dots and color centers for quantum communications
Russo, A., Barnes, E., & Economou, S. E. (2018) · Physical review. B./Physical review. B · doi:10.1103/physrevb.98.085303 · Cited by 40 · see citing works
Entanglement in eight-qubit graph states
Cabello, A., López-Tarrida, A. J., Moreno, P., & Portillo, J. R. (2009) · Physics Letters A · doi:10.1016/j.physleta.2009.04.055 · Cited by 39 · see citing works
Local unitary versus local Clifford equivalence of stabilizer and graph states
Zeng, B., Chung, H., Cross, A. W., & Chuang, I. L. (2007) · Physical Review A · doi:10.1103/physreva.75.032325 · Cited by 39 · see citing works
Optical generation of matter qubit graph states
Benjamin, S. C., Eisert, J., & Stace, T. M. (2005) · CERN Document Server (European Organization for Nuclear Research) · Cited by 39 · see citing works
Solutions of Modular Bootstrap Constraints from Quantum Codes
Dymarsky, A. Y., & Shapere, A. D. (2021) · Physical Review Letters · doi:10.1103/physrevlett.126.161602 · Cited by 38 · see citing works
- Authors
- Schlingemann, D., & Werner, R. F.
- Affiliations
- Technische Universität Braunschweig (DE)
- ORCID
- Werner, R. F.
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2001-12-11
- Volume
- 65
- Issue
- 1
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W1503834475
- Cited by
- 406
- References
- 19
- Citations by year
- 2026: 13 · 2025: 18 · 2024: 16 · 2023: 20 · 2022: 15 · 2021: 16 · 2020: 21 · 2019: 13 · 2018: 10 · 2017: 10 · 2016: 15 · 2015: 11 · 2014: 16 · 2013: 22 · 2012: 24
- FWCI
- 8.19
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Funders
- European Commission
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Computer Science › Artificial Intelligence › Coding theory and cryptography
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Keywords
- quantum error-correcting codes, graph codes, finite abelian groups, code construction, error correction capability, MDS codes, Singleton bound
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