The DOI matches its Crossref record; 59 of the 59 references it cites were found in a registry or an index.
An introduction to quantum error correction and fault-tolerant quantum computation
Open accessAbstract
Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers.The theory of quantum error-correcting codes has some close ties to and some striking differences from the theory of classical error-correcting codes.Many quantum codes can be described in terms of the stabilizer of the codewords.The stabilizer is a finite Abelian group, and allows a straightforward characterization of the error-correcting properties of the code.The stabilizer formalism for quantum codes also illustrates the relationships to classical coding theory, particularly classical codes over GF(4), the finite field with four elements.To build a quantum computer which behaves correctly in the presence of errors, we also need a theory of fault-tolerant quantum computation, instructing us how to perform quantum gates on qubits which are encoded in a quantum errorcorrecting code.The threshold theorem states that it is possible to create a quantum computer to perform an arbitrary quantum computation provided the error rate per physical gate or time step is below some constant threshold value.
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Citations
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×
“1 We might try a quantum repetition code: (3) However, no such code exists because of the No-Cloning theorem [ 17, 54 ]: Theorem 1 (No-Cloning) .”
MethodMixed-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
Scheme for reducing decoherence in quantum computer memory
Shor, P. W. (1995) · Physical Review A · doi:10.1103/physreva.52.r2493 · Cited by 4,479
Error Correcting Codes in Quantum Theory
Steane, A. M. (1996) · Physical Review Letters · doi:10.1103/physrevlett.77.793 · Cited by 2,677
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 · cited 1×
“We could have used any two classical codes C 1 and C 2 [ 14, 47 ].”
MethodDynamical Decoupling of Open Quantum Systems
Viola, L., Knill, E., & Lloyd, S. (1999) · Physical Review Letters · doi:10.1103/physrevlett.82.2417 · Cited by 1,808
Theory of quantum error-correcting codes
Knill, E., & Laflamme, R. (1997) · Physical Review A · doi:10.1103/physreva.55.900 · Cited by 1,593
Universal quantum computation with ideal Clifford gates and noisy ancillas
Bravyi, S., & Kitaev, A. (2005) · Physical Review A · doi:10.1103/physreva.71.022316 · Cited by 1,525
Dennis, E., Kitaev, A., Landahl, A., & Preskill, J. (2001) · CERN Document Server (European Organization for Nuclear Research) · Cited by 1,485
Dieks, D. (1982) · Physics Letters A · doi:10.1016/0375-9601(82)90084-6 · Cited by 1,461
Cited by
Quantum Computing in the NISQ era and beyond
Preskill, J. (2018) · Quantum · doi:10.22331/q-2018-08-06-79 · Cited by 8,830
“materials and control and fabrication to get where we are now. Eventually we expect to be able to protect quantum systems and scale up quantum computers using the principle of quantum errorcorrection [10]. The essential idea of quantum error correction is that if we want to protect a quantum system from damage then we…”
BackgroundQuantum error correction for quantum memories
Terhal, B. M. (2015) · Reviews of Modern Physics · doi:10.1103/revmodphys.87.307 · Cited by 1,354
Quantum error correction for beginners
Devitt, S. J., Munro, W. J., & Nemoto, K. (2013) · Reports on Progress in Physics · doi:10.1088/0034-4885/76/7/076001 · Cited by 759
Quantum Algorithms for Quantum Field Theories
Jordan, S. P., Lee, K. S. M., & Preskill, J. (2012) · Science · doi:10.1126/science.1217069 · Cited by 517
The resource theory of stabilizer quantum computation
Veitch, V., Hamed Mousavian, S. A., Gottesman, D., & Emerson, J. (2014) · New Journal of Physics · doi:10.1088/1367-2630/16/1/013009 · Cited by 501
Self-citation
Metadata
- Authors
- Gottesman, D.
- Venue
- Proceedings of Symposia in Applied Mathematics
- Publisher
- American Mathematical Society
- Published
- 2010
- Pages
- 13-58
- ISSN
- 0160-7634 (ISSN-L)
- 2324-7088
- OpenAlex
- W1675244148
- Cited by
- 370
- References
- 59
- Type
- other
- Language
- en
- Open access
- bronze
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
