Good quantum error-correcting codes exist

Good quantum error-correcting codes exist. Calderbank, A. R. & Shor, P. W. Physical Review A, 54(2):1098–1105, August, 1996. Publisher: American Physical Society

Paper doi abstract bibtex

A quantum error-correcting code is defined to be a unitary mapping (encoding) of k qubits (two-state quantum systems) into a subspace of the quantum state space of n qubits such that if any t of the qubits undergo arbitrary decoherence, not necessarily independently, the resulting n qubits can be used to faithfully reconstruct the original quantum state of the k encoded qubits. Quantum error-correcting codes are shown to exist with asymptotic rate k/n=1-2H2(2t/n) where H2(p) is the binary entropy function -plog2p-(1-p)log2(1-p). Upper bounds on this asymptotic rate are given. © 1996 The American Physical Society.

@article{calderbank_good_1996,
	title = {Good quantum error-correcting codes exist},
	volume = {54},
	url = {https://link.aps.org/doi/10.1103/PhysRevA.54.1098},
	doi = {10.1103/PhysRevA.54.1098},
	abstract = {A quantum error-correcting code is defined to be a unitary mapping (encoding) of k qubits (two-state quantum systems) into a subspace of the quantum state space of n qubits such that if any t of the qubits undergo arbitrary decoherence, not necessarily independently, the resulting n qubits can be used to faithfully reconstruct the original quantum state of the k encoded qubits. Quantum error-correcting codes are shown to exist with asymptotic rate k/n=1-2H2(2t/n) where H2(p) is the binary entropy function -plog2p-(1-p)log2(1-p). Upper bounds on this asymptotic rate are given. © 1996 The American Physical Society.},
	number = {2},
	urldate = {2024-03-17},
	journal = {Physical Review A},
	author = {Calderbank, A. R. and Shor, Peter W.},
	month = aug,
	year = {1996},
	note = {Publisher: American Physical Society},
	pages = {1098--1105},
}

Downloads: 0

{"_id":"gyTBGyb2kJkxtZQQ6","bibbaseid":"calderbank-shor-goodquantumerrorcorrectingcodesexist-1996","authorIDs":[],"author_short":["Calderbank, A. R.","Shor, P. W."],"bibdata":{"bibtype":"article","type":"article","title":"Good quantum error-correcting codes exist","volume":"54","url":"https://link.aps.org/doi/10.1103/PhysRevA.54.1098","doi":"10.1103/PhysRevA.54.1098","abstract":"A quantum error-correcting code is defined to be a unitary mapping (encoding) of k qubits (two-state quantum systems) into a subspace of the quantum state space of n qubits such that if any t of the qubits undergo arbitrary decoherence, not necessarily independently, the resulting n qubits can be used to faithfully reconstruct the original quantum state of the k encoded qubits. Quantum error-correcting codes are shown to exist with asymptotic rate k/n=1-2H2(2t/n) where H2(p) is the binary entropy function -plog2p-(1-p)log2(1-p). Upper bounds on this asymptotic rate are given. © 1996 The American Physical Society.","number":"2","urldate":"2024-03-17","journal":"Physical Review A","author":[{"propositions":[],"lastnames":["Calderbank"],"firstnames":["A.","R."],"suffixes":[]},{"propositions":[],"lastnames":["Shor"],"firstnames":["Peter","W."],"suffixes":[]}],"month":"August","year":"1996","note":"Publisher: American Physical Society","pages":"1098–1105","bibtex":"@article{calderbank_good_1996,\n\ttitle = {Good quantum error-correcting codes exist},\n\tvolume = {54},\n\turl = {https://link.aps.org/doi/10.1103/PhysRevA.54.1098},\n\tdoi = {10.1103/PhysRevA.54.1098},\n\tabstract = {A quantum error-correcting code is defined to be a unitary mapping (encoding) of k qubits (two-state quantum systems) into a subspace of the quantum state space of n qubits such that if any t of the qubits undergo arbitrary decoherence, not necessarily independently, the resulting n qubits can be used to faithfully reconstruct the original quantum state of the k encoded qubits. Quantum error-correcting codes are shown to exist with asymptotic rate k/n=1-2H2(2t/n) where H2(p) is the binary entropy function -plog2p-(1-p)log2(1-p). Upper bounds on this asymptotic rate are given. © 1996 The American Physical Society.},\n\tnumber = {2},\n\turldate = {2024-03-17},\n\tjournal = {Physical Review A},\n\tauthor = {Calderbank, A. R. and Shor, Peter W.},\n\tmonth = aug,\n\tyear = {1996},\n\tnote = {Publisher: American Physical Society},\n\tpages = {1098--1105},\n}\n\n\n\n\n\n\n\n","author_short":["Calderbank, A. R.","Shor, P. W."],"key":"calderbank_good_1996","id":"calderbank_good_1996","bibbaseid":"calderbank-shor-goodquantumerrorcorrectingcodesexist-1996","role":"author","urls":{"Paper":"https://link.aps.org/doi/10.1103/PhysRevA.54.1098"},"metadata":{"authorlinks":{}},"downloads":0,"html":""},"bibtype":"article","biburl":"https://bibbase.org/zotero/kyledebry","creationDate":"2020-05-31T17:07:22.674Z","downloads":0,"keywords":[],"search_terms":["good","quantum","error","correcting","codes","exist","calderbank","shor"],"title":"Good quantum error-correcting codes exist","year":1996,"dataSources":["Z5Dp3qAJiMzxtvKMq","3FvuEbLv3ARps4emr"]}