CSS code - Revision history

Citation bot: Alter: pages. Add: s2cid, bibcode, pmid, authors 1-1. Removed parameters. Formatted dashes. Some additions/deletions were parameter name changes. | Use this bot. Report bugs. | Suggested by Abductive | Category:Quantum information science | #UCB_Category 149/171

2023-10-06T06:56:17Z

Alter: pages. Add: s2cid, bibcode, pmid, authors 1-1. Removed parameters. Formatted dashes. Some additions/deletions were parameter name changes. | Use this bot. Report bugs. | Suggested by Abductive | Category:Quantum information science | #UCB_Category 149/171

← Previous revision		Revision as of 06:56, 6 October 2023
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	\| volume = 54		\| volume = 54
	\| issue = 2		\| issue = 2
	\| pages = ~~1098-1105~~		\| pages = 1098–1105
	\| year = 1996		\| year = 1996
	\| doi = 10.1103/PhysRevA.54.1098		\| doi = 10.1103/PhysRevA.54.1098
			\| pmid = 9913578
	\|arxiv=quant-ph/9512032		\|arxiv=quant-ph/9512032
			\| bibcode = 1996PhRvA..54.1098C
⚫	}}</ref>
			\| s2cid = 11524969
		⚫	}}</ref>
	and [[Andrew Steane]],<ref>{{cite journal		and [[Andrew Steane]],<ref>{{cite journal
	\|last=Steane		\|last=Steane
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	<!--- See [[Wikipedia:Footnotes]] on how to create references using <ref></ref> tags which will then appear here automatically -->		<!--- See [[Wikipedia:Footnotes]] on how to create references using <ref></ref> tags which will then appear here automatically -->
	{{Reflist}}		{{Reflist}}
	{{Cite book\|last1=Nielsen\|~~first~~=Michael A.\|authorlink1=Michael Nielsen\|last2=Chuang\|first2=Isaac L.\|authorlink2=Isaac Chuang\|title=[[Quantum Computation and Quantum Information (book)\|Quantum Computation and Quantum Information]]\|publisher=Cambridge University Press\|location=Cambridge\|year=2010\|edition=2nd\|oclc=844974180\|isbn=978-1-107-00217-3}}		{{Cite book\|last1=Nielsen\|first1=Michael A.\|authorlink1=Michael Nielsen\|last2=Chuang\|first2=Isaac L.\|authorlink2=Isaac Chuang\|title=[[Quantum Computation and Quantum Information (book)\|Quantum Computation and Quantum Information]]\|publisher=Cambridge University Press\|location=Cambridge\|year=2010\|edition=2nd\|oclc=844974180\|isbn=978-1-107-00217-3}}

	== External links ==		== External links ==

Thatsme314: formatting

2022-11-17T12:17:53Z

formatting

← Previous revision		Revision as of 12:17, 17 November 2022
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	{{Short description\|Class of quantum error correcting codes}}		{{Short description\|Class of quantum error correcting codes}}
	{{For\|the document presentation language\|CSS}}		{{For\|the document presentation language\|CSS}}
	In [[quantum error correction]], '''CSS codes''', named after their inventors, [[Robert Calderbank]], [[Peter Shor]]		In [[quantum error correction]], '''CSS codes''', named after their inventors, [[Robert Calderbank]], [[Peter Shor]]<ref>{{cite journal
	<ref>{{cite journal
	\| author = [[Robert Calderbank]] and [[Peter Shor]]		\| author = [[Robert Calderbank]] and [[Peter Shor]]
	\| title = Good quantum error-correcting codes exist		\| title = Good quantum error-correcting codes exist
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	\|arxiv=quant-ph/9512032		\|arxiv=quant-ph/9512032
	}}</ref>		}}</ref>
	and [[Andrew Steane]]		and [[Andrew Steane]],<ref>{{cite journal
	<ref>{{cite journal
	\|last=Steane		\|last=Steane
	\|first=Andrew		\|first=Andrew
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	\|bibcode=1996RSPSA.452.2551S		\|bibcode=1996RSPSA.452.2551S
	\|s2cid=8246615		\|s2cid=8246615
		⚫	}}</ref> are a special type of [[stabilizer code]] constructed from classical codes with some special properties. An example of a CSS code is the [[Steane code]].
	}}</ref>
⚫	, are a special type of [[stabilizer code]]s constructed from classical codes with some special properties. An example of a CSS code is the [[Steane code]].

	== Construction ==		== Construction ==

GhostInTheMachine: Changing short description from "class of quantum error correcting codes" to "Class of quantum error correcting codes"

2022-10-18T22:06:02Z

Changing short description from "class of quantum error correcting codes" to "Class of quantum error correcting codes"

← Previous revision		Revision as of 22:06, 18 October 2022
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	{{~~short~~ description\|~~class~~ of quantum error correcting codes}}		{{Short description\|Class of quantum error correcting codes}}
	{{For\|the document presentation language\|CSS}}		{{For\|the document presentation language\|CSS}}
	In [[quantum error correction]], '''CSS codes''', named after their inventors, [[Robert Calderbank]], [[Peter Shor]]		In [[quantum error correction]], '''CSS codes''', named after their inventors, [[Robert Calderbank]], [[Peter Shor]]

MJMcEwen: Add arxiv link

2022-10-18T21:46:32Z

Add arxiv link

← Previous revision		Revision as of 21:46, 18 October 2022
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	\| year = 1996		\| year = 1996
	\| doi = 10.1103/PhysRevA.54.1098		\| doi = 10.1103/PhysRevA.54.1098
			\|arxiv=quant-ph/9512032
	}}</ref>		}}</ref>
	and [[Andrew Steane]]		and [[Andrew Steane]]
	<ref>{{cite journal		<ref>{{cite journal
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	\|title=Multiple-Particle Interference and Quantum Error Correction		\|title=Multiple-Particle Interference and Quantum Error Correction
	\|journal=Proc. R. Soc. Lond. A		\|journal=Proc. R. Soc. Lond. A
	\|volume=452 \| year=1996		\|volume=452
			\|year=1996
	\|pages=2551–2577		\|pages=2551–2577
	\|doi=10.1098/rspa.1996.0136		\|doi=10.1098/rspa.1996.0136
	\|issue=1954\|arxiv=quant-ph/9601029		\|issue=1954
			\|arxiv=quant-ph/9601029
	\|bibcode=1996RSPSA.452.2551S \|s2cid=8246615		\|bibcode=1996RSPSA.452.2551S
			\|s2cid=8246615
	}}</ref>		}}</ref>
	, are a special type of [[stabilizer code]]s constructed from classical codes with some special properties. An example of a CSS code is the [[Steane code]].		, are a special type of [[stabilizer code]]s constructed from classical codes with some special properties. An example of a CSS code is the [[Steane code]].

MJMcEwen: Add references to original CSS papers

2022-10-18T21:44:30Z

Add references to original CSS papers

@@ Line 1: / Line 1: @@
-{{short description|Linear algebra}}
+{{short description|class of quantum error correcting codes}}
 {{For|the document presentation language|CSS}}
-In [[quantum error correction]], '''CSS codes''', named after their inventors, [[Robert Calderbank]], [[Peter Shor]] and [[Andrew Steane]], are a special type of [[stabilizer code]]s constructed from classical codes with some special properties. An example of a CSS code is the [[Steane code]].
+In [[quantum error correction]], '''CSS codes''', named after their inventors, [[Robert Calderbank]], [[Peter Shor]]
 == Construction ==

EthanGaming7640 at 12:50, 21 September 2021

2021-09-21T12:50:20Z

← Previous revision		Revision as of 12:50, 21 September 2021
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	{{short description\|Linear algebra}}		{{short description\|Linear algebra}}
	{{For\|the document presentation language\|~~Cascading Style Sheets~~}}		{{For\|the document presentation language\|CSS}}
	In [[quantum error correction]], '''CSS codes''', named after their inventors, [[Robert Calderbank]], [[Peter Shor]] and [[Andrew Steane]], are a special type of [[stabilizer code]]s constructed from classical codes with some special properties. An example of a CSS code is the [[Steane code]].		In [[quantum error correction]], '''CSS codes''', named after their inventors, [[Robert Calderbank]], [[Peter Shor]] and [[Andrew Steane]], are a special type of [[stabilizer code]]s constructed from classical codes with some special properties. An example of a CSS code is the [[Steane code]].

ReyHahn: style

2021-05-06T14:34:53Z

style

← Previous revision		Revision as of 14:34, 6 May 2021
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	{{short description\|Linear algebra}}		{{short description\|Linear algebra}}
	{{For\|the document presentation language\|Cascading Style Sheets}}		{{For\|the document presentation language\|Cascading Style Sheets}}
	In [[quantum error correction]], '''CSS codes''', named after their inventors, [[Robert Calderbank]], [[Peter Shor]] and [[Andrew Steane]], are a special type of [[~~Stabilizer~~ code]]s constructed from classical codes with some special properties. An example of a CSS code is the [[Steane code]].		In [[quantum error correction]], '''CSS codes''', named after their inventors, [[Robert Calderbank]], [[Peter Shor]] and [[Andrew Steane]], are a special type of [[stabilizer code]]s constructed from classical codes with some special properties. An example of a CSS code is the [[Steane code]].

	== Construction ==		== Construction ==

The Eloquent Peasant: Importing Wikidata short description: "Linear algebra" (Shortdesc helper)

2021-01-14T16:40:25Z

Importing Wikidata short description: "Linear algebra" (Shortdesc helper)

← Previous revision		Revision as of 16:40, 14 January 2021
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			{{short description\|Linear algebra}}
	{{For\|the document presentation language\|Cascading Style Sheets}}		{{For\|the document presentation language\|Cascading Style Sheets}}
	In [[quantum error correction]], '''CSS codes''', named after their inventors, [[Robert Calderbank]], [[Peter Shor]] and [[Andrew Steane]], are a special type of [[Stabilizer code]]s constructed from classical codes with some special properties. An example of a CSS code is the [[Steane code]].		In [[quantum error correction]], '''CSS codes''', named after their inventors, [[Robert Calderbank]], [[Peter Shor]] and [[Andrew Steane]], are a special type of [[Stabilizer code]]s constructed from classical codes with some special properties. An example of a CSS code is the [[Steane code]].

Holting at 12:20, 18 November 2020

2020-11-18T12:20:54Z

← Previous revision		Revision as of 12:20, 18 November 2020
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	== Construction ==		== Construction ==

	Let <math>C_1</math> and <math>C_2</math> be two (classical) <math> [n,k_1]</math>, <math> [n,k_2]</math> codes such, that <math> C_2~~^\perp~~ \subset C_1 </math> and <math> C_1 , C_2^\perp</math> both have [[Block code\|minimal distance]] <math> \geq 2t+1</math>, where <math> C_2^\perp</math> is the code [[Dual code\|dual]] to <math> C_2</math>. Then define <math> \text{CSS}(C_1,C_2)</math>, the CSS code of <math> C_1</math> over <math> C_2</math> as an <math> [n,k_1 - k_2, d]</math> code, with <math> d \geq 2t+1 </math> as follows:		Let <math>C_1</math> and <math>C_2</math> be two (classical) <math> [n,k_1]</math>, <math> [n,k_2]</math> codes such, that <math> C_2 \subset C_1 </math> and <math> C_1 , C_2^\perp</math> both have [[Block code\|minimal distance]] <math> \geq 2t+1</math>, where <math> C_2^\perp</math> is the code [[Dual code\|dual]] to <math> C_2</math>. Then define <math> \text{CSS}(C_1,C_2)</math>, the CSS code of <math> C_1</math> over <math> C_2</math> as an <math> [n,k_1 - k_2, d]</math> code, with <math> d \geq 2t+1 </math> as follows:

	Define for <math> x \in C_1 : {{\|}} x + C_2 \rangle := </math> <math> 1 / \sqrt{ {{\|}} C_2 {{\|}} } </math> <math> \sum_{y \in C_2} {{\|}} x + y \rangle</math>, where <math> + </math> is bitwise addition modulo 2. Then <math> \text{CSS}(C_1,C_2) </math> is defined as <math> \{ {{\|}} x + C_2 \rangle \mid x \in C_1 \} </math>.		Define for <math> x \in C_1 : {{\|}} x + C_2 \rangle := </math> <math> 1 / \sqrt{ {{\|}} C_2 {{\|}} } </math> <math> \sum_{y \in C_2} {{\|}} x + y \rangle</math>, where <math> + </math> is bitwise addition modulo 2. Then <math> \text{CSS}(C_1,C_2) </math> is defined as <math> \{ {{\|}} x + C_2 \rangle \mid x \in C_1 \} </math>.

Holting: Added a missing \perp to the construction.

2020-10-07T09:43:06Z

Added a missing \perp to the construction.

← Previous revision		Revision as of 09:43, 7 October 2020
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	== Construction ==		== Construction ==

	Let <math>C_1</math> and <math>C_2</math> be two (classical) <math> [n,k_1]</math>, <math> [n,k_2]</math> codes such, that <math> C_2 \subset C_1 </math> and <math> C_1 , C_2^\perp</math> both have [[Block code\|minimal distance]] <math> \geq 2t+1</math>, where <math> C_2^\perp</math> is the code [[Dual code\|dual]] to <math> C_2</math>. Then define <math> \text{CSS}(C_1,C_2)</math>, the CSS code of <math> C_1</math> over <math> C_2</math> as an <math> [n,k_1 - k_2, d]</math> code, with <math> d \geq 2t+1 </math> as follows:		Let <math>C_1</math> and <math>C_2</math> be two (classical) <math> [n,k_1]</math>, <math> [n,k_2]</math> codes such, that <math> C_2^\perp \subset C_1 </math> and <math> C_1 , C_2^\perp</math> both have [[Block code\|minimal distance]] <math> \geq 2t+1</math>, where <math> C_2^\perp</math> is the code [[Dual code\|dual]] to <math> C_2</math>. Then define <math> \text{CSS}(C_1,C_2)</math>, the CSS code of <math> C_1</math> over <math> C_2</math> as an <math> [n,k_1 - k_2, d]</math> code, with <math> d \geq 2t+1 </math> as follows:

	Define for <math> x \in C_1 : {{\|}} x + C_2 \rangle := </math> <math> 1 / \sqrt{ {{\|}} C_2 {{\|}} } </math> <math> \sum_{y \in C_2} {{\|}} x + y \rangle</math>, where <math> + </math> is bitwise addition modulo 2. Then <math> \text{CSS}(C_1,C_2) </math> is defined as <math> \{ {{\|}} x + C_2 \rangle \mid x \in C_1 \} </math>.		Define for <math> x \in C_1 : {{\|}} x + C_2 \rangle := </math> <math> 1 / \sqrt{ {{\|}} C_2 {{\|}} } </math> <math> \sum_{y \in C_2} {{\|}} x + y \rangle</math>, where <math> + </math> is bitwise addition modulo 2. Then <math> \text{CSS}(C_1,C_2) </math> is defined as <math> \{ {{\|}} x + C_2 \rangle \mid x \in C_1 \} </math>.