NDLI: Fidelity Lower Bounds for Stabilizer and CSS Quantum Codes

Content Provider	IEEE Xplore Digital Library
Author	Ashikhmin, A.
Copyright Year	1963
Abstract	In this paper, we estimate the fidelity of stabilizer and CSS codes. First, we derive a lower bound on the fidelity of a stabilizer code via its quantum enumerator. Next, we find the average quantum enumerators of the ensembles of finite length stabilizer and CSS codes. We use the average quantum enumerators for obtaining lower bounds on the average fidelity of these ensembles. We further improve the fidelity bounds by estimating the quantum enumerators of expurgated ensembles of stabilizer and CSS codes. Finally, we derive fidelity bounds in the asymptotic regime when the code length tends to infinity. These results tell us which code rate we can afford for achieving a target fidelity with codes of a given length. The results also show that in symmetric depolarizing channel a typical stabilizer code has better performance, in terms of fidelity and code rate, compared with a typical CSS codes, and that balanced CSS codes significantly outperform other CSS codes. Asymptotic results demonstrate that CSS codes have a fundamental performance loss compared with stabilizer codes.
Sponsorship	IEEE Information Theory Society
Starting Page	3104
Ending Page	3116
Page Count	13
File Size	1213356
File Format	PDF
ISSN	00189448
Volume Number	60
Issue Number	6
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2014-01-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Vectors Cascading style sheets Standards Arrays Quantum mechanics Quantum computing Linear codes stabilizer codes CSS codes fidelity bounds quantum codes
Content Type	Text
Resource Type	Article
Subject	Library and Information Sciences Information Systems Computer Science Applications

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Quantum LDPC Codes With Positive Rate and Minimum Distance Proportional to the Square Root of the Blocklength

CSS-Like Constructions of Asymmetric Quantum Codes

A Family of Asymptotically Good Quantum Codes Based on Code Concatenation

On the Construction of Nonbinary Quantum BCH Codes

Efficient Quantum Stabilizer Codes: LDPC and LDPC-Convolutional Constructions

High Performance Single-Error-Correcting Quantum Codes for Amplitude Damping

A Construction of Quantum Stabilizer Codes Based on Syndrome Assignment by Classical Parity-Check Matrices

Quantum codes from concatenated algebraic-geometric codes

A Construction of Quantum LDPC Codes From Cayley Graphs

Fidelity Lower Bounds for Stabilizer and CSS Quantum Codes

Similar Documents

Quantum LDPC Codes With Positive Rate and Minimum Distance Proportional to the Square Root of the Blocklength

CSS-Like Constructions of Asymmetric Quantum Codes

A Family of Asymptotically Good Quantum Codes Based on Code Concatenation

On the Construction of Nonbinary Quantum BCH Codes

Efficient Quantum Stabilizer Codes: LDPC and LDPC-Convolutional Constructions

High Performance Single-Error-Correcting Quantum Codes for Amplitude Damping

A Construction of Quantum Stabilizer Codes Based on Syndrome Assignment by Classical Parity-Check Matrices

Quantum codes from concatenated algebraic-geometric codes

A Construction of Quantum LDPC Codes From Cayley Graphs

Fidelity Lower Bounds for Stabilizer and CSS Quantum Codes