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Updated: Jul 11, 2026
06:42
Generation and Coherent Control of Pulsed Quantum Frequency Combs
Published on: June 8, 2018
Simple family of nonadditive quantum codes
John A Smolin1, Graeme Smith, Stephanie Wehner
1IBM T.J. Watson Research Center, Yorktown Heights, New York 10598, USA. smolin@watson.ibm.com
Physical Review Letters
|October 13, 2007
Summary
We introduce novel nonadditive quantum codes for all odd block lengths. These simple codes offer superior performance in detecting errors and encoding higher dimensional spaces compared to existing additive quantum codes.
Area of Science:
- Quantum Information Science
- Quantum Error Correction
- Coding Theory
Background:
- Most quantum error-correcting codes are additive, limiting their performance in certain applications.
- Constructing high-performance nonadditive quantum codes remains a significant challenge in the field.
Purpose of the Study:
- To present a new family of nonadditive quantum codes with a simple structure.
- To demonstrate their effectiveness in error detection and space encoding.
Main Methods:
- Development of a novel construction for nonadditive quantum codes.
- Analysis of code properties including error detection capabilities and encoded space dimension.
- Characterization of encoding circuits and automorphism groups.
Main Results:
- A family of distance 2 nonadditive quantum codes for all odd block lengths n is presented.
- These codes detect single qubit errors or correct single qubit erasures.
- The codes encode a higher dimensional space than previously known additive codes or other nonadditive codes for n>=11.
Conclusions:
- The developed nonadditive quantum codes offer improved performance over existing additive codes.
- This work provides a new avenue for constructing efficient quantum error-correcting codes.
- The simple form and superior encoding capabilities make these codes promising for practical quantum information processing.
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