Extends ZX-calculus to dynamical stabilizer codes via gauge fixing to construct measurement-based logical automorphisms, shown with a distance-preserving phase gate on the seven-qubit code.
Fault-tolerant conversion between stabilizer codes by Clifford operations
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abstract
We propose a scheme that converts a stabilizer code into another stabilizer code in a fault tolerant manner. The scheme first puts both codes in specific forms, and proceeds the conversion from a source code to a target code by applying Clifford gates. The Clifford gates are chosen from the comparisons between both codes. The fault tolerance of the conversion is guaranteed by quantum error correction in every step during the entire conversion process. As examples, we show three conversions: the $[[5,1,3]]$ stabilizer code and Steane code, Steane code and $[[15,1,3]]$ Reed-Muller code, and Steane code and $(3,4)$-QPC code.
fields
quant-ph 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
The paper compiles a curated handbook reference of error-correcting codes, their symbol-based classifications, and interrelations with mathematical objects and physical phases.
citing papers explorer
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Chutes and Ladders: Dynamical Automorphisms via the ZX-Calculus
Extends ZX-calculus to dynamical stabilizer codes via gauge fixing to construct measurement-based logical automorphisms, shown with a distance-preserving phase gate on the seven-qubit code.
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Handbook of Error-Correcting Codes
The paper compiles a curated handbook reference of error-correcting codes, their symbol-based classifications, and interrelations with mathematical objects and physical phases.