Fault-Tolerant Logical Clifford Gates from Code Automorphisms

We study the implementation of fault-tolerant logical Clifford gates on stabilizer quantum error-correcting codes based on their symmetries. Our approach is to map the stabilizer code to a binary linear code, compute its automorphism group, and impose constraints based on the Clifford operators perm...

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Published inPRX quantum Vol. 6; no. 3; p. 030343
Main Authors Sayginel, Hasan, Koutsioumpas, Stergios, Webster, Mark, Rajput, Abhishek, Browne, Dan E.
Format Journal Article
LanguageEnglish
Published American Physical Society 01.09.2025
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ISSN2691-3399
2691-3399
DOI10.1103/vf7v-cpq9

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Abstract We study the implementation of fault-tolerant logical Clifford gates on stabilizer quantum error-correcting codes based on their symmetries. Our approach is to map the stabilizer code to a binary linear code, compute its automorphism group, and impose constraints based on the Clifford operators permitted. We provide a rigorous formulation of the method for finding automorphisms of stabilizer codes and generalize the Z X dualities previously introduced for Calderbank-Shor-Steane (CSS) codes to non-CSS codes. We provide a package implementing our algorithms that uses the computational-algebra software system for certain subroutines. Our algorithms map automorphism-group generators to physical circuits, calculate Pauli corrections based on the destabilizers of the code, and determine their logical action. We discuss the fault tolerance of the circuits and include examples of gates through automorphisms for the [ [ 4 , 2 , 2 ] ] and perfect [ [ 5 , 1 , 3 ] ] codes, bivariate bicycle codes, and the best-known distance codes.
AbstractList We study the implementation of fault-tolerant logical Clifford gates on stabilizer quantum error-correcting codes based on their symmetries. Our approach is to map the stabilizer code to a binary linear code, compute its automorphism group, and impose constraints based on the Clifford operators permitted. We provide a rigorous formulation of the method for finding automorphisms of stabilizer codes and generalize the ZX dualities previously introduced for Calderbank-Shor-Steane (CSS) codes to non-CSS codes. We provide a python package implementing our algorithms that uses the computational-algebra magma software system for certain subroutines. Our algorithms map automorphism-group generators to physical circuits, calculate Pauli corrections based on the destabilizers of the code, and determine their logical action. We discuss the fault tolerance of the circuits and include examples of gates through automorphisms for the [[4,2,2]] and perfect [[5,1,3]] codes, bivariate bicycle codes, and the best-known distance codes.
We study the implementation of fault-tolerant logical Clifford gates on stabilizer quantum error-correcting codes based on their symmetries. Our approach is to map the stabilizer code to a binary linear code, compute its automorphism group, and impose constraints based on the Clifford operators permitted. We provide a rigorous formulation of the method for finding automorphisms of stabilizer codes and generalize the Z X dualities previously introduced for Calderbank-Shor-Steane (CSS) codes to non-CSS codes. We provide a package implementing our algorithms that uses the computational-algebra software system for certain subroutines. Our algorithms map automorphism-group generators to physical circuits, calculate Pauli corrections based on the destabilizers of the code, and determine their logical action. We discuss the fault tolerance of the circuits and include examples of gates through automorphisms for the [ [ 4 , 2 , 2 ] ] and perfect [ [ 5 , 1 , 3 ] ] codes, bivariate bicycle codes, and the best-known distance codes.
ArticleNumber 030343
Author Webster, Mark
Browne, Dan E.
Koutsioumpas, Stergios
Sayginel, Hasan
Rajput, Abhishek
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Title Fault-Tolerant Logical Clifford Gates from Code Automorphisms
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