Jiaxin Huang (Dept. of Computer Science, Hong Kong University of Science and Technology) |
Sarah Meng Li (Institute for Quantum Computing, Dept. of Combinatorics & Optimization, University of Waterloo) |
Lia Yeh (Dept. of Computer Science, University of Oxford, Quantinuum) |
Aleks Kissinger (Dept. of Computer Science, University of Oxford) |
Michele Mosca (Institute for Quantum Computing, Dept. of Combinatorics & Optimization, University of Waterloo, Perimeter Institute for Theoretical Physics) |
Michael Vasmer (Institute for Quantum Computing, University of Waterloo, Perimeter Institute for Theoretical Physics) |
In this work, we present a generic approach to transform CSS codes by building upon their equivalence to phase-free ZX diagrams. Using the ZX calculus, we demonstrate diagrammatic transformations between encoding maps associated with different codes. As a motivating example, we give explicit transformations between the Steane code and the quantum Reed-Muller code, since by switching between these two codes, one can obtain a fault-tolerant universal gate set. To this end, we propose a bidirectional rewrite rule to find a (not necessarily transversal) physical implementation for any logical ZX diagram in any CSS code.
Then we focus on two code transformation techniques: code morphing, a procedure that transforms a code while retaining its fault-tolerant gates, and gauge fixing, where complimentary codes can be obtained from a common subsystem code (e.g., the Steane and the quantum Reed-Muller codes from the [[15,1,3,3]] code). We provide explicit graphical derivations for these techniques and show how ZX and graphical encoder maps relate several equivalent perspectives on these code-transforming operations. |
ArXived at: https://dx.doi.org/10.4204/EPTCS.384.1 | bibtex | |
Comments and questions to: eptcs@eptcs.org |
For website issues: webmaster@eptcs.org |