Graphical CSS Code Transformation Using ZX Calculus
| dc.contributor.author | Li, Sarah Meng | |
| dc.date.accessioned | 2023-12-21T19:45:22Z | |
| dc.date.available | 2023-12-21T19:45:22Z | |
| dc.date.issued | 2023-12-21 | |
| dc.date.submitted | 2023-12-19 | |
| dc.description.abstract | 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. We then 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. | en |
| dc.identifier.uri | http://hdl.handle.net/10012/20193 | |
| dc.language.iso | en | en |
| dc.pending | false | |
| dc.publisher | University of Waterloo | en |
| dc.subject | ZX calculus | en |
| dc.subject | Quantum error correction | en |
| dc.subject | CSS codes | en |
| dc.subject | Code morphing | en |
| dc.subject | Code switching | en |
| dc.subject | Subsystem code gauge fixing | en |
| dc.subject | Fault tolerance | en |
| dc.title | Graphical CSS Code Transformation Using ZX Calculus | en |
| dc.type | Master Thesis | en |
| uws-etd.degree | Master of Mathematics | en |
| uws-etd.degree.department | Combinatorics and Optimization | en |
| uws-etd.degree.discipline | Combinatorics and Optimization (Quantum Information) | en |
| uws-etd.degree.grantor | University of Waterloo | en |
| uws-etd.embargo.terms | 0 | en |
| uws.comment.hidden | Adjusted the figures and its descriptions so that the page number is at the very bottom center of the page. | en |
| uws.contributor.advisor | Mosca, Michele | |
| uws.contributor.affiliation1 | Faculty of Mathematics | en |
| uws.peerReviewStatus | Unreviewed | en |
| uws.published.city | Waterloo | en |
| uws.published.country | Canada | en |
| uws.published.province | Ontario | en |
| uws.scholarLevel | Graduate | en |
| uws.typeOfResource | Text | en |