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dc.contributor.authorLi, Sarah Meng 19:45:22 (GMT) 19:45:22 (GMT)
dc.description.abstractIn 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.publisherUniversity of Waterlooen
dc.subjectZX calculusen
dc.subjectQuantum error correctionen
dc.subjectCSS codesen
dc.subjectCode morphingen
dc.subjectCode switchingen
dc.subjectSubsystem code gauge fixingen
dc.subjectFault toleranceen
dc.titleGraphical CSS Code Transformation Using ZX Calculusen
dc.typeMaster Thesisen
dc.pendingfalse and Optimizationen and Optimization (Quantum Information)en of Waterlooen
uws-etd.degreeMaster of Mathematicsen
uws.contributor.advisorMosca, Michele
uws.contributor.affiliation1Faculty of Mathematicsen

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