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DTSTART:20261101T010000
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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.  \n\nThen 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 (such as the Steane and quantum Reed-Muller codes) can be obtained from a common subsystem 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.
X-ALT-DESC;FMTTYPE=text/html: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.  <br><br>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 (such as the Steane and quantum Reed-Muller codes) can be obtained from a common subsystem 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.
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SUMMARY:IQC Student Seminar Featuring Sarah Meng Li
DTSTART;TZID=America/New_York:20230523T120000
DTEND;TZID=America/New_York:20230523T130000
DTSTAMP:20260429T104100Z
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SEQUENCE:0
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