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Triorthogonal Codes and Self-dual Codes

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arxiv 2408.09685 v1 pith:XDKIF325 submitted 2024-08-19 cs.IT math.ITquant-ph

Minjia Shi , Haodong Lu , Jon-Lark Kim , Patrick Sole This is my paper · ORCID
classification cs.ITmath.ITquant-ph
keywords codestriorthogonalbinarygivematricesself-dualalgorithmbravyi
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Triorthogonal matrices were introduced in Quantum Information Theory in connection with distillation of magic states (Bravyi and Haah (2012)). We give an algorithm to construct binary triorthogonal matrices from binary self-dual codes. Further, we generalize to this setting the classical coding techniques of shortening and extending. We also give some simple propagation rules.

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  1. Exploring the landscape of compact magic-state distillation factories

    quant-ph 2026-06 unverdicted novelty 8.0 of 10

    Classical repetition-code framing plus SAT search yields no-go theorems (no d>3 T-to-T on <8 qubits) and the smallest known unitary factories for d=4,5 T-states (10–11 qubits) and d=3,4 CCZ-states (9–10 qubits).

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