



@article {3403,
	title = {Subsystem CSS codes, a tighter stabilizer-to-CSS mapping, and Goursat{\textquoteright}s Lemma},
	year = {2023},
	month = {11/29/2023},
	abstract = {<p>The CSS code construction is a powerful framework used to express features of a quantum code in terms of a pair of underlying classical codes. Its subsystem extension allows for similar expressions, but the general case has not been fully explored. Extending previous work of Aly et. al. [quant-ph/0610153], we determine subsystem CSS code parameters, express codewords, and develop a Steane-type decoder using only data from the two underlying classical codes. We show that any subsystem stabilizer code can be {\textquoteleft}{\textquoteleft}doubled\&$\#$39;\&$\#$39; to yield a subsystem CSS code with twice the number of physical, logical, and gauge qudits and up to twice the code distance. This mapping preserves locality and is tighter than the Majorana-based mapping of Bravyi, Leemhuis, and Terhal [New J. Phys. 12 083039 (2010)]. Using Goursat\&$\#$39;s Lemma, we show that every subsystem stabilizer code can be constructed from two nested subsystem CSS codes satisfying certain constraints, and we characterize subsystem stabilizer codes based on the nested codes\&$\#$39; properties.</p>},
	url = {https://arxiv.org/abs/2311.18003},
	author = {Michael Liaofan Liu and Nathanan Tantivasadakarn and Victor V. Albert}
}
