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Strictly speaking of course the “mid-way” point of a parity check circuit is only well-defined if the circuit has an even depth — which is satisfied for all the new circuits constructed in this Letter
Cited in the paper.
See Supplemental Material, which includes Refs. [ 20 , 21 , 25 , 26 , 27 , 28 ]
Cited in the paper.
Note that different homomorphisms applied to the same mid-cycle BB code can indeed lead to distinct end-cycle codes that are unrelated via the mappings of Ref. [ 6 ]
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We leave investigations into the Z X ZX -duality to future work, since even for the codes of Ref. [ 1 ] , more work must be done to optimize the gate sequence before it can be implemented in practice
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https://github.com/Mac-Shaw/morphing_qec_circuits
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2024
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