Boundary checks for a locally realized one-step Majorana code

Construct suitable boundary checks that complete the open-boundary local Majorana realization of the one-step rectangle protocol, so that the resulting local stabilizer group reproduces the periodic one-step code and can support implementations in experimentally motivated architectures.

Background

The direct microscopic Majorana construction uses an open spatial direction to avoid nonlocal Jordan–Wigner strings. The even-size two- and three-step protocols can be realized locally with four- and eight-Majorana parity measurements, but simply truncating the rectangle family for the one-step protocol does not reproduce the periodic stabilizer rank.

The paper therefore leaves unresolved the construction of additional boundary measurements or checks needed to complete the local one-step realization. The main text further notes that suitable boundary checks could broaden the direct Majorana implementation and facilitate experimentally motivated architectures.