Qudit stabilizers beyond the free case and the twisted Kitaev model

Abstract:We study the stabiliser formalism for qudits of arbitrary dimension $d$. In the free case, we show that the basic theorem of the stabiliser formalism remains valid: if the stabiliser subgroup $H$ is free as a $Z/dZ$-module and contains no non-trivial scalars, then the protected space $V^H$ is naturally identified with the state space of a smaller number of qudits of the same dimension, and the quotient $N(H)/H$ is identified with the Pauli group on a smaller number of qudits. We then remove the freeness assumption and describe the resulting structure in general. In this case, the protected space is identified with a tensor product of qudit spaces of possibly smaller dimensions, and the quotient $N(H)/H$ is described by a corresponding product of qudit Pauli groups, possibly of smaller dimensions, over a common center. We also characterise the shifted free case, which is exactly the situation in which $N(H)/H$ is again an ordinary qudit Pauli group. Our approach is algebraic and uniform, and applies in particular to the qudit Kitaev model and to its shifted and twisted variants.

Quantum Algebra (math.QA); Quantum Physics (quant-ph)

arXiv:2603.29896 [math.QA]

(or arXiv:2603.29896v1 [math.QA] for this version)

https://doi.org/10.48550/arXiv.2603.29896 Focus to learn more arXiv-issued DOI via DataCite

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