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arXiv · 2407.11319

The Structure of the Majorana Clifford Group

Valérie Bettaque·Brian Swingle
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Abstract

In quantum information science, Clifford operators and stabilizer codes play a central role for systems of qubits (or qudits). In this paper, we study their analogues for systems composed of Majorana fermions. In this case, a crucial role is played by fermion parity symmetry, which is an unbreakable symmetry present in any system with fundamentally fermionic degrees of freedom. We prove that the subgroup of parity-preserving Majorana Cliffords can be represented by the orthogonal group over the binary field $\F$, and we show how it can be generated by braiding operators and used to construct any (even-parity) Majorana stabilizer code. We also analyze the frame potential for this so-called p-Clifford group when acting on a fixed-parity sector of the Hilbert space, proving that it is equivalent to the frame potential of the ordinary Clifford group acting on the same sector.

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Valérie Bettaque, Brian Swingle. 2024-07-16. The Structure of the Majorana Clifford Group. https://arxiv.org/abs/2407.11319

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