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 analogs 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 ${\mathbb{F}}_2$, 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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• Gravity in dimensions other than four
• Majorana bound states
• Majorana fermions
• Quantum algorithms
• Quantum circuits
• Quantum computation
• Quantum error correction
• Quantum gates
• Quantum gravity
• Quantum information theory
• Quantum simulation
• Quantum tomography
• Topological quantum computing
• Quantum aspects of black holes
• Computational complexity
• Information theory
• Sachdev-Ye-Kitaev model