Fold-Transversal Clifford Gates for Quantum Codes

• URL: http://arxiv.org/abs/2202.06647v3
• Date: Mon, 10 Jun 2024 13:53:11 GMT
• Title: Fold-Transversal Clifford Gates for Quantum Codes
• Authors: Nikolas P. Breuckmann, Simon Burton,
• Abstract summary: We generalize the concept of folding from surface codes to CSS codes. We consider a hyperbolic quantum code called Bring's code. We show that by restricting the logical subspace of Bring's code to four qubits, we can obtain the full Clifford group.
• Score: 9.843798303860343
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: We generalize the concept of folding from surface codes to CSS codes by considering certain dualities within them. In particular, this gives a general method to implement logical operations in suitable LDPC quantum codes using transversal gates and qubit permutations only. To demonstrate our approach, we specifically consider a [[30, 8, 3]] hyperbolic quantum code called Bring's code. Further, we show that by restricting the logical subspace of Bring's code to four qubits, we can obtain the full Clifford group on that subspace.

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