Non-Clifford gates between stabilizer codes via non-Abelian topological order

• URL: http://arxiv.org/abs/2505.18265v1
• Date: Fri, 23 May 2025 18:01:38 GMT
• Title: Non-Clifford gates between stabilizer codes via non-Abelian topological order
• Authors: Rohith Sajith, Zijian Song, Brenden Roberts, Varun Menon, Yabo Li,
• Abstract summary: We propose protocols to implement non-Clifford logical gates between stabilizer codes by entangling into a non-Abelian topological order as an intermediate step.<n>Generalizing previous approaches, we provide a framework that generates a large class of non-Clifford and non-diagonal logical gates between qudit surface codes.
• Score: 2.3662819244688182
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We propose protocols to implement non-Clifford logical gates between stabilizer codes by entangling into a non-Abelian topological order as an intermediate step. Generalizing previous approaches, we provide a framework that generates a large class of non-Clifford and non-diagonal logical gates between qudit surface codes by gauging the topological symmetry of symmetry-enriched topological orders. As our main example, we concretely detail a protocol that utilizes the quantum double of $S_3$ to generate a controlled-charge conjugation ($C\mathcal{C}$) gate between a qubit and qutrit surface code. Both the preparation of non-Abelian states and logical state injection between the Abelian and non-Abelian codes are executed via finite-depth quantum circuits with measurement and feedforward. We discuss aspects of the fault-tolerance of our protocol, presenting insights on how to construct a heralded decoder for the quantum double of $S_3.$ We also outline how analogous protocols can be used to obtain logical gates between qudit surface codes by entangling into $\mathcal{D}(G),$ where $G$ is a semidirect product of Abelian groups. This work serves as a step towards classifying the computational power of non-Abelian quantum phases beyond the paradigm of anyon braiding on near-term quantum devices.

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