Non-Clifford gates between stabilizer codes via non-Abelian topological order
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912391962296320 |
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| author | Sajith, Rohith Song, Zijian Roberts, Brenden Menon, Varun Li, Yabo |
| author_facet | Sajith, Rohith Song, Zijian Roberts, Brenden Menon, Varun Li, Yabo |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_18265 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-Clifford gates between stabilizer codes via non-Abelian topological order Sajith, Rohith Song, Zijian Roberts, Brenden Menon, Varun Li, Yabo Quantum Physics Strongly Correlated Electrons 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. |
| title | Non-Clifford gates between stabilizer codes via non-Abelian topological order |
| topic | Quantum Physics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2505.18265 |