Planar fault-tolerant circuits for non-Clifford gates on the 2D color code
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909604584095744 |
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| author | Bauer, Andreas de la Fuente, Julio C. Magdalena |
| author_facet | Bauer, Andreas de la Fuente, Julio C. Magdalena |
| contents | We introduce a family of scalable planar fault-tolerant circuits that implement logical non-Clifford operations on a 2D color code, such as a logical $T$ gate or a logical non-Pauli measurement that prepares a magic $|T\rangle$ state. The circuits are relatively simple, consisting only of physical $T$ gates, $CX$ gates, and few-qubit measurements. They can be implemented with an array of qubits on a 2D chip with nearest-neighbor couplings, and no wire crossings. The construction is based on a spacetime path integral representation of a non-Abelian 2+1D topological phase, which is related to the 3D color code. We turn the path integral into a circuit by expressing it as a spacetime $ZX$ tensor network, and then traversing it in some chosen time direction. We describe in detail how fault tolerance is achieved using a "just-in-time" decoding strategy, for which we repurpose and extend state-of-the-art color-code matching decoders. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_05175 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Planar fault-tolerant circuits for non-Clifford gates on the 2D color code Bauer, Andreas de la Fuente, Julio C. Magdalena Quantum Physics Strongly Correlated Electrons We introduce a family of scalable planar fault-tolerant circuits that implement logical non-Clifford operations on a 2D color code, such as a logical $T$ gate or a logical non-Pauli measurement that prepares a magic $|T\rangle$ state. The circuits are relatively simple, consisting only of physical $T$ gates, $CX$ gates, and few-qubit measurements. They can be implemented with an array of qubits on a 2D chip with nearest-neighbor couplings, and no wire crossings. The construction is based on a spacetime path integral representation of a non-Abelian 2+1D topological phase, which is related to the 3D color code. We turn the path integral into a circuit by expressing it as a spacetime $ZX$ tensor network, and then traversing it in some chosen time direction. We describe in detail how fault tolerance is achieved using a "just-in-time" decoding strategy, for which we repurpose and extend state-of-the-art color-code matching decoders. |
| title | Planar fault-tolerant circuits for non-Clifford gates on the 2D color code |
| topic | Quantum Physics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2505.05175 |