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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.07265 |
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| _version_ | 1866913736939274240 |
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| author | Bauer, Andreas |
| author_facet | Bauer, Andreas |
| contents | The path-integral approach to topological quantum error correction provides a unified way to construct and analyze fault-tolerant circuits in spacetime. In this work, we demonstrate its utility and versatility at hand of a simple example: We construct a new fault-tolerant circuit for the toric-code phase by traversing its path integral on a $(x,y,z)$ cubic lattice in the $x+y$ direction. The circuit acts on qubits on a square lattice, and alternates between horizontal nearest-neighbor $CX$ gates and vertical nearest-neighbor $ZZ$ and $XX$ measurements. We show how to incorporate boundaries and corners into the fault-tolerant circuit and how to perform topologically protected logic gates. As a specific example, we consider performing a fault-tolerant logical $ZZ$ measurement via lattice surgery of two spatial rectangular blocks of our fault-tolerant circuit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_07265 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The x+y Floquet code: A simple example for topological quantum computation in the path integral approach Bauer, Andreas Quantum Physics The path-integral approach to topological quantum error correction provides a unified way to construct and analyze fault-tolerant circuits in spacetime. In this work, we demonstrate its utility and versatility at hand of a simple example: We construct a new fault-tolerant circuit for the toric-code phase by traversing its path integral on a $(x,y,z)$ cubic lattice in the $x+y$ direction. The circuit acts on qubits on a square lattice, and alternates between horizontal nearest-neighbor $CX$ gates and vertical nearest-neighbor $ZZ$ and $XX$ measurements. We show how to incorporate boundaries and corners into the fault-tolerant circuit and how to perform topologically protected logic gates. As a specific example, we consider performing a fault-tolerant logical $ZZ$ measurement via lattice surgery of two spatial rectangular blocks of our fault-tolerant circuit. |
| title | The x+y Floquet code: A simple example for topological quantum computation in the path integral approach |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2408.07265 |