Code switching revisited: Low-overhead magic state preparation using color codes
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arXiv
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| Format: | Preprint |
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2024
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| author | Daguerre, Lucas Kim, Isaac H. |
| author_facet | Daguerre, Lucas Kim, Isaac H. |
| contents | We propose a protocol to prepare a high-fidelity magic state on a two-dimensional (2D) color code using a three-dimensional (3D) color code. Our method modifies the known code switching protocol with (i) a recently discovered transversal gate between the 2D and the 3D code and (ii) a judicious use of flag-based postselection. We numerically demonstrate that these modifications lead to a significant improvement in the fidelity of the magic state. For instance, subjected to a uniform circuit-level noise of $10^{-3}$ (excluding idling noise), our code switching protocol yields a magic state encoded in the distance-$3$ 2D color code with a logical infidelity of $4.6\times 10^{-5}\pm 1.6 \times 10^{-5}$ (quantified by an error-corrected logical state tomography) with an $84\%$ of acceptance rate. Used in conjunction with a postselection approach, extrapolation from a polynomial fit suggests a fidelity improvement to $5.1 \times 10^{-7}$ for the same code. Our protocol is aimed for architectures that allow nonlocal connectivity and should be readily implementable in near-term devices. Finally, we also present a simulation technique akin to an extended stabilizer simulator which effectively incorporates the non-Clifford $T$-gate, that permits to simulate the protocol without resorting to a resource intensive state-vector simulation. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_07327 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Code switching revisited: Low-overhead magic state preparation using color codes Daguerre, Lucas Kim, Isaac H. Quantum Physics We propose a protocol to prepare a high-fidelity magic state on a two-dimensional (2D) color code using a three-dimensional (3D) color code. Our method modifies the known code switching protocol with (i) a recently discovered transversal gate between the 2D and the 3D code and (ii) a judicious use of flag-based postselection. We numerically demonstrate that these modifications lead to a significant improvement in the fidelity of the magic state. For instance, subjected to a uniform circuit-level noise of $10^{-3}$ (excluding idling noise), our code switching protocol yields a magic state encoded in the distance-$3$ 2D color code with a logical infidelity of $4.6\times 10^{-5}\pm 1.6 \times 10^{-5}$ (quantified by an error-corrected logical state tomography) with an $84\%$ of acceptance rate. Used in conjunction with a postselection approach, extrapolation from a polynomial fit suggests a fidelity improvement to $5.1 \times 10^{-7}$ for the same code. Our protocol is aimed for architectures that allow nonlocal connectivity and should be readily implementable in near-term devices. Finally, we also present a simulation technique akin to an extended stabilizer simulator which effectively incorporates the non-Clifford $T$-gate, that permits to simulate the protocol without resorting to a resource intensive state-vector simulation. |
| title | Code switching revisited: Low-overhead magic state preparation using color codes |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2410.07327 |