Universal transversal gates
Fuente:
arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913564381413376 |
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| author | Gupta, Pragati Morello, Andrea Sanders, Barry C. |
| author_facet | Gupta, Pragati Morello, Andrea Sanders, Barry C. |
| contents | A long-standing challenge in quantum error correction is the infeasibility of universal transversal gates, as shown by the Eastin-Knill theorem. We obtain a necessary and sufficient condition for a quantum code to have universal transversal gates and show that the Eastin-Knill no-go result is a special case that does not hold for a general error model. We present a code construction using $n$ $d$-dimensional systems that changes the logical error probability from a lower bound $Ω(1/n\log d)$ to an upper bound $\mathcal O (1/n d)$ and allows exact correction of both local and correlated errors. Our universality condition determines the existence of a universal gate set for any quantum error-correcting code. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_07045 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Universal transversal gates Gupta, Pragati Morello, Andrea Sanders, Barry C. Quantum Physics A long-standing challenge in quantum error correction is the infeasibility of universal transversal gates, as shown by the Eastin-Knill theorem. We obtain a necessary and sufficient condition for a quantum code to have universal transversal gates and show that the Eastin-Knill no-go result is a special case that does not hold for a general error model. We present a code construction using $n$ $d$-dimensional systems that changes the logical error probability from a lower bound $Ω(1/n\log d)$ to an upper bound $\mathcal O (1/n d)$ and allows exact correction of both local and correlated errors. Our universality condition determines the existence of a universal gate set for any quantum error-correcting code. |
| title | Universal transversal gates |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2410.07045 |