Low Overhead Qutrit Magic State Distillation
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arXiv
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| Format: | Preprint |
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2024
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| author | Prakash, Shiroman Saha, Tanay |
| author_facet | Prakash, Shiroman Saha, Tanay |
| contents | We show that using qutrits rather than qubits leads to a substantial reduction in the overhead cost associated with an approach to fault-tolerant quantum computing known as magic state distillation. We construct a family of $[[9m-k, k, 2]]_3$ triorthogonal qutrit error-correcting codes for any positive integers $m$ and $k$ with $k \leq 3m-2$ that are suitable for magic state distillation. In magic state distillation, the number of ancillae required to produce a magic state with target error rate $ε$ is $O(\log^γε^{-1})$, where the yield parameter $γ$ characterizes the overhead cost. For $k=3m-2$, our codes have $γ= \log_2 (2+\frac{6}{3 m-2})$, which tends to $1$ as $m \to \infty$. Moreover, the $[[20,7,2]]_3$ qutrit code that arises from our construction when $m=3$ already has a yield parameter of $1.51$ which outperforms all known qubit triorthogonal codes of size less than a few hundred qubits. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_06228 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Low Overhead Qutrit Magic State Distillation Prakash, Shiroman Saha, Tanay Quantum Physics We show that using qutrits rather than qubits leads to a substantial reduction in the overhead cost associated with an approach to fault-tolerant quantum computing known as magic state distillation. We construct a family of $[[9m-k, k, 2]]_3$ triorthogonal qutrit error-correcting codes for any positive integers $m$ and $k$ with $k \leq 3m-2$ that are suitable for magic state distillation. In magic state distillation, the number of ancillae required to produce a magic state with target error rate $ε$ is $O(\log^γε^{-1})$, where the yield parameter $γ$ characterizes the overhead cost. For $k=3m-2$, our codes have $γ= \log_2 (2+\frac{6}{3 m-2})$, which tends to $1$ as $m \to \infty$. Moreover, the $[[20,7,2]]_3$ qutrit code that arises from our construction when $m=3$ already has a yield parameter of $1.51$ which outperforms all known qubit triorthogonal codes of size less than a few hundred qubits. |
| title | Low Overhead Qutrit Magic State Distillation |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2403.06228 |