Breaking even with magic: demonstration of a high-fidelity logical non-Clifford gate
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arXiv
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| Format: | Preprint |
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2025
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| author | Dasu, Shival Burton, Simon Mayer, Karl Amaro, David Gerber, Justin A. Gilmore, Kevin Gresh, Dan DelVento, Davide Potter, Andrew C. Hayes, David |
| author_facet | Dasu, Shival Burton, Simon Mayer, Karl Amaro, David Gerber, Justin A. Gilmore, Kevin Gresh, Dan DelVento, Davide Potter, Andrew C. Hayes, David |
| contents | Encoding quantum information to protect it from errors is essential for performing large-scale quantum computations. Performing a universal set of quantum gates on encoded states demands a potentially large resource overhead and minimizing this overhead is key for the practical development of large-scale fault-tolerant quantum computers. We propose and experimentally implement a magic-state preparation protocol to fault-tolerantly prepare a pair of logical magic states in a [[6,2,2]] quantum error-detecting code using only eight physical qubits. Implementing this protocol on H1-1, a 20 qubit trapped-ion quantum processor, we prepare magic states with experimental infidelity $7^{+3}_{-1}\times 10^{-5}$ with a $14.8^{+1}_{-1}\%$ discard rate and use these to perform a fault-tolerant non-Clifford gate, the controlled-Hadamard (CH), with logical infidelity $\leq 2.3^{+9}_{-9}\times 10^{-4}$. Notably, this significantly outperforms the unencoded physical CH infidelity of $10^{-3}$. Through circuit-level stabilizer simulations, we show that this protocol can be self-concatenated to produce extremely high-fidelity magic states with low space-time overhead in a [[36,4,4]] quantum error correcting code, with logical error rates of $6\times 10^{-10}$ ($5\times 10^{-14}$) at two-qubit error rate of $10^{-3}$ ($10^{-4}$) respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_14688 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Breaking even with magic: demonstration of a high-fidelity logical non-Clifford gate Dasu, Shival Burton, Simon Mayer, Karl Amaro, David Gerber, Justin A. Gilmore, Kevin Gresh, Dan DelVento, Davide Potter, Andrew C. Hayes, David Quantum Physics Encoding quantum information to protect it from errors is essential for performing large-scale quantum computations. Performing a universal set of quantum gates on encoded states demands a potentially large resource overhead and minimizing this overhead is key for the practical development of large-scale fault-tolerant quantum computers. We propose and experimentally implement a magic-state preparation protocol to fault-tolerantly prepare a pair of logical magic states in a [[6,2,2]] quantum error-detecting code using only eight physical qubits. Implementing this protocol on H1-1, a 20 qubit trapped-ion quantum processor, we prepare magic states with experimental infidelity $7^{+3}_{-1}\times 10^{-5}$ with a $14.8^{+1}_{-1}\%$ discard rate and use these to perform a fault-tolerant non-Clifford gate, the controlled-Hadamard (CH), with logical infidelity $\leq 2.3^{+9}_{-9}\times 10^{-4}$. Notably, this significantly outperforms the unencoded physical CH infidelity of $10^{-3}$. Through circuit-level stabilizer simulations, we show that this protocol can be self-concatenated to produce extremely high-fidelity magic states with low space-time overhead in a [[36,4,4]] quantum error correcting code, with logical error rates of $6\times 10^{-10}$ ($5\times 10^{-14}$) at two-qubit error rate of $10^{-3}$ ($10^{-4}$) respectively. |
| title | Breaking even with magic: demonstration of a high-fidelity logical non-Clifford gate |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2506.14688 |