A note on polynomial-time tolerant testing stabilizer states
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914997017247744 |
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| author | Arunachalam, Srinivasan Bravyi, Sergey Dutt, Arkopal |
| author_facet | Arunachalam, Srinivasan Bravyi, Sergey Dutt, Arkopal |
| contents | We show an improved inverse theorem for the Gowers-$3$ norm of $n$-qubit quantum states $|ψ\rangle$ which states that: for every $γ\geq 0$, if the $\textsf{Gowers}(|ψ\rangle,3)^8 \geq γ$ then the stabilizer fidelity of $|ψ\rangle$ is at least $γ^C$ for some constant $C>1$. This implies a constant-sample polynomial-time tolerant testing algorithm for stabilizer states which accepts if an unknown state is $\varepsilon_1$-close to a stabilizer state in fidelity and rejects when $|ψ\rangle$ is $\varepsilon_2 \leq \varepsilon_1^C$-far from all stabilizer states, promised one of them is the case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_22220 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on polynomial-time tolerant testing stabilizer states Arunachalam, Srinivasan Bravyi, Sergey Dutt, Arkopal Quantum Physics Computational Complexity Data Structures and Algorithms We show an improved inverse theorem for the Gowers-$3$ norm of $n$-qubit quantum states $|ψ\rangle$ which states that: for every $γ\geq 0$, if the $\textsf{Gowers}(|ψ\rangle,3)^8 \geq γ$ then the stabilizer fidelity of $|ψ\rangle$ is at least $γ^C$ for some constant $C>1$. This implies a constant-sample polynomial-time tolerant testing algorithm for stabilizer states which accepts if an unknown state is $\varepsilon_1$-close to a stabilizer state in fidelity and rejects when $|ψ\rangle$ is $\varepsilon_2 \leq \varepsilon_1^C$-far from all stabilizer states, promised one of them is the case. |
| title | A note on polynomial-time tolerant testing stabilizer states |
| topic | Quantum Physics Computational Complexity Data Structures and Algorithms |
| url | https://arxiv.org/abs/2410.22220 |