A note on polynomial-time tolerant testing stabilizer states

• URL: http://arxiv.org/abs/2410.22220v1
• Date: Tue, 29 Oct 2024 16:49:33 GMT
• Title: A note on polynomial-time tolerant testing stabilizer states
• Authors: Srinivasan Arunachalam, Sergey Bravyi, Arkopal Dutt,
• Abstract summary: We show an improved inverse theorem for the Gowers-$3$ of $n$-qubit quantum states $|psirangle. For every $gammageq 0$, if the $textsfGowers(|psi rangle,3)8 geq gamma then stabilizer fidelity of $|psirangle$ is at least $gammaC$ for some constant $C>1$.
• Score: 6.458742319938316
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• Abstract: We show an improved inverse theorem for the Gowers-$3$ norm of $n$-qubit quantum states $|\psi\rangle$ which states that: for every $\gamma\geq 0$, if the $\textsf{Gowers}(|\psi \rangle,3)^8 \geq \gamma$ then the stabilizer fidelity of $|\psi\rangle$ is at least $\gamma^C$ 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 $|\psi\rangle$ is $\varepsilon_2 \leq \varepsilon_1^C$-far from all stabilizer states, promised one of them is the case.

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