A note on polynomial-time tolerant testing stabilizer states

Srinivasan Arunachalam; Sergey Bravyi; Arkopal Dutt

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arXiv · 2410.22220

A note on polynomial-time tolerant testing stabilizer states

Srinivasan Arunachalam·Sergey Bravyi·Arkopal Dutt

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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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Srinivasan Arunachalam, Sergey Bravyi, Arkopal Dutt. 2024-10-29. A note on polynomial-time tolerant testing stabilizer states. https://arxiv.org/abs/2410.22220

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