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2024

A note on polynomial-time tolerant testing stabilizer states

Arunachalam, Srinivasan, Bravyi, Sergey, Dutt, Arkopal

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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.

A note on polynomial-time tolerant testing stabilizer states · Around

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Entanglement in the stabilizer formalism
David Fattal, Toby S Cubitt, Yoshihisa Yamamoto, Sergey Bravyi, and Isaac L Chuang · 2004
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Ashley Montanaro · 2017
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Schur–Weyl duality for the Clifford group with applications: Property testing, a robust Hudson theorem, and de Finetti representations
David Gross, Sepehr Nezami, and Michael Walter · 2021
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