A note on polynomial-time tolerant testing stabilizer states
A note on polynomial-time tolerant testing stabilizer states
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 …