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Benchmarking a high-precision quantum operation is a big challenge for manyquantum systems in the presence of various noises as well as control errors.Here we propose an $O(1)$ benchmarking of a dynamically corrected rotation bytaking the quantum advantage of a squeezed spin state in a spin-1 Bose-Einsteincondensate. Our analytical and numerical results show that tiny rotationinfidelity, defined by $1-F$ with $F$ the rotation fidelity, can be calibratedin the order of $1/N^2$ by only several measurements of the rotation error for$N$ atoms in an optimally squeezed spin state. Such an $O(1)$ benchmarking ispossible not only in a spin-1 BEC but also in other many-spin or many-qubitsystems if a squeezed or entangled state is available.

O(1) benchmarking of precise rotation in a spin-squeezed Bose-Einstein condensate