Resource-efficient shadow tomography using equatorial stabilizer measurements

Understand

We propose a resource-efficient shadow-tomography scheme using equatorial-stabilizer measurements generated from subsets of Clifford unitaries.

• For $n$-qubit systems, equatorial-stabilizer-based shadow-tomography schemes can estimate $M$ observables (up to an additive error $\varepsilon$) using $\mathcal{O}(\log(M),\mathrm{poly}(n),1/\varepsilon^2)$ sampling copies for a large class of observables, including those with traceless parts possessing polynomially-bounded Frobenius norms.
• For arbitrary quantum-state observables with a constant Frobenius norm, sampling complexity becomes $n$-independent.
• Our scheme only requires an $n$-depth controlled-$Z$~(CZ) circuit [$\mathcal{O}(n^2)$ CZ~gates] and Pauli measurements per sampling copy.