Mitchell Institute for Fundamental Physics & Astronomy
College Station, Texas 77843
Quantum state tomography is an essential task in quantum information processing, which aims to reconstruct an unknown quantum state from data collected from repeated measurements. Classical shadow tomography is recently proposed as efficient quantum state tomography approach based on randomized measurements. We generalize the classical shadow tomography scheme to a broad class of finite-depth or finite-time local unitary ensembles, known as locally scrambled quantum dynamics, where the unitary ensemble is invariant under local basis transformations. In this case, the reconstruction map for the classical shadow tomography depends only on the average entanglement feature of classical snapshots. We provide an unbiased estimator of the quantum state as a linear combination of reduced classical snapshots in all subsystems, where the combination coefficients are solely determined by the entanglement feature. We numerically demonstrate our approach for finite-depth local unitary circuits and finite-time local-Hamiltonian generated evolutions. The shallow-circuit measurement can achieve a lower tomography complexity compared to the existing method based on Pauli or Clifford measurements. Our approach significantly broadens the application of classical shadow tomography on near-term quantum devices, such as trapped ion or Rydberg atom quantum simulators.