Selective and efficient quantum state tomography for multiqubit systems

Quantum state tomography (QST) is a crucial tool for characterizing quantum states. However, performing full QST becomes impractical for reconstructing multiqubit density matrices since datasets and computational costs grow exponentially with qubit number. To bypass full QST, we introduce selective and efficient QST (SEEQST)—a method that enables efficient estimation of multiple selected elements of an arbitrary multiqubit density matrix. We show that any N -qubit density matrix can be partitioned into 2 N disjoint subsets, each containing 2 N elements. With SEEQST, any such subset can be accurately estimated from just two experiments with only single-qubit measurements. The complexity for estimating any subset remains constant regardless of Hilbert-space dimension, so, if desired, SEEQST can reconstruct the full density matrix, using 2 N + 1 − 1 experiments, where standard methods would use 3 N experiments. We provide a circuit decomposition for the SEEQST experiments, demonstrating that their maximum circuit depth scales logarithmically with N assuming all-to-all connectivity.