Reconstructing Quantum States from Sparse Measurements

Quantum state tomography (QST) is a central technique to fully characterize an unknown quantum state. However, standard QST requires exponentially growing number of measurements against the system size, which limits its application smaller systems. Here, we explore sparsity underlying and propose scheme that combines matrix product states’ representation with supervised machine learning algorithm. Our method could reconstruct sparse states very high precision using only portion measurement data in randomly selected basis set. In particular, demonstrate Wolfgang be faithfully reconstructed around 25% whole basis, generated states, efficiently represented as bases scales sub-exponentially size.