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Full quantum state tomography (FQST) plays a unique role in the estimation ofthe state of a quantum system without \emph{a priori} knowledge or assumptions.Unfortunately, since FQST requires informationally (over)complete measurements,both the number of measurement bases and the computational complexity of dataprocessing suffer an exponential growth with the size of the quantum system. A14-qubit entangled state has already been experimentally prepared in an iontrap, and the data processing capability for FQST of a 14-qubit state seems tobe far away from practical applications. In this paper, the computationalcapability of FQST is pushed forward to reconstruct a 14-qubit state with a runtime of only 3.35 hours using the linear regression estimation (LRE) algorithm,even when informationally overcomplete Pauli measurements are employed. Thecomputational complexity of the LRE algorithm is first reduced from$O(10^{19})$ to $O(10^{15})$ for a 14-qubit state, by dropping all the zeroelements, and its computational efficiency is further sped up by fullyexploiting the parallelism of the LRE algorithm with parallel GraphicProcessing Unit (GPU) programming. Our result can play an important role inquantum information technologies with large quantum systems.

Full reconstruction of a 14-qubit state within four hours