Full reconstruction of a 14-qubit state within four hours

Full quantum state tomography (FQST) plays a unique role in the estimation of the state of a quantum without a priori knowledge or assumptions. Unfortunately, since FQST requires (over) complete measurements, both the number of measurement bases and the complexity of data processing suffer an exponential growth with the size of the system. A 14-qubit entangled state has already been experimentally prepared in an ion trap, the data processing capability for FQST of a 14-qubit state seems to be far away from practical. In this paper, the computational capability of FQST is pushed forward to reconstruct a14-qubit state with a run time of only 3. 35 hours using the linear regression estimation (LRE), even when informationally overcomplete Pauli measurements are employed. The complexity of the LRE algorithm is first reduced from∼1019 to∼1015 for a 14-qubit, by dropping all the zero elements, and its computational efficiency is further sped up by fully the parallelism of the LRE algorithm with parallel Graphic Processing Unit (GPU). Our result demonstrates the effectiveness of using parallel computation to speed up the for FQST, and can play an important role in quantum information technologies with quantum systems.