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Full reconstruction of a 14-qubit state within four hours

Zhibo Hou, Han-Sen Zhong, Ye Tian, Daoyi Dong, Bo Qi, Li Li, Yuanlong Wang, Franco Nori, Guo-Yong Xiang, Chuan-Feng Li, Guang-Can Guo
Key Laboratory of Quantum Information, University of Science and Technology of China, CAS, Hefei, 230026, People’s Republic of China
arXiv:1602.08604 [quant-ph], (27 Feb 2016)
@article{hou2016full,

   title={Full reconstruction of a 14-qubit state within four hours},

   author={Hou, Zhibo and Zhong, Han-Sen and Tian, Ye and Dong, Daoyi and Qi, Bo and Li, Li and Wang, Yuanlong and Nori, Franco and Xiang, Guo-Yong and Li, Chuan-Feng and Guo, Guang-Can},

   year={2016},

   month={feb},

   archivePrefix={"arXiv"},

   primaryClass={quant-ph}

}

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Full quantum state tomography (FQST) plays a unique role in the estimation of the state of a quantum system without a priori knowledge or assumptions. Unfortunately, since FQST requires informationally (over)complete measurements, both the number of measurement bases and the computational complexity of data processing suffer an exponential growth with the size of the quantum system. A 14-qubit entangled state has already been experimentally prepared in an ion trap, and the data processing capability for FQST of a 14-qubit state seems to be far away from practical applications. In this paper, the computational capability of FQST is pushed forward to reconstruct a 14-qubit state with a run time of only 3.35 hours using the linear regression estimation (LRE) algorithm, even when informationally overcomplete Pauli measurements are employed. The computational 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 zero elements, and its computational efficiency is further sped up by fully exploiting the parallelism of the LRE algorithm with parallel Graphic Processing Unit (GPU) programming. Our result can play an important role in quantum information technologies with large quantum systems.
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