A convex-optimization-based quantum process tomography method for reconstructing quantum channels

Quantum process tomography is often used to completely characterize an unknown quantum process. However, it may lead to an unphysical process matrix, which will cause the loss of information with respect to the tomography result. Professor Xian-Min Jin and his group from Center for Quantum Information Technologies in Shanghai Jiao Tong University (SJTU) reported a new quantum process tomography method which is based on convex optimization. They demonstrated that this new method is able to minimize the errors between the process matrix and the experimental results effectively and works well both in unitary and non-unitary quantum channels. This work was published in Science Bulletin.

As for a general quantum channel, it might include a series of non-unitary operations. However, previous researches mainly focus on the unitary and near-unitary operations while there are few studies on the non-unitary operations.

Professor Jin chose the seawater channel as a benchmark to test their method. The seawater channel is one of the key channels for global quantum communication, which can serve as a typical representation for the general quantum channel. Their method revealed the true action of the seawater quantum channel more accurately and could well maintain the physical properties. They further tested it on the seven fundamental gates, showing that this new method can reveal the quantum channel more precisely and robustly without preliminary parameter adjustments. In addition, they prepared a series of non-unitary quantum channel. Compared with previous tomography methods, they still can reach up to 99.5% accuracy in this scenario.

Because each element of the process matrix represents different operations, it is necessary to determine each value precisely if we want to reveal the true action of the quantum channel. The work from Professor Xian-Min Jin and his group offers a more universal tool for further analyses on the general quantum channels.

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Xuan-Lun Huang, Jun Gao, Zhi-Qiang Jiao, Zeng-Quan Yan, Zhe-Yong Zhang, Dan-Yang Chen, Xi Zhang, Ling Ji, Xian-MinJin. Reconstruction of quantum channel via convex optimization. Science Bulletin, 2020, 65(4):286-292. doi: 10.1016/j.scib.2019.11.009

https://www.sciencedirect.com/science/article/pii/S2095927319306413