Quantum state and process tomography via adaptive measurements

• Published in: Science China. Physics, mechanics & astronomy Vol. 59; no. 10; pp. 25 - 32
• Main Authors: Wang, HengYan, Zheng, WenQiang, Yu, NengKun, Li, KeRen, Lu, DaWei, Xin, Tao, Li, Carson, Ji, ZhengFeng, Kribs, David, Zeng, Bei, Peng, XinHua, Du, JiangFeng
• Format: Journal Article
• Language: English
• Published: Beijing Science China Press 01.10.2016; Springer Nature B.V
• Subjects: Astronomy; Channels; Classical and Continuum Physics; Data processing; Hadamard门; Hilbert space; NMR; Nuclear magnetic resonance; Observations and Techniques; Physics; Physics and Astronomy; Quantum phenomena; Quantum theory; Qubits (quantum computing); Tomography; 希尔伯特空间; 核磁共振系统; 渠道系统; 自适应测量; 过程层析成像; 量子信息处理; 量子态; quantum tomography; state reconstruction; nuclear magnetic resonance
• ISSN: 1674-7348; 1869-1927
• DOI: 10.1007/s11433-016-0287-y

We investigate quantum state tomography（QST） for pure states and quantum process tomography（QPT） for unitary channels via adaptive measurements. For a quantum system with a d-dimensional Hilbert space, we first propose an adaptive protocol where only 2d. 1 measurement outcomes are used to accomplish the QST for all pure states. This idea is then extended to study QPT for unitary channels, where an adaptive unitary process tomography（AUPT） protocol of d2＋d.1measurement outcomes is constructed for any unitary channel. We experimentally implement the AUPT protocol in a 2-qubit nuclear magnetic resonance system. We examine the performance of the AUPT protocol when applied to Hadamard gate, T gate（/8 phase gate）, and controlled-NOT gate,respectively, as these gates form the universal gate set for quantum information processing purpose. As a comparison, standard QPT is also implemented for each gate. Our experimental results show that the AUPT protocol that reconstructing unitary channels via adaptive measurements significantly reduce the number of experiments required by standard QPT without considerable loss of fidelity.