Univ Sci & Technol China, Hefei Natl Lab Phys Sci Microscale, Hefei 230026, Peoples R China. Univ Sci & Technol China, Dept Modern Phys, Hefei 230026, Peoples R China. Zhejiang Univ Technol, Dept Appl Phys, Hangzhou 310023, Zhejiang, Peoples R China. Univ Waterloo, Inst Quantum Comp, Waterloo, ON N2L 3G1, Canada. Univ Guelph, Dept Math & Stat, Guelph, ON N1G 2W1, Canada. Univ Technol Sydney, Ctr Quantum Computat & Intelligent Syst, Fac Engn & Informat Technol, Sydney, NSW 2007, Australia. Tsinghua Univ, State Key Lab Low Dimens Quantum Phys, Beijing 100084, Peoples R China. Tsinghua Univ, Dept Phys, Beijing 100084, Peoples R China. Univ Guelph, Dept Phys, Guelph, ON N1G 2W1, Canada. Chinese Acad Sci, Inst Software, State Key Lab Comp Sci, Beijing 100190, Peoples R China. Canadian Inst Adv Res, Toronto, ON M5G 1Z8, Canada.
Abstract:
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 d(2)+d-1 measurement 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 (pi/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.
English Abstract:
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 d(2)+d-1 measurement 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 (pi/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.
Wang, HY,Zheng, WQ,Yu, NK,et al. Quantum state and process tomography via adaptive measurements[J]. SCIENCE CHINA-PHYSICS MECHANICS & ASTRONOMY,2016-01-01,59(10).
