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Direct measurement of the winding number in quantum walks
Prof. Chuan-Feng Li, Prof. Yong-Jian Han and Dr. Xiao-Ye Xu, from Key Laboratory of Quantum Information, and their team, have made breakthrough in the field of quantum walks and their topology. They built a large-scale quantum-walk platform up to 50 steps based on the time multiplexing protocol. Further they directly measured the winding number in a quantum walk with chiral symmetry for the first time. The result was published online in ‘Physical Review Letters’ on June 27.
Quantum walks, extended from the classical random walks theory, have always been useful models in quantum information. It has been pointed out that even universal quantum computation can be built up based on quantum walks. Although quantum walks have been well understood in theory, the experimental implementations, no matter in what physical systems, always face challenges both in scale and in complexity. Photons, acted as good walkers, can walk in time line, between beams or in orbital angular momentum, while the improvement of scale, especially in the scenario with genuine single photons, keeps challenging scientists. The group led by Prof. Li found a novel way to improve the scale of the walk. They implemented 'spin-orbit' coupling by using the birefringent crystals cut collinearly. Their scheme avoid the intrinsic loss in traditional time multiplexing protocols. For the collinear structure of the interferometer, the system is ultra-stable, as a result, is very useful for implementing quantum walks with adopting genuine single photons as the walker. The group demonstrate a 50-step Hadamard quantum walk of herald single photons within a high fidelity.
As pure dynamic systems with spin-orbit couplings, recently quantum walks have been extended to investigate topology. Theoretical proceedings make the complete topological classifications of quantum walks clear, it is found that two bulk invariants can completely determine the topological phases. Experimental observations of the topology in quantum walks have been presented in various schemes. However, these methods are indirect, which based on the bulk-edge corresponding. Direct measurement of the bulk topological invariants in quantum walks have never been attempted before. The challenges are derived from the requirement of the full knowledge of the system’s ground wave function. The group developed a method to measure and reconstruct the final wave function, furthermore directly read out the bulk topological invariants, i.e., winding numbers, in a quantum walk with chiral symmetry.
The results provide an intuitive perspective for understanding the topology in periodically driven quantum systems. The novel platform provides a significant tool for investigating the topology. The scheme for implementing large scale quantum walks can be further developed to quantum information.
The research gets supports by Chinese Academy of Sciences, Ministry of Science and Technology, National Natural Science Foundation, Ministry of Education and China Postdoctoral Science Foundation.
(School of Physical Sciences,USTC)