Abstract
Quantum image retrieval is an exhaustive work due to exponential measurements. Casting aside the background of image processing, quantum image is a pure many-body state, and the retrieval task is a physical process named as quantum state tomography. Tomography of a special class of states, permutationally symmetric states, just needs quadratic measurement scales with the number of qubits. In order to take advantage of this result, we propose a method to map the main energy of the image to these states. First, we deduce that \(n+1\) permutationally symmetric states can be constructed as bases of \(2^n\) Hilbert space (n qubits) at least. Second, we execute Schmidt decomposition by continually bipartite splitting of the quantum image (state). At last, we select \(n+1\) maximum coefficients, do base transformation to map these coefficients to new bases (permutationally symmetric states). By these means, the quantum image with high retrieval performance can be gotten.
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Acknowledgments
This work is supported by the National Natural Science Foundation of China (Grant No. 61170321,61502101), Natural Science Foundation of Jiangsu Province, China (Grant No. BK20140651), Research Fund for the Doctoral Program of Higher Education (Grant No. 20110092110024) and the open fund of Key Laboratory of Computer Network and Information Integration In Southeast University, Ministry of Education, China (Grant No. K93-9-2015-10C).
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Ruan, Y., Chen, H., Liu, Z. et al. Quantum image with high retrieval performance. Quantum Inf Process 15, 637–650 (2016). https://doi.org/10.1007/s11128-015-1208-5
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DOI: https://doi.org/10.1007/s11128-015-1208-5