Abstract
Quantum superposition is a fundamental principle of quantum mechanics, so it is not surprising that equal superposition states (ESS) serve as powerful resources for quantum information processing. In this work, we propose a quantum circuit that creates an arbitrary dimensional ESS. The circuit construction is efficient as the number of required elementary gates scales polynomially with the number of required qubits. For experimental realization of the method, we use techniques of nuclear magnetic resonance (NMR).We have succeeded in preparing a 9-dimensional ESS on a 4-qubit NMR quantum register. The full tomography indicates that the fidelity of our prepared state with respect to the ideal 9-dimensional ESS is over 96%. We also prove the prepared state is pseudo-entangled by directly measuring an entanglement witness operator. Our result can be useful for the implementation of those quantum algorithms that require an ESS as an input state.
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Acknowledgments
This work was supported by the National Key Basic Research Program of China (Grant Nos. 2013CB921800, and 2014CB848700), the National Natural Science Foundation of China (Grant Nos. 11425523, 11375167, 11575173, and 11227901), the Strategic Priority Research Program (B) of the Chinese Academy of Sciences (Grant No. XDB01030400), and the Key Research Program of Frontier Sciences of the Chinese Academy of Sciences (Grant No. QYZDY-SSW-SLH004). The authors also thank ShenSen Zhao and LiHao Yang from University of Science and Technology of China for Python programming and discussion.
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Yu, Q., Zhang, Y., Li, J. et al. Generic preparation and entanglement detection of equal superposition states. Sci. China Phys. Mech. Astron. 60, 070313 (2017). https://doi.org/10.1007/s11433-017-9040-3
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DOI: https://doi.org/10.1007/s11433-017-9040-3