In order to gain comprehensive knowledge of an arbitrary unknown quantum state,one feasible way is to reconstruct it,which can be realized by finding a series of quantum operations that can refactor the unitary evolution producing the unknown state.We design an adaptive framework that can reconstruct unknown quantum states at high fidelities,which utilizes SWAP test,parameterized quantum circuits(PQCs)and layerwise learning strategy.We conduct benchmarking on the framework using numerical simulations and reproduce states of up to six qubits at more than 96％overlaps with original states on average using PQCs trained by our framework,revealing its high applicability to quantum systems of different scales theoretically.Moreover,we perform experiments on a five-qubit IBM Quantum hardware to reconstruct random unknown single qubit states,illustrating the practical performance of our framework.For a certain reconstructing fidelity,our method can effectively construct a PQC of suitable length,avoiding barren plateaus of shadow circuits and overuse of quantum resources by deep circuits,which is of much significance when the scale of the target state is large and there is no a priori information on it.This advantage indicates that it can learn credible information of unknown states with limited quantum resources,giving a boost to quantum algorithms based on parameterized circuits on near-term quantum processors.

Junxiang Xiao;Jingwei Wen;Shijie Wei;Guilu Long

State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics,Tsinghua University,Beijing 100084,China;Beijing Academy of Quantum Information Sciences,Beijing 100193,China;Frontier Science Center for Quantum Information,Beijing 100084,China;Beijing National Research Center for Information Science and Technology,Beijing 100084,China

物理学前沿

[1]Junxiang Xiao;Jingwei Wen;Shijie Wei;Guilu Long-.Reconstructing unknown quantum states using variational layerwise method)[J].物理学前沿,2022(05):130-141

layerwise,refactor,PQCs

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