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Intelligent optimization based density matrix reconstruction method with semi-positive constraint.

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Názov: Intelligent optimization based density matrix reconstruction method with semi-positive constraint.
Autori: Meng, Xiaomin1 (AUTHOR) 21220854000161@hainanu.edu.cn, Han, Zhiguang1 (AUTHOR) hanzhiguang@hainanu.edu.cn, Cong, Jingyu1 (AUTHOR) jingyuconghnu@126.com, Guo, Xiaowan1 (AUTHOR) xiaowanguo2021@163.com
Zdroj: Results in Physics. Aug2023, Vol. 51, pN.PAG-N.PAG. 1p.
Abstrakt: • We propose a method that combines maximum likelihood (ML) estimation with a population intelligence optimization algorithm. • The proposed method was used to successfully reconstruct the separable and entangled states of multiple qubits on an IBM quantum processor. • Our method ensures that a physically valid density matrix is reconstructed with higher fidelity than the standard QST method. • The maximum likelihood method based on a population intelligence optimization algorithm proved to be more effective with a limited number of measurements. Quantum state tomography (QST) is a technique used to reconstruct the density matrix of unknown quantum states based on experimentally obtained measurements. QST is a fundamental tool in the field of quantum information and quantum technology. It is commonly employed to assess the quality and limitations of experimental platforms. However, the density matrix reconstructed using the standard QST method often fails to guarantee semi-positive definiteness, which is physically unacceptable, due to limitations imposed by the randomness of quantum state measurements, noise in practical applications, and the number of measurements. To address this issue, a method is proposed that combines maximum likelihood (ML) estimation with population intelligence optimization algorithms. First, the issue of guaranteeing the semi-positive definiteness of the density matrix reconstructed using standard QST methods is analyzed. Subsequently, the ML method is introduced, and four commonly used population intelligence optimization algorithms are applied to find the density matrix that maximizes the likelihood of reproducing the experimental measurements. Finally, the superiority of the proposed method is demonstrated using an IBM Quantum (IBMQ) processor in scenarios involving separable and entangled states of multiple qubits, and compared with the standard QST method. [ABSTRACT FROM AUTHOR]
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Abstrakt:• We propose a method that combines maximum likelihood (ML) estimation with a population intelligence optimization algorithm. • The proposed method was used to successfully reconstruct the separable and entangled states of multiple qubits on an IBM quantum processor. • Our method ensures that a physically valid density matrix is reconstructed with higher fidelity than the standard QST method. • The maximum likelihood method based on a population intelligence optimization algorithm proved to be more effective with a limited number of measurements. Quantum state tomography (QST) is a technique used to reconstruct the density matrix of unknown quantum states based on experimentally obtained measurements. QST is a fundamental tool in the field of quantum information and quantum technology. It is commonly employed to assess the quality and limitations of experimental platforms. However, the density matrix reconstructed using the standard QST method often fails to guarantee semi-positive definiteness, which is physically unacceptable, due to limitations imposed by the randomness of quantum state measurements, noise in practical applications, and the number of measurements. To address this issue, a method is proposed that combines maximum likelihood (ML) estimation with population intelligence optimization algorithms. First, the issue of guaranteeing the semi-positive definiteness of the density matrix reconstructed using standard QST methods is analyzed. Subsequently, the ML method is introduced, and four commonly used population intelligence optimization algorithms are applied to find the density matrix that maximizes the likelihood of reproducing the experimental measurements. Finally, the superiority of the proposed method is demonstrated using an IBM Quantum (IBMQ) processor in scenarios involving separable and entangled states of multiple qubits, and compared with the standard QST method. [ABSTRACT FROM AUTHOR]
ISSN:22113797
DOI:10.1016/j.rinp.2023.106661