Reinforcement learning for semi-autonomous approximate quantum eigensolver

Description

The characterization of an operator by its eigenvectors and eigenvalues allows us to know its action over any quantum state. Here, we propose a protocol to obtain an approximation of the eigenvectors of an arbitrary Hermitian quantum operator. This protocol is based on measurement and feedback processes, which characterize a reinforcement learning protocol. Our proposal is composed of two systems, a black box named environment and a quantum state named agent. The role of the environment is to change any quantum state by a unitary matrix UˆE = e −iτOˆE where OˆE is a Hermitian operator, and τ is a real parameter. The agent is a quantum state which adapts to some eigenvector of OˆE by repeated interactions with the environment, feedback process, and semi-random rotations. With this proposal, we can obtain an approximation of the eigenvectors of a random qubit operator with average fidelity over 90% in less than 10 iterations, and surpass 98% in less than 300 iterations. Moreover, for the two-qubit cases, the four eigenvectors are obtained with fidelities above 89% in 8000 iterations for a random operator, and fidelities of 99% for an operator with the Bell states as eigenvectors. This protocol can be useful to implement semi-autonomous quantum devices which should be capable of extracting information and deciding with minimal resources and without human intervention.

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Programa de Financiamiento Basal para Centros Científicos y Tecnológicos de Excelencia (CONICYT)-FB0807

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EU FET-QMiCS (820505) y OpenSuperQ (820363)

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Gobierno Vasco-IT986-16

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Ministerio de Ciencia e Innovación (MICIN), Agencia Estatal de Investigación de España (AEI) y Fondo Europeo de Desarrollo Regional (FEDER)-PGC2018-095113-B-I00

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