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Generation of Density Matrices for Two Qubits Using Coherent and Incoherent Controls

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Abstract

In this work, we consider a pair of qubits controlled by coherent and incoherent controls. The dynamics of the two-qubit system is driven by a Gorini–Kossakowsky–Sudarchhan–Lindblad master equation where coherent control enters into the Hamiltonian and incoherent control inters into both the Hamiltonian (via Lamb shift) and the dissipative superoperator. Two classes of interaction between the system and the coherent field are considered. For this system, we analyze the control problem of generating a given target density matrix which is formulated as minimizing the Hilbert–Schmidt distance between the final density matrix and the target density matrix. Incoherent control is modeled as a sum of constant in time Gaussians with centers related with the transitions frequencies between the energy levels of the qubits. Coherent control in general formulation is considered as measurable function and in numerical experiments as piecewise constant function with constraints on magnitudes and variations. Finite-dimensional numerical optimization is performed using the dual annealing method; the corresponding results are described for some initial and target density matrices and for some set of the parameters of the control problem.

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Funding

This work is performed within the State Program of the Ministry of Science and Higher Education of the Russian Federation (project no. 0718-2020-0025).

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Authors and Affiliations

  1. Department of Mathematical Methods for Quantum Technologies, Steklov Mathematical Institute of Russian Academy of Sciences, 119991, Moscow, Russia

    O. V. Morzhin & A. N. Pechen

  2. National University of Science and Technology ‘‘MISiS’’, 119991, Moscow, Russia

    A. N. Pechen

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  1. O. V. Morzhin
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Correspondence to O. V. Morzhin or A. N. Pechen.

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O. V. Morzhin http://www.mathnet.ru/eng/person30382; A. N. Pechen is a corresponding author, http://www.mathnet.ru/eng/person17991.

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(Submitted by E. A. Turilova)

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Morzhin, O.V., Pechen, A.N. Generation of Density Matrices for Two Qubits Using Coherent and Incoherent Controls. Lobachevskii J Math 42, 2401–2412 (2021). https://doi.org/10.1134/S1995080221100176

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