arXiv subjects

Oleg Morzhin

Publications and source records attributed to Oleg Morzhin.

7 recordsLinked to original sources

arXiv2025

Gradient projection method for constrained quantum control

In this work, we adopt the Gradient Projection Method (GPM) to problems of quantum control. For general $N$-level closed and open quantum systems, we derive the corresponding adjoint systems and gradients of the objective functionals, and provide the projection versions of the Pontryagin maximum principle and the GPM, all directly in terms of quantum objects such as evolution operator, Hamiltonians, density matrices, etc. Various forms of the GPM, including one- and two-step, are provided and compared. We formulate the GPM both for closed and open quantum systems, latter for the general case with simultaneous coherent and incoherent controls. The GPM is designed to perform local gradient based optimization in the case when bounds are imposed on the controls. The main advantage of the method is that it allows to exactly satisfy the bounds, in difference to other approaches such as adding constraints as weight to objective. We apply the GPM to several examples including generation of one- and two-qubit gates and two-qubit Bell and Werner states for models of superconducting qubits under the constraint when controls are zero at the initial and final times, and steering an open quantum system state to a target density matrix for simulating action of the Werner-Holevo channel, etc.

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arXiv2024

Control of the von Neumann Entropy for an Open Two-Qubit System Using Coherent and Incoherent Drives

This article is devoted to developing an approach for manipulating the von Neumann entropy $S(ρ(t))$ of an open two-qubit system with coherent control and incoherent control inducing time-dependent decoherence rates. The following goals are considered: (a) minimizing or maximizing the final entropy $S(ρ(T))$; (b) steering $S(ρ(T))$ to a given target value; (c) steering $S(ρ(T))$ to a target value and satisfying the pointwise state constraint $S(ρ(t)) \leq \overline{S}$ for a given $\overline{S}$; (d) keeping $S(ρ(t))$ constant at a given time interval. Under the Markovian dynamics determined by a Gorini--Kossakowski--Sudarshan--Lindblad type master equation, which contains coherent and incoherent controls, one- and two-step gradient projection methods and genetic algorithm have been adapted, taking into account the specifics of the objective functionals. The corresponding numerical results are provided and discussed.

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arXiv2023

Generation of C-NOT, SWAP, and C-Z Gates for Two Qubits Using Coherent and Incoherent Controls and Stochastic Optimization

In this work, we consider a general form of the dynamics of open quantum systems determined by the Gorini-Kossakowsky-Sudarchhan-Lindblad type master equation with simultaneous coherent and incoherent controls with three particular forms of the two-qubit Hamiltonians. Coherent control enters in the Hamiltonian and incoherent control enters in both the Hamiltonian and the superoperator of dissipation. For these systems, we analyze the control problems of generating two-qubit C-NOT, SWAP, and C-Z gates using with piecewise constant controls and stochastic optimization in the form of an adapted version of the dual annealing algorithm. In the numerical experiment, we analyze the minimal infidelity obtained by the dual annealing for various values of strength of the interaction between the system and the environment.

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arXiv2023

Krotov Type Optimization of Coherent and Incoherent Controls for Open Two-Qubit Systems

This work considers two-qubit open quantum systems driven by coherent and incoherent controls. Incoherent control induces time-dependent decoherence rates via time-dependent spectral density of the environment which is used as a resource for controlling the system. The system evolves according to the Gorini-Kossakowski-Sudarshan-Lindblad master equation with time-dependent coefficients. For two types of interaction with coherent control, three types of objectives are considered: 1) maximizing the Hilbert-Schmidt overlap between the final and target density matrices; 2) minimizing the Hilbert-Schmidt distance between these matrices; 3) steering the overlap to a given value. For the first problem, we develop the Krotov type methods directly in terms of density matrices with or without regularization for piecewise continuous constrained controls and find the cases where the methods produce (either exactly or with some precision) zero controls which satisfy the Pontryagin maximum principle and produce the overlap's values close to their upper estimates. For the problems 2) and 3), we find cases when the dual annealing method steers the objectives close to zero and produces a non-zero control.

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arXiv2023

Optimization of Time-Dependent Decoherence Rates and Coherent Control for a Qutrit System

The work considers an open qutrit system whose density matrix $ρ(t)$ evolution is governed by the Gorini-Kossakowski-Sudarshan-Lindblad master equation with simultaneous coherent (in the Hamiltonian) and incoherent (in the superoperator of dissipation) controls. Incoherent control makes the decoherence rates depending on time in a specific controlled manner and within clear physical mechanics. We consider the problem of maximizing the Hilbert-Schmidt overlap between the system's final state $ρ(T)$ and a given target state $ρ_{\rm target}$ and the problem of minimizing the squared Hilbert-Schmidt distance between these states. For the both problems, we perform their realifications, derive the corresponding Pontryagin function, adjount system (with the two cases of transversality conditions in view of the two terminal objectives), and gradients of the objectives, adapt the one-, two-, three-step gradient projection methods. For the problem of maximizing the overlap, we also adapt the regularized first-order Krotov method. In the numerical experiments, we analyze, first, the methods' operation and, second, the obtained control processes, in respect to considering the environment as a resource via incoherent control.

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arXiv2023

Optimal State Manipulation for a Two-Qubit System Driven by Coherent and Incoherent Controls

Optimal control of two-qubit quantum systems attracts high interest due to applications ranging from two-qubit gate generation to optimization of receiver for transferring coherence matrices along spin chains. State preparation and manipulation is among important tasks to study for such systems. Typically coherent control, e.g. a shaped laser pulse, is used to manipulate two-qubit systems. However, the environment can also be used $\unicode{x2013}$ as an incoherent control resource. In this article, we consider optimal state manipulation for a two-qubit system whose dynamics is governed by the Gorini-Kossakowski-Sudarshan-Lindblad master equation, where coherent control enters into the Hamiltonian and incoherent control into both the Hamiltonian (via Lamb shift) and the superoperator of dissipation. We exploit two physically different classes of interaction with coherent control and optimize the Hilbert-Schmidt overlap between final and target density matrices, including optimization of its steering to a given value. We find the conditions when zero coherent and incoherent controls satisfy the Pontryagin maximum principle, and in addition, when they form a stationary point of the objective functional. Moreover, we find a case when this stationary point provides the globally minimal value of the overlap. Using upper and lower bounds for the overlap, we develop one- and two-step gradient projection methods operating with functional controls.

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arXiv2019

Krotov Method for Optimal Control in Closed Quantum Systems

Mathematical problems of optimal control in quantum systems attract high interest in connection with fundamental questions and existing and prospective applications. An important problem is the development of methods for constructing controls for quantum systems. One of the commonly used methods is the Krotov method initially proposed beyond quantum control in the articles by V.F.~Krotov and I.N.~Feldman (1978, 1983). The method was used to develop a novel approach for finding optimal controls for quantum systems in [D.J. Tannor, V. Kazakov, V. Orlov, In: Time-Dependent Quantum Molecular Dynamics, Boston, Springer, 347--360 (1992)] and [J.~Somlói, V.A.~Kazakov, D.J.~Tannor, Chem. Phys., 172:1, 85--98 (1993)], and in many works of various scientists, as described in details in this review. The review discusses mathematical aspects of this method for optimal control of closed quantum systems. It outlines various modifications with respect to defining the improvement function (which in most cases is linear or linear-quadratic), constraints on control spectrum and on the states of a quantum system, regularizers, etc. The review describes applications of the Krotov method to control of molecular dynamics, manipulation of Bose-Einstein condensate, quantum gate generation. We also discuss comparison with GRAPE (GRadient Ascent Pulse Engineering), CRAB (Chopped Random-Basis), the Zhu---Rabitz and the Maday---Turinici methods.

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