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

Моржин, О. В.; Pechen, Alexander

doi:10.1134/s1995080221100176

Cited by 12 publications

(14 citation statements)

References 33 publications

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“…Global search genetic evolutionary algorithm was used for optimization of time-independent incoherent control in such systems driven by a GKSL master equation in [6]. The recent article [50] considers a two-qubit system with timedependent coherent control and time-independent incoherent control.…”

Section: Introductionmentioning

confidence: 99%

“…The interaction operator V u(t) = V u(t) is defined, in general, with some arbitrary Hermitian matrix V and, in particular, as in [50], we consider the following two types:…”

Section: Introductionmentioning

confidence: 99%

“…Following [50], the computational approach reduces the system (1) including ( 2), ( 3), ( 7), (8), and ( 9) with interaction operator V defined either by (5) or by (6) to the corresponding form in terms of real states by considering real and imaginary parts of the matrix elements of density matrix ρ. Taking into account the Hermiticity of the density matrix, denote…”

Section: Introductionmentioning

confidence: 99%

“…For the two types of V , we have two different dynamical systems written in [50] with 16-dimensional real-valued state x. Both these systems belong to the following general class of bilinear homogeneous systems:…”

Section: Introductionmentioning

confidence: 99%

“…For both types of V , the explicit forms for all the 16 differential equations and the corresponding initial conditions in (12) were obtained in [50]. For brevity, we do not reproduce here these 32 differential equations and the corresponding 16 × 16 matrices.…”

Section: Introductionmentioning

confidence: 99%

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Optimal control for state preparation in two-qubit open quantum systems driven by coherent and incoherent controls via GRAPE approach

Petruhanov

Pechen

2022

Int. J. Mod. Phys. A

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In this work, we consider a model of two qubits driven by coherent and incoherent time-dependent controls. The dynamics of the system is governed by a Gorini–Kossakowski–Sudarshan–Lindblad master equation, where coherent control enters into the Hamiltonian and incoherent control enters into both the Hamiltonian (via Lamb shift) and the dissipative superoperator. We consider two physically different classes of interaction with coherent control and study the optimal control problem of state preparation formulated as minimization of the Hilbert–Schmidt distance’s square between the final density matrix and a given target density matrix at some fixed target time. Taking into account that incoherent control by its physical meaning is a non-negative function of time, we derive an analytical expression for the gradient of the objective and develop optimization approaches based on adaptation for this problem of GRadient Ascent Pulse Engineering (GRAPE). We study evolution of the von Neumann entropy, purity, and one-qubit reduced density matrices under optimized controls and observe a significantly different behavior of GRAPE optimization for the two classes of interaction with coherent control in the Hamiltonian.

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Section: Introductionmentioning

confidence: 99%

“…The interaction operator V u(t) = V u(t) is defined, in general, with some arbitrary Hermitian matrix V and, in particular, as in [50], we consider the following two types:…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Optimal control for state preparation in two-qubit open quantum systems driven by coherent and incoherent controls via GRAPE approach

Petruhanov

Pechen

2022

Int. J. Mod. Phys. A

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Optimal state manipulation for a two-qubit system driven by coherent and incoherent controls

Моржин

Pechen

2023

Quantum Inf Process

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GRAPE optimization for open quantum systems with time-dependent decoherence rates driven by coherent and incoherent controls

Petruhanov¹,

Pechen²

2023

J. Phys. A: Math. Theor.

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The GRadient Ascent Pulse Engineering (GRAPE) method is widely used for optimization in quantum control. GRAPE is gradient search method based on exact expressions for gradient of the control objective. It has been applied to various coherently controlled closed and open quantum systems. In this work, we adopt the GRAPE method for optimizing objective functionals in open quantum systems driven by both coherent and incoherent controls. In our case, a tailored or engineered environment acts on the controlled system as control via time-dependent decoherence rates γ i ( t ) or, equivalently, via spectral density n ω ( t ) of the environment. To develop the GRAPE approach for this problem, we compute gradient of various objectives for general N-level open quantum systems for the piecewise constant class of control. The case of a single qubit is considered in details and solved analytically. For this case, an explicit analytical expression for evolution and objective gradient is obtained via diagonalization of a 3 × 3 matrix determining the system’s dynamics in the Bloch ball. The diagonalization is obtained by solving a cubic equation via Cardano’s method. The efficiency of the algorithm is demonstrated through numerical simulations for the state-to-state transition problem and its complexity is estimated. Robustness of the optimal controls is also studied.

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

Cited by 12 publications

References 33 publications

Optimal control for state preparation in two-qubit open quantum systems driven by coherent and incoherent controls via GRAPE approach

Optimal control for state preparation in two-qubit open quantum systems driven by coherent and incoherent controls via GRAPE approach

Optimal state manipulation for a two-qubit system driven by coherent and incoherent controls

GRAPE optimization for open quantum systems with time-dependent decoherence rates driven by coherent and incoherent controls

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