On optimization of coherent and incoherent controls for two-level quantum systems

Моржин, О. В.; Pechen, Alexander

doi:10.48550/arxiv.2205.02521

Cited by 4 publications

(4 citation statements)

References 52 publications

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“…Numerical experiments suggest that if (φ W , T ) ∈ D 1 , then f 0 is a point of global maximum [40]. Note that the numbers of positive and negative eigenvalues mentioned in item 2 of this theorem, as well as their magnitudes, were not computed in [22].…”

Section: Conclusion In § 5 Summarize This Work § 2 Previous Resultsmentioning

confidence: 99%

“…In this work, we compute the numbers of negative and positive eigenvalues of the Hessian at this saddle point, give estimates on magnitude of the eigenvalues and also significantly simplify our previous proof of the theorem about the Hessian at this saddle point [22]. Numerical experiments for the problem of single-qubit phase shift gate generation on the fast time scale were performed in [22], [40].…”

Section: § 1 Introductionmentioning

confidence: 99%

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On the detailed structure of quantum control landscape for fast single qubit phase-shift gate generation

Volkov,

Pechen

2023

Izv. Math.

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In this work, we study the detailed structure of quantum control landscape for the problem of single-qubit phase shift gate generation on the fast time scale. In previous works, the absence of traps for this problem was proved on various time scales. A special critical point which was known to exist in quantum control landscapes was shown to be either a saddle or a global extremum, depending on the parameters of the control system. However, in case of a saddle, the numbers of negative and positive eigenvalues of the Hessian at this point and their magnitudes have not been studied. At the same time, these numbers and magnitudes determine the relative ease or difficulty for practical optimization in a vicinity of the critical point. In this work, we compute the numbers of negative and positive eigenvalues of the Hessian at this saddle point and, moreover, give estimates on magnitude of these eigenvalues. We also significantly simplify our previous proof of the theorem about this saddle point of the Hessian (Theorem 3 in [22]).

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Section: Conclusion In § 5 Summarize This Work § 2 Previous Resultsmentioning

confidence: 99%

Section: § 1 Introductionmentioning

confidence: 99%

On the detailed structure of quantum control landscape for fast single qubit phase-shift gate generation

Volkov,

Pechen

2023

Izv. Math.

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“…The structuring of the substrates led to a further decrease in the switching voltage, most likely due to the formation of 1D chains of FG:V 2 O 5 particles. G:BN particles on a structured and activated substrate demonstrate significantly higher conductivity (10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20) Racetrack memory is a new concept of non-volatile memory spintronics application. It is widely discussed in modern literature [1].…”

Section: Methods Of Control Diagnostics and Characterization Of Nanog...mentioning

confidence: 99%

Micro- and Nanoelectronics - 2023

2023

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The Book of Abstracts contains the abstracts of the papers presented at the biannual International Conference "Micro- and Nanoelectronics - 2023" (ICMNE-2023) including the extended Session "Quantum Informatics" (QI-2023). The Conference topics cover the most of the areas dedicated to the physics of integrated micro- and nanoelectronic devices and related micro- and nanotechnologies. The Conference is focused on recent progress in those areas. It continues the series of the AllRussian Conferences (since 1994) and the International Conferences (since 2003).

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“…Uncomputability of discrete quantum control was shown via establishing a relation with Diophantine equations and tenth Hilbert problem [39]. Numerical optimization schemes for a qubit driven by coherent and incoherent controls were studied in [40,41,42,43,44,45] for various objective criteria, for studying reachable and controllability sets, and for exploiting machine learning.…”

Section: Introductionmentioning

confidence: 99%

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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On optimization of coherent and incoherent controls for two-level quantum systems

Cited by 4 publications

References 52 publications

On the detailed structure of quantum control landscape for fast single qubit phase-shift gate generation

On the detailed structure of quantum control landscape for fast single qubit phase-shift gate generation

Micro- and Nanoelectronics - 2023

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

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