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The non-linear optimization method developed by Konnov and Krotov [Automation and Remote Control 60, 1427 (1999)] has been used previously to extend the capabilities of optimal control theory from the linear to the non-linear Schr\"odinger…
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…
Many numerical simulations in quantum (bilinear) control use the monotonically convergent algorithms of Krotov (introduced by Tannor), Zhu & Rabitz or the general form of Maday & Turinici. This paper presents an analysis of the limit set of…
Optimizing open quantum system evolution is an important step on the way to achieving quantum computing and quantum thermodynamic tasks. In this article, we approach optimisation via variational principles and derive an open quantum system…
Efficient algorithms for the discovery of optimal control designs for coherent control of quantum processes are of fundamental importance. One important class of algorithms are sequential update algorithms generally attributed to Krotov.…
We apply the Krotov method for open and closed quantum systems with the objective of finding optimized controls to manipulate qubit/qutrit systems in the presence of the external environment. In the case of unitary optimization, the Krotov…
We develop a perturbation theory of quantum (and classical) master equations with slowly varying parameters, applicable to systems which are externally controlled on a time scale much longer than their characteristic relaxation time. We…
When simulating the dynamics of open quantum systems with quantum computers, it is essential to accurately approximate the system's behaviour while preserving the physicality of its evolution. Traditionally, for Markovian open quantum…
We investigate the optimal control of open quantum systems, in particular, the mutual influence of driving and dissipation. A stochastic approach to open-system control is developed, using a generalized version of Krotov's iterative…
Adopting a resource theory framework of thermodynamics for quantum and nano systems pioneered by Janzing et al. [Int. J. Th. Phys. 39, 2717 (2000)], we formulate the cost in useful work of transforming one resource state into another as a…
Quantum coherence inherently affects the dynamics and the performances of a quantum machine. Coherent control can, at least in principle, enhance the work extraction and boost the velocity of evolution in an open quantum system. Using…
Dirac-Frenkel variational method with Davydov D2 trial wavefunction is extended by introducing a thermalization algorithm and applied to simulate dynamics of a general open quantum system. The algorithm allows to control temperature…
We present a modified optimal control scheme based on the Krotov method, which allows for strict limitations on the spectrum of the optimized laser fields, without losing monotonic convergence of the algorithm. The method guarantees a close…
In classical Markov jump processes, current fluctuations can only be reduced at the cost of increased dissipation. To explore how quantum effects influence this trade-off, we analyze the uncertainty of steady-state currents in Markovian…
We consider the optimal control of quantum systems interacting non-linearly with an electromagnetic field. We propose new monotonically convergent algorithms to solve the optimal equations. The monotonic behavior of the algorithm is ensured…
We present a new formulation of monotonically convergent algorithms which allows to optimize both the control duration and the field fluence. A standard algorithm designs a control field of fixed duration which both brings the system close…
In recent years, there has been growing interest in characterizing the complexity of quantum evolutions of interacting many-body systems. When a time-independent Hamiltonian governs the dynamics, Krylov complexity has emerged as a powerful…
Quantum systems are inherently sensitive to environmental noise and imperfections in external control fields, posing a significant challenge for the practical implementation of quantum technologies. These noise sources degrade the fidelity…
In this paper, for continuous, linearly-controllable quadratic control systems with a single input, an explicit, constructive method is proposed for studying their Brunovsky forms, initially studied in [W. Kang and A. J. Krener, Extended…
Simulation of a quantum many-body system at finite temperatures is crucially important but quite challenging. Here we present an experimentally feasible quantum algorithm assisted with continuous-variable for simulating quantum systems at…