Related papers: Quantum control landscape for a $\Lambda$-atom in …
In this work we study extrema of objective functionals for ultrafast manipulation by a qubit. Traps are extrema of the objective functionals which are optimal for manipulation by quantum systems only locally but not globally. Much effort in…
In various physical implementations of quantum information processing, qubits are realized in a Lambda type system configuration as two stable lower energy levels coupled indirectly via an unstable higher energy level, that is, in…
Robust quantum control is crucial for realizing practical quantum technologies. Energy landscape shaping offers an alternative to conventional dynamic control, providing theoretically enhanced robustness and simplifying implementation for…
Gradient-based (a.k.a. `first order') optimization algorithms are routinely used to solve large scale non-convex problems. Yet, it is generally hard to predict their effectiveness. In order to gain insight into this question, we revisit the…
A quantum control landscape is defined as the expectation value of a target observable $\Theta$ as a function of the control variables. In this work control landscapes for open quantum systems governed by Kraus map evolution are analyzed.…
A systematic scheme is proposed to numerically estimate the quantum speed limit and temporal shape of optimal control in two-level and three-level quantum systems with bounded amplitude. For the two-level system, two quantum state…
The Gradient Ascent Pulse Engineering (GRAPE) is a celebrated control algorithm with excellent converging rates, owing to a piece-wise-constant ansatz for the control function that allows for cheap objective gradients. However, the…
In optimal quantum control, control landscape phase transitions (CLPTs) indicate sharp changes occurring in the set of optimal protocols, as a physical model parameter is varied. Here, we demonstrate the existence of a new class of CLPTs,…
The core problem in optimal control theory applied to quantum systems is to determine the temporal shape of an applied field in order to maximize the expectation of value of some physical observable. The functional which maps the control…
We develop an optimal control algorithm for robust quantum gate preparation in open environments with the state of the quantum system represented using the Lindblad master equation. The algorithm is based on adaptive linearization and…
We describe algorithms, and experimental strategies, for the Pareto optimal control problem of simultaneously driving an arbitrary number of quantum observable expectation values to their respective extrema. Conventional quantum optimal…
The methods of mathematical control theory are widely used in the modern physics, but still they are less popular in quantum science. We will discuss the aspects of control theory, which are the most useful in applications to the real…
We derive and implement a second-order adjoint method to compute exact gradients and Hessians for a prototypical quantum optimal control problem, that of solving for the minimal energy applied electric field that drives a molecule from a…
In the present work the extrema of the objective functional for the problem of generation of quantum gates (logical elements for quantum computations) for two--level systems are investigated for short duration of the control. The problem of…
We investigate the time and the energy minimum optimal solutions for the robust control of two-level quantum systems against offset or control field uncertainties. Using the Pontryagin Maximum Principle, we derive the global optimal pulses…
The growing successes in performing quantum control experiments motivated the development of control landscape analysis as a basis to explain these findings.When a quantum system is controlled by an electromagnetic field, the observable as…
This paper considers the control landscape of quantum transitions in multi-qubit systems driven by unitary transformations with single-qubit interaction terms. The two-qubit case is fully analyzed to reveal the features of the landscape…
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 proven on various…
The optimal control of unitary transformations is a fundamental problem in quantum control theory and quantum information processing. The feasibility of performing such optimizations is determined by the computational and control resources…
The recent promises of Model Predictive Control in robotics have motivated the development of tailored second-order methods to solve optimal control problems efficiently. While those methods benefit from strong convergence properties,…