Related papers: Beyond bilinear controllability : applications to …
Often considered in numerical simulations related to the control of quantum systems, the so-called monotonic schemes have not been so far much studied from the functional analysis point of view. Yet, these procedures provide an efficient…
In this paper we explicitly calculate the control sets associated with a linear control system on the two dimensional solvable Lie group. We show that a linear control system of such kind admits exactly one control set or infinite control…
Taking a two-level system as an example, we show that a strong control field may enhance the efficiency of optimal Lyapunov quantum control in [Hou et al., Phys. Rev. A \textbf{86}, 022321 (2012)] but could decrease its control fidelity. A…
This paper introduces a new notion of quantum recursion of which the control flow of the computation is quantum rather than classical as in the notions of recursion considered in the previous studies of quantum programming. A typical…
Deriving minimum evolution times is of paramount importance in quantum mechanics. Bounds on the speed of evolution are given by the so called quantum speed limit (QSL). In this work we use quantum optimal control methods to study the QSL…
We study the changes if any of the expectation value of a general observable in a quantum system, the difficulties associated with the detection of these changes, and the possible methods for correcting the system through unitary control to…
In this paper, we are concerned with local controllability properties of degenerate parabolic equations in bounded domains that evolve in time. More precisely, we deal with the exact controllability to a positive trajectory of a…
The controller design of the so-called "difference algebraic equation" (DAE) systems that are frequently shown in industrial processes, tend to be challenging because of the combination of algebraic equations and high state dimensions. In…
A variety of physically relevant bilinear Schr\"odinger equations are known to be approximately controllable in large times. There are however examples which are approximately controllable in large times, but not in small times. This…
We provide algebraic criteria for the unitarity of linear quantum cellular automata, i.e. one dimensional quantum cellular automata. We derive these both by direct combinatorial arguments, and by adding constraints into the model which do…
We consider Schr{\"o}dinger equations with logarithmic nonlinearity and bilinear controls, posed on $\mathbb{T}^d$ or $\mathbb{R}^d$. We prove their small-time global $L^2$-approximate controllability. The proof consists in extending to…
We study quantum systems with even numbers N of levels that are completely state-controlled by unitary transformations generated by Lie algebras isomorphic to sp(N) of dimension N(N+1)/2. These Lie algebras are smaller than the respective…
Relaxation effects impose fundamental limitations on our ability to coherently control quantum mechanical phenomena. In this letter, we establish physical limits on how closely can a quantum mechanical system be steered to a desired target…
In this paper we are concerned with the approximate controllability of a multidimensional semilinear reaction-diffusion equation governed by a multiplicative control, which is locally distributed in the reaction term. For a given initial…
A control problem with terminal overdetermination is considered for the higher order nonlinear Schr\"odinger equation on a bounded interval. The boundary condition on the space derivative is chosen as the control. Results on global…
In this Note, we review the main existing results, methods, and some key open problems on the controllability of nonlinear hyperbolic and parabolic equations. Especially, we describe our recent universal approach to solve the local…
One of the difficulties in adiabatic quantum computation is the limit on the computation time. Here we propose two schemes to speed-up the adiabatic evolution. To apply this controlled adiabatic evolution to adiabatic quantum computation,…
We show that combining ideas from the fields of quantum invariants and of optimal control can be used to design optimal quantum control solutions without explicit reference to quantum states. The states are specified only implicitly in…
Control of quantum systems is a central element of high-precision experiments and the development of quantum technological applications. Control pulses that are typically temporally or spatially modulated are often designed based on…
Just as any state of a single qubit or 2-level system can be obtained from any other state by a rotation operator parametrized by three real Euler angles, we show how any state of an n-qubit or 2^n-level system can be obtained from any…