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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…
We address the path-wise control of systems described by a set of nonlinear stochastic differential equations. For this class of systems, we introduce a notion of stochastic relative degree and a change of coordinates which transforms the…
We examine a quantum dot with $N_{\rm dot}$ levels which is strongly coupled to leads for varying number of channels $N$ in the leads. It is shown both analytically and numerically that for strong couplings between the dot and the leads, at…
We investigate the performance of dynamical decoupling methods at suppressing electron spin decoherence from a low-temperature nuclear spin reservoir in a quantum dot. The controlled dynamics is studied through exact numerical simulation,…
We study the quantum dynamics generated by the repeated action of a non-unitary evolution operator on a system of qubits. Breaking unitarity can lead to the purification of mixed initial states, which corresponds to the loss of sensitivity…
The measurement of topological number is crucial in the research of topological systems. Recently, the relations between the topological number and the dynamics are built. But a direct method to read out the topological number via the…
We study dynamics of the measurement process in quantum dot systems, where a particular state out of coherent superposition is observed. The ballistic point-contact placed near one of the dots is taken as a noninvasive detector. We…
In this paper we study a perturbative approach to the problem of quantization of measures in the plane. Motivated by the fact that, as the number of points tends to infinity, hexagonal lattices are asymptotically optimal from an energetic…
Impurity motion in one dimensional ultra cold quantum liquids confined in an optical trap has attracted much interest recently. As a step towards its full understanding, we construct a generating functional from which we derive the position…
The 2-dimensional density of states of an electron is studied for a Poissonian random distribution of point vortices carrying $\alpha$ flux in unit of the quantum of flux. It is shown that, for any given density of impurities, there is a…
We study the behavior of the Hall coefficient, $R_H$, in a system exhibiting $d_{{x^2}-{y^2}}$ density-wave (DDW) order in a regime in which the carrier concentration, $x$, is tuned to approach a quantum critical point at which the order is…
In this paper, we explore how to constructively manipulate qubits by rotating Bloch spheres. It is revealed that three-rotation and one-rotation Hamiltonian controls can be constructed to steer qubits when two tunable Hamiltonian controls…
In this paper we study a mean field control problem in which particles are absorbed when they reach the boundary of a smooth domain. The value of the N-particle problem is described by a hierarchy of Hamilton-Jacobi equations which are…
Dynamical decoupling (DD) is a key technique for suppressing decoherence and preserving the performance of quantum algorithms. We introduce a measurement-based DD (MDD) protocol that determines control unitary gates from partial…
Accurate control of two-level systems is a longstanding problem in quantum mechanics. One such quantum system is the frequency-bin qubit: a single photon existing in superposition of two discrete frequency modes. %and a potential building…
We introduce a new and efficient numerical method for multicriterion optimal control and single criterion optimal control under integral constraints. The approach is based on extending the state space to include information on a "budget"…
The finite horizon $H_2/H_\infty$ control problem of mean-field type for discrete-time systems is considered in this paper. Firstly, we derive a mean-field stochastic bounded real lemma (SBRL). Secondly, a sufficient condition for the…
The need to retain the relative phases in quantum mechanics implies an addition law parametrized by a phase of two density operators required for the purification of a density matrix. This is shown with quantum tomography and the Wigner…
We consider an elliptic optimal control problem where the objective functional contains evaluations of the state at a finite number of points. In particular, we use a fidelity term that encourages the state to take certain values at these…
We study discrete-time finite-horizon optimal control problems in probability spaces, whereby the state of the system is a probability measure. We show that, in many instances, the solution of dynamic programming in probability spaces…