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We propose a coarse-grained picture to control ``complex'' quantum dynamics, i.e., multi-level-multi-level transition with a random interaction. Assuming that optimally controlled dynamics can be described as a Rabi-like oscillation between…
The ability to implement any desired quantum logic gate on a quantum processing unit is equivalent to evolution-operator controllability of the qubits. Conversely, controllability analysis can be used to minimize the resources, i.e., the…
Invariant sets define regions of the state space where system constraints are always satisfied. The majority of numerical techniques for computing invariant sets have been developed for discrete-time systems with a fixed sampling time.…
This paper presents a computationally efficient robust model predictive control law for discrete linear time invariant systems subject to additive disturbances that may depend on the state and/or input norms. Despite the dependency being…
In this paper, we analyze the chain control sets of linear control systems on connected Lie groups. Our main result shows that the compactness of the central subgroup associated with the drift is a necessary and sufficient condition to…
In this paper, we use the derivative of the exponential map to derive the exact evolution of the logarithm of the tracking error for mixed-invariant systems, a class of systems capable of describing rigid body tracking problems in Lie…
We consider the task of intrinsic control system identification for quantum devices. The problem of experimental determination of subspace confinement is considered, and simple general strategies for full Hamiltonian identification and…
In this paper we use the recent developments in the representation theory of locally compact quantum groups, to assign, to each locally compact quantum group $\mathbb{G}$, a locally compact group $\tilde \mathbb{G}$ which is the quantum…
We discuss measures, invariant measures on definable groups, and genericity, often in an NIP (failure of the independence property) environment. We complete the proof of the third author's conjectures relating definably compact groups $G$…
We have shown that quantum interference in a driven quasi-degenerate two-level atomic system can be controlled by an externally applied magnetic field. We demonstrate that the mechanism of optical control is based on quantum interference,…
We present a theoretical proposal for preparing and manipulating a state of a single continuous-variable degree of freedom confined to a nonharmonic potential. By utilizing optimally controlled modulation of the potential's position and…
We exploit a novel approximation scheme to obtain a new and compact formula for the parameters underlying coherent-state control of the evolution of a pair of entangled two-level systems. It is appropriate for long times and for relatively…
Accurate control of quantum evolution is an essential requirement for quantum state engineering, laser chemistry, quantum information and quantum computing. Conditions of controllability for systems with a finite number of energy levels…
In this paper we show that a complete characterization of the controllability property for linear control system on three-dimensional solvable nonnilpotent Lie groups is possible by the LARC and the knowledge of the eigenvalues of the…
This article provides a review of recent developments in the formulation and execution of optimal control strategies for the dynamics of quantum systems. A brief introduction to the concept of optimal control, the dynamics of of open…
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…
Finite-state models of control systems were proposed by several researchers as a convenient mechanism to synthesize controllers enforcing complex specifications. Most techniques for the construction of such symbolic models have two main…
We investigate how the concepts of optimal control of measurables of a system with a time dependent Hamiltonian may be mixed with the level set technique to keep the desired entity invariant. We derive sets of equations for this purpose and…
This paper presents a constructive proof of complete kinematic state controllability of finite-dimensional open quantum systems whose dynamics are represented by Kraus maps. For any pair of states (pure or mixed) on the Hilbert space of the…
This is the second one in our series of papers on indirect quantum control assisted by quantum accessor. In this paper we propose and study a new class of indirect quantum control(IDQC) scheme based on the initial states preparation of the…