Related papers: Control by quantum dynamics on graphs
We propose a new quantum numerical scheme to control the dynamics of a quantum walker in a two dimensional space-time grid. More specifically, we show how, introducing a quantum memory for each of the spatial grid, this result can be…
A quantum theory in a finite-dimensional Hilbert space can be geometrically formulated as a proper Hamiltonian theory as explained in [2, 3, 7, 8]. From this point of view a quantum system can be described in a classical-like framework…
This paper explores the structural controllability of switched linear continuous-time systems. It first identifies a gap in the proof for a pivotal criterion for the structural controllability of switched linear systems in the literature.…
Linear systems on Lie groups are a natural generalization of linear system on Euclidian spaces. For such systems, this paper studies the properties of the maximal sets of approximate controllability.
We undertake a study of the notion of a quantum graph over arbitrary finite-dimensional $C^*$-algebras $B$ equipped with arbitrary faithful states. Quantum graphs are realised principally as either certain operators on $L^2(B)$, the quantum…
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…
In this work, we consider the controllability of a discrete-time linear dynamical system with sparse control inputs. Sparsity constraints on the input arises naturally in networked systems, where activating each input variable adds to the…
We develop a microscopic theory for biasing the quantum trajectories of an open quantum system, which renders rare trajectories typical. To this end we consider a discrete-time quantum dynamics, where the open system collides sequentially…
At the heart of quantum technology development is the control of quantum systems at the level of individual quanta. Mathematically, this is realised through the study of Hamiltonians and the use of methods to solve the dynamics of quantum…
Quantum computing (QC) is a new computational paradigm whose foundations relate to quantum physics. Notable progress has been made, driving the birth of a series of quantum-based algorithms that take advantage of quantum computational…
In this paper, we study the control of a class of time-invariant linear ensemble systems whose natural dynamics are linear in the system parameter. This class of ensemble control systems arises from practical engineering and physical…
We consider the problem of controlling in minimum time a two-level quantum system which can be subject to a drift. The control is assumed to be bounded in magnitude, and to affect two or three independent generators of the dynamics. We…
We develop the theory of linear evolution equations associated with the adjacency matrix of a graph, focusing in particular on infinite graphs of two kinds: uniformly locally finite graphs as well as locally finite line graphs. We discuss…
We consider the problem of controlling a partially-observed dynamic process on a graph by a limited number of interventions. This problem naturally arises in contexts such as scheduling virus tests to curb an epidemic; targeted marketing in…
Many proposals have been put forth for controlling quantum phenomena, including open-loop, adaptive feedback, and real-time feedback control. Each of these approaches has been viewed as operationally, and even physically, distinct from the…
Continuous time quantum walks on exponentially large, sparse graphs form a powerful paradigm for quantum computing: On the one hand, they can be efficiently simulated on a quantum computer. On the other hand, they are themselves…
Control over the quantum dynamics of chaotic kicked rotor systems is demonstrated. Specifically, control over a number of quantum coherent phenomena is achieved by a simple modification of the kicking field. These include the enhancement of…
Some simple examples from quantum physics and control theory are used to illustrate the application of the theory of Lie systems. We will show, in particular, that for certain physical models both of the corresponding classical and quantum…
Characterizing graphs by their spectra is an important topic in spectral graph theory, which has attracted a lot of attention of researchers in recent years. It is generally very hard and challenging to show a given graph to be determined…
Positive linear systems on arbitrary time scales are studied. The theory developed in the paper unifies and extends concepts and results known for continuous-time and discrete-time systems. A necessary and sufficient condition for a linear…