Related papers: Beyond bilinear controllability : applications to …
Quantum computing comes with the potential to push computational boundaries in various domains including, e.g., cryptography, simulation, optimization, and machine learning. Exploiting the principles of quantum mechanics, new algorithms can…
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…
Quantum Lyapunov control, an important class of quantum control methods, aims at generating converging dynamics guided by Lyapunov-based theoretical tools. However, unlike the case of classical systems, disturbance caused by quantum…
Precise definitions for different degrees of controllability for quantum systems are given, and necessary and sufficient conditions are discussed. The results are applied to determine the degree of controllability for various atomic systems…
Optimal control of bilinear systems has been a well-studied subject in the area of mathematical control. However, techniques for solving emerging optimal control problems involving an ensemble of structurally identical bilinear systems are…
We present a comprehensive study of the behavioral theory of an untyped $\lambda$-calculus extended with the delimited-control operators shift and reset. To that end, we define a contextual equivalence for this calculus, that we then aim to…
Structured decompositions of a desired unitary operator are employed to derive control schemes that achieve certain control objectives for finite-level quantum systems using only sequences of simple control pulses such as square waves with…
Different ways of modelling quantum control systems, formulating control problems and solving the resulting problems are considered and compared. In particular, we compare the performance of geometric and optimal control, as well as…
We study a bilinear OCP for an evolution equation governed by the fractional Laplacian of order $0 < s < 1$, incorporating a nonlocal time component modeled by an integral kernel. After establishing well-posedness of the problem, we analyze…
Typically, quantum mechanics is thought of as a linear theory with unitary evolution governed by the Schr\"odinger equation. While this is technically true and useful for a physicist, with regards to computation it is an unfortunately…
We study possibilities to control an ensemble (a parameterized family) of nonlinear control systems by a single parameter-independent control. Proceeding by Lie algebraic methods we establish genericity of exact controllability property for…
Extended formulations are an important tool in polyhedral combinatorics. Many combinatorial optimization problems require an exponential number of inequalities when modeled as a linear program in the natural space of variables. However, by…
This paper presents a survey on quantum control theory and applications from a control systems perspective. Some of the basic concepts and main developments (including open-loop control and closed-loop control) in quantum control theory are…
An infinite-dimensional bilinear optimal control problem with infinite-time horizon is considered. The associated value function can be expanded in a Taylor series around the equilibrium, the Taylor series involving multilinear forms which…
Kullback-Leibler (KL) control enables efficient numerical methods for nonlinear optimal control problems. The crucial assumption of KL control is the full controllability of the transition distribution. However, this assumption is often…
A major application of the mathematical concept of graph in quantum mechanics is to model networks of electrical wires or electromagnetic wave-guides. In this paper, we address the dynamics of a particle trapped on such a network in…
The control landscape of a quantum system $A$ interacting with another quantum system $B$ is studied. Only system $A$ is accessible through time dependent controls, while system B is not accessible. The objective is to find controls that…
Completely integrable Hamiltonian systems look promising for controllability since their first integrals are stable under an internal evolution, and one may hope to find a perturbation of a Hamiltonian which drives the first integrals at…
A study of the linear quadratic (LQ) control problem on a finite time interval for a model equation in Hilbert spaces which comprehends the memory of the inputs was performed recently by the authors. The outcome included a closed-loop…
We develop a means of simulating the evolution and measurement of a multipartite quantum state under discrete or continuous evolution using another quantum system with states and operators lying in a real Hilbert space. This extends…