Related papers: Quantum Control and Representation Theory
Quantum theory can be formulated as a theory of operations, more specific, of complex represented operations from real Lie groups. Hilbert space eigenvectors of acting Lie operations are used as states or particles. The simplest simple Lie…
We consider a perturbation of an ``integrable'' Hamiltonian and give an expression for the canonical or unitary transformation which ``simplifies'' this perturbed system. The problem is to invert a functional defined on the Lie- algebra of…
This paper considers a generalization of the notion of quantum observables in ontological models of quantum mechanics. Within this framework it is possible to construct physical models where quantum noncommutativity can arise dynamically.…
An understanding of quantum theory in terms of new, underlying descriptions capable of explaining the existence of non-classical correlations, non-commutativity of measurements and other unique and counter-intuitive phenomena remains still…
It is shown that the basic equations of quantum theory can be obtained from a straightforward application of logical inference to experiments for which there is uncertainty about individual events and for which the frequencies of the…
Recent advances in classical machine learning have shown that creating models with inductive biases encoding the symmetries of a problem can greatly improve performance. Importation of these ideas, combined with an existing rich body of…
This paper provides a brief introduction to learning control of quantum systems. In particular, the following aspects are outlined, including gradient-based learning for optimal control of quantum systems, evolutionary computation for…
This paper considers quantum communication involving an ensemble of states. Apart from the von Neumann entropy, it considers other measures one of which may be useful in obtaining information about an unknown pure state and another that may…
A rigorous theory of quantum state reduction, the state change of the measured system caused by a measurement conditional upon the outcome of measurement, is developed fully within quantum mechanics without leading to the vicious circle…
Construction of explicit quantum circuits follows the notion of the "standard circuit model" introduced in the solid and profound analysis of elementary gates providing quantum computation. Nevertheless the model is not always optimal (e.g.…
The behavior coordinate system and the ideal individual model are presented. The behavior state of an ideal individual is assumed to be represented by a behavior state function. Based on the ideal individual model, the behavior coordinate…
The objective of this paper is to study the controllability of discrete-time linear control systems in solvable Lie groups. In the special case of nilpotent Lie groups, a necessary and sufficient condition for controllability is…
An essential element of classical computation is the "if-then" construct, that accepts a control bit and an arbitrary gate, and provides conditional execution of the gate depending on the value of the controlling bit. On the other hand,…
Antiunitary representations of Lie groups take values in the group of unitary and antiunitary operators on a Hilbert space H. In quantum physics, antiunitary operators implement time inversion or a PCT symmetry, and in the modular theory of…
This is a brief introduction to control theory in finite-dimensional spaces. The material is partly based on my lectures for the Master 1 program in Math\'ematiques et applications at Sorbonne University, delivered over the past few years.…
The only evidence we have for a discrete reality comes from quantum measurements; without invoking these measurements, quantum theory describes continuous entities. This seeming contradiction can be resolved via analysis that treats…
In this sequence of papers, noncommutative analysis is used to give a consistent axiomatic approach to a unified conceptual foundation of classical and quantum physics. The present Part I defines the concepts of observables, states and…
In a recent paper, a realizability technique has been used to give a semantics of a quantum lambda calculus. Such a technique gives rise to an infinite number of valid typing rules, without giving preference to any subset of those. In this…
K. He, J. Hou, and M. Li have recently given a sufficient and necessary condition for unitary equivalence of quantum states. This condition is based on the von Neumann entropy. In this note we first give a short proof of their result, and…
Applications of quantum mechanics have led to many successful predictions and explanations of puzzling phenomena, and we now apply quantum mechanics to gain, process, and communicate information in novel ways. We can understand quantum…