Related papers: Algebraic Structure of Quantum Controlled States a…
We derive the equations of motion describing the feedback control of quantum systems in the regime of "good control", in which the control is sufficient to keep the system close to the desired state. One can view this regime as the quantum…
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…
Unitary fusion categories formalise the algebraic theory of topological quantum computation. These categories come naturally enriched in a subcategory of the category of Hilbert spaces, and by looking at this subcategory, one can identify a…
Within this chapter (published as [49]) we introduce the overall idea of the algebraic formalism of QFT on a fixed globally hyperbolic spacetime in the framework of unital $*$-algebras. We point out some general features of CCR algebras,…
Recent work has exposed the idea that interesting quantum-like probability laws, including interference effects, can be manifest in classical systems. Here we propose a model for quantum-like (QL) states and QL bits. We suggest a way that…
Two geometric interpretations of the bar automorphism in the positive part of a quantized enveloping algebra are given. The first is in terms of numbers of rational points over finite fields of quiver analogues of orbital varieties; the…
We present new results on the quantum control of systems with infinitely large Hilbert spaces. A control-theoretic analysis of the control of trapped ion quantum states via optical pulses is performed. We demonstrate how resonant…
The linear quadratic regulator problem is central in optimal control and was investigated since the very beginning of control theory. Nevertheless, when it includes affine state constraints, it remains very challenging from the classical…
Contemporary quantum computers encode and process quantum information in binary qubits (d = 2). However, many architectures include higher energy levels that are left as unused computational resources. We demonstrate a superconducting…
The use of geometric methods has proved useful in the hamiltonian description of classical constrained systems. In this note we provide the first steps toward the description of the geometry of quantum constrained systems. We make use of…
The manifold of pure quantum states is a complex projective space endowed with the unitary-invariant geometry of Fubini and Study. According to the principles of geometric quantum mechanics, the detailed physical characteristics of a given…
The aim of this paper is to introduce a new graphic representation of quantum states by means of a specific application: the analysis of two models of quantum copying machines. The graphic representation by diagrams of states offers a clear…
The mathematical formalism of Quantum Mechanics is derived or "reconstructed" from more basic considerations of probability theory and information geometry. The starting point is the recognition that probabilities are central to QM: the…
These results stem from a course on ring theory. Quantum planes are rings in two variables $x$ and $y$ such that $yx=qxy$ where $q$ is a nonzero constant. When $q=1$ a quantum plane is simply a commutative polynomial ring in two variables.…
Efficient methods for the representation and simulation of quantum states and quantum operations are crucial for the optimization of quantum circuits. Decision diagrams (DDs), a well-studied data structure originally used to represent…
Precision measurements of molecules offer an unparalleled paradigm to probe physics beyond the Standard Model. The rich internal structure within these molecules makes them exquisite sensors for detecting fundamental symmetry violations,…
Photons are a natural resource in quantum information, and the last decade showed significant progress in high-quality single photon generation and detection. Furthermore, photonic qubits are easy to manipulate and do not require…
Controllability -- the possibility of performing any target dynamics by applying a set of available operations -- is a fundamental requirement for the practical use of any physical system. For finite-dimensional systems, as for instance…
Arrays of quantum dots (QDs) are a promising candidate system to realize scalable, coupled qubit systems and serve as a fundamental building block for quantum computers. In such semiconductor quantum systems, devices now have tens of…
Quantum splines are curves in a Hilbert space or, equivalently, in the corresponding Hilbert projective space, which generalize the notion of Riemannian cubic splines to the quantum domain. In this paper, we present a generalization of this…