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Complete controllability of finite dimensional quantum systems with energy level degeneracy is investigated using two different approaches. One approach is to apply a weak constant field to eliminate the degeneracy and then control it using…
Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…
Complete controllability of degenerate quantum system using quantum accessor modeled as a qubit chain with nearest neighborhood coupling is investigated. Sufficient conditions on the length of accessor and the way of coupling between…
We define a "quantum spherical model", a quantum lattice model.
Simulating the dynamics of non-equilibrium matter under extreme conditions lies beyond the capabilities of classical computation alone. Remarkable advances in quantum information science and technology are profoundly changing how we…
Classification of states of quantum channels of information transfer is built on the basis of unreducible representations of qubit state space group of symmetry and properties of density matrix spectrum. It is shown that pure disentangled…
Degenerate dynamical systems are characterized by symplectic structures whose rank is not constant throughout phase space. Their phase spaces are divided into causally disconnected, nonoverlapping regions such that there are no classical…
Quantum computing is currently gaining significant attention, not only from the academic community but also from industry, due to its potential applications across several fields for addressing complex problems. For any practical problem…
Molecular science is governed by the dynamics of electrons, atomic nuclei, and their interaction with electromagnetic fields. A reliable physicochemical understanding of these processes is crucial for the design and synthesis of chemicals…
This review article will present some recent results and methods in the study of 1-particle quantum or wave scattering systems, in the semiclassical/high frequency limit, in cases where the corresponding classical/ray dynamics is chaotic.…
We consider three different approaches to analyze the quantum mechanical problems in multi-well potentials: i) the standard matrix diagonalization technique in the basis sets of harmonic oscillator eigenfunctions or plain waves; ii) the…
Quantum graphs are a paradigmatic model for quantum chaos as well as for spectral theory. We give a concise didactical introduction to quantum graphs, or Schr\"odinger Hamiltonians on metric graphs, with a focus on results related to…
Quantum technologies are increasingly pervasive, underpinning the operation of numerous electronic, optical and medical devices. Today, we are also witnessing rapid advancements in quantum computing and communication. However, access to…
While we expect quantum computers to surpass their classical counterparts in the future, current devices are prone to high error rates and techniques to minimise the impact of these errors are indispensable. There already exists a variety…
We review the construction of the supersymmetric sigma model for unitary maps, using the color- flavor transformation. We then illustrate applications by three case studies in quantum chaos. In two of these cases, general Floquet maps and…
There is a unique finite group that lies inside the 2-dimensional unitary group but not in the special unitary group, and maps by the symmetric square to an irreducible subgroup of the 3-dimensional real special orthogonal group. In an…
The development of quantum technologies relies on creating and manipulating quantum systems of increasing complexity, with key applications in computation, simulation, and sensing. This poses severe challenges in efficient control,…
Quantum graphs have recently been introduced as model systems to study the spectral statistics of linear wave problems with chaotic classical limits. It is proposed here to generalise this approach by considering arbitrary, directed graphs…
The random matrix ensembles are applied to the quantum statistical two-dimensional systems of electrons. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The…
Motivated by far-reaching applications ranging from quantum simulations of complex processes in physics and chemistry to quantum information processing, a broad effort is currently underway to build large-scale programmable quantum systems.…