Related papers: Universal families and quantum control in infinite…
An infinite family of exactly-solvable and integrable potentials on a plane is introduced. It is shown that all already known rational potentials with the above properties allowing separation of variables in polar coordinates are particular…
Conventional approaches for controlling open quantum systems use coherent control which affects the system's evolution through the Hamiltonian part of the dynamics. Such control, although being extremely efficient for a large variety of…
We present a scheme for controlling the state of a quantum system by modifying the boundary conditions. This constitutes an infinite-dimensional control problem. We provide conditions for the existence of solutions of the dynamics and prove…
Operator controllability refers to the ability to implement an arbitrary unitary in SU(N) and is a prerequisite for universal quantum computing. Controllability tests can be used in the design of quantum devices to reduce the number of…
Quantum measurement is universal for quantum computation. This universality allows alternative schemes to the traditional three-step organisation of quantum computation: initial state preparation, unitary transformation, measurement. In…
The optimal control of unitary transformations is a fundamental problem in quantum control theory and quantum information processing. The feasibility of performing such optimizations is determined by the computational and control resources…
Landmark manifolds consist of a collection of distinct points, and dynamics on this manifold can be used to represent flows, such as solutions of ODEs and flows deforming a shape. We will consider landmark configurations in the Euclidean…
Results obtained by us are overviewed from a general set up. The universal $R$-matrix is exploited to obtain various important relations and structures involved in quantum group algebra, which are used subsequently for generating different…
In quantum control theory, the fundamental issue of controllability covers the questions whether and under which conditions a system can be steered from one pure state into another by suitably tuned time evolution operators. Even though Lie…
A quantum control landscape is defined as the observable as a function(al) of the system control variables. Such landscapes were introduced to provide a basis to understand the increasing number of successful experiments controlling quantum…
Unitary operations are a fundamental component of quantum algorithms, but they seem to be far more useful if given with a "quantum control" as a controlled unitary operation. However, quantum operations are not limited to unitary…
The density matrix formalism which is widely used in the theory of measurements, quantum computing, quantum description of chemical and biological systems always imply the averaging over the states of the environment. In practice this is…
Matrices are very popular and widely used in mathematics and other fields of science. Every mathematician has known the properties of finite-sized matrices since the time of study. In this paper, we consider the basic theory of infnite…
Compact categories have lately seen renewed interest via applications to quantum physics. Being essentially finite-dimensional, they cannot accomodate (co)limit-based constructions. For example, they cannot capture protocols such as quantum…
Many phenomena in physics, chemistry, and biology involve seeking an optimal control to maximize an objective for a classical or quantum system which is open and interacting with its environment. The complexity of finding an optimal control…
Quantum measurement is universal for quantum computation. This universality allows alternative schemes to the traditional three-step organisation of quantum computation: initial state preparation, unitary transformation, measurement. In…
The convenient setting for smooth mappings, holomorphic mappings, and real analytic mappings in infinite dimension is sketched. Infinite dimensional manifolds are discussed with special emphasis on smooth partitions of unity and tangent…
Quantum mechanics, with its counterintuitive principles and probabilistic nature, has long been confined to the microscopic realm of atoms and photons. Yet, recent breakthroughs have pushed the boundaries of quantum behavior into the…
Identifying the real and imaginary parts of wave functions with coordinates and momenta, quantum evolution may be mapped onto a classical Hamiltonian system. In addition to the symplectic form, quantum mechanics also has a positive-definite…
Group symmetry is inherent in a wide variety of data distributions. Data processing that preserves symmetry is described as an equivariant map and often effective in achieving high performance. Convolutional neural networks (CNNs) have been…