Related papers: Introduction to the multiple-quantum operator spac…
In this article I will describe how NMR techniques may be used to build simple quantum information processing devices, such as small quantum computers, and show how these techniques are related to more conventional NMR experiments.
Convenient and simple numerical techniques for performing quantum computations based on matrix representations of Hilbert space operators are presented and illustrated by various examples. The applications include the calculations of…
This paper addresses the three following questions. (i) How the structures of group and of chain of groups enter nuclear, atomic and molecular spectroscopy? (ii) How these structures can be exploited, in a quantum- mechanical framework, in…
Multiscale modeling is essential for understanding the complex behavior of materials. However, accurately transferring all relevant information from one scale to another has remained an outstanding challenge. Neural operators,…
The language of operator algebras is of great help for the formulation of questions and answers in quantum statistical mechanics. In Chapter 1 we present a minimal mathematical introduction to operator algebras, with physical applications…
The multiple quantum (MQ) NMR dynamics in the system of equivalent spins with the dipolar ordered initial state is considered. The high symmetry of the MQ Hamiltonian is used in order to develop the analytical and numerical methods for an…
This paper is devoted to the multiple-quantum (MQ) NMR spectroscopy in nanopores filled by a gas of spin-carrying molecules (s=1/2) in a strong external magnetic field. It turned out that the high symmetry of the spin system in nanopores…
We study the tomography of multispin quantum states in the context of finite-dimensional Wigner representations. An arbitrary operator can be completely characterized and visualized using multiple shapes assembled from linear combinations…
People are witnessing quantum computing revolutions nowadays. Progress in the number of qubits, coherence times and gate fidelities are happening. Although quantum error correction era has not arrived, the research and development of…
Nuclear Magnetic Resonance (NMR) forms a natural test-bed to perform quantum information processing (QIP) and has so far proven to be one of the most successful quantum information processors. The nuclear spins in a molecule treated as…
In this master thesis, I discuss how the theory of operator algebras, also called operator theory, can be applied in quantum computer science.
The quantum search problem is an important problem due to the fact that a general NP problem can be solved efficiently by an unsorted quantum search algorithm. Here it has been shown that the quantum search problem could be solved in…
Accurate models for open quantum systems -- quantum states that have non-trivial interactions with their environment -- may aid in the advancement of a diverse array of fields, including quantum computation, informatics, and the prediction…
Quantum algorithms are a very promising field. However, creating and manipulating these kind of algorithms is a very complex task, specially for software engineers used to work at higher abstraction levels. The work presented here is part…
Nuclear magnetic resonance spectroscopy is one of the few remaining areas of physical chemistry for which polynomially scaling simulation methods have not so far been available. Here, we report such a method and illustrate its performance…
This paper explores the Invariant Subspace Problem in operator theory and functional analysis, examining its applications in various branches of mathematics and physics. The problem addresses the existence of invariant subspaces for bounded…
Nuclear Magnetic Resonance (NMR) and Magnetic Resonance Imaging (MRI) represent versatile tools with diverse applications spanning physics, chemistry, geology, and medical science. This comprehensive review explores the foundational…
Future quantum computers are anticipated to be able to perform simulations of quantum many-body systems and quantum field theories that lie beyond the capabilities of classical computation. This will lead to new insights and predictions for…
We investigate quantum algorithms derived from tensor networks to simulate the static and dynamic properties of quantum many-body systems. Using a sequentially prepared quantum circuit representation of a matrix product state (MPS) that we…
While the recent demonstration of accurate computations of classically intractable simulations on noisy quantum processors brings quantum advantage closer, there is still the challenge of demonstrating it for practical problems. Here we…