Related papers: Quantum Complexity: restrictions on algorithms and…
This thesis (Habilitation \`a diriger des recherches) presents some of my research contributions since my Ph.D defense in 2008. I have had the chance to participate in the development of quantum programming languages since their early…
PhD thesis dealing with various aspects of multipartite entanglement, such as entanglement measures, absolutely maximally entangled states, bell inequalities, entanglement spectrum and quantum frustration. Also some quantum algorithms run…
The ultimate limits of computation are not just logical, but physical. We investigate the physical resources -- time, energy, entropy, and free energy -- required to perform computational work. We apply the resulting measures of physical…
In our thesis, we try to shed more light onto the complexity of quantum complexity classes by refining the related part of the hierarchy. First, we review the basic concepts of quantum computing in general. Then, inspired by BQP, we define…
Quantum complexity quantifies the difficulty of preparing a state or implementing a unitary transformation with limited resources. Applications range from quantum computation to condensed matter physics and quantum gravity. We seek to…
The complexity of quantum computation remains poorly understood. While physicists attempt to find ways to create quantum computers, we still do not have much evidence one way or the other as to how useful these machines will be. The tools…
This is an updated version of my PhD thesis, defended at the University of Waterloo on the 2nd of April 2025, uploaded to the ArXiv with the goal of reaching a wider audience. The thesis is divided into 5 chapters, respectively containing…
In quantum chemistry, the price paid by all known efficient model chemistries is either the truncation of the Hilbert space or uncontrolled approximations. Theoretical computer science suggests that these restrictions are not mere…
This is the introductory part of my Ph.D thesis, defended at the Faculty of Science and Technology, NTNU on December 10, 2012.
Query complexity is a model of computation in which we have to compute a function $f(x_1, \ldots, x_N)$ of variables $x_i$ which can be accessed via queries. The complexity of an algorithm is measured by the number of queries that it makes.…
These are notes for a graduate course in quantum gravity planned at IFT-UAM/CSIC for the spring term of 2020, but delayed for an indefinite period of time (although a shortened version was given in the Escuela de Fisica (Institute of…
This is a PhD dissertation on the latest numerical quantum estimation schemes as of 2012, submitted to the National University of Singapore. The main content of the thesis focuses on accessing quantum information with informationally…
The development of quantum computing systems has been a staple of academic research since the mid-1990s when the first proposal for physical platforms were proposed using Nuclear Magnetic Resonance and Ion-Trap hardware. These first…
It has long been known that any Boolean function that depends on n input variables has both degree and exact quantum query complexity of Omega(log n), and that this bound is achieved for some functions. In this paper we study the case of…
I describe my path to unconventionality in my exploration of theoretical and applied aspects of computation towards revealing the algorithmic and reprogrammable properties and capabilities of the world, in particular related to applications…
Most continuous mathematical formulations arising in science and engineering can only be solved numerically and therefore approximately. We shall always assume that we're dealing with a numerical approximation to the solution. There are two…
This Bachelor's thesis, written in Russian, is devoted to a relatively new direction in the field of machine learning and artificial intelligence, namely probabilistic programming. The thesis gives a brief overview to the already existing…
The great promise of quantum computers comes with the dual challenges of building them and finding their useful applications. We argue that these two challenges should be considered together, by co-designing full-stack quantum computer…
This is a brief review of the experimental and theoretical quantum computing. The hopes for eventually building a useful quantum computer rely entirely on the so-called "threshold theorem". In turn, this theorem is based on a number of…
A major part of computability theory focuses on the analysis of a few structures of central importance. As a tool, the method of coding with first-order formulas has been applied with great success. For instance, in the c.e. Turing degrees,…