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These lecture notes give an overview of recent results in geometric Langlands correspondence which may yield applications to quantum field theory. We start with a motivated introduction to the Langlands Program, including its geometric…
Tensor network methods are incredibly effective for simulating quantum circuits. This is due to their ability to efficiently represent and manipulate the wave-functions of large interacting quantum systems. We describe the challenges faced…
These notes are an expanded version of lectures given at the Croatian School on Black Holes at Trpanj, June 21-25, 2010. The aim is to provide a practical introduction to quantum field theory in curved spacetime and related black hole…
We present a brief overview of the current theoretical and experimental progresses in the study of quantum dot-based quantum computing schemes, then focus on the spin-based varieties, which are generally regarded as the most scalable…
A recently introduced numerical approach to quantum systems is analyzed. The basis of a Fock space is restricted and represented in an algebraic program. Convergence with increasing size of basis is proved and the difference between…
Exact diagonalization (ED) is one of the most reliable and established numerical methods of quantum many-body theory. The main limiting factor of the method is the exponential scaling of Hilbert space dimension with system size.…
Quantum Computing is an exciting field that draws from information theory, computer science, mathematics, and quantum physics to process information in fundamentally new ways. There is an ongoing race to develop practical quantum computers…
Extra-dimensions are a common topic in popular descriptions of theoretical physics with which undergraduate student most often have no contact in physics courses. This paper shows how students could be introduced to this topic by presenting…
I present an introduction to the field of Quantum Chromodynamics (QCD) with emphasis on nucleon spin structure and perturbative methods. After a somewhat comprehensive overview of perturbative QCD, including the systematics of…
These Lecture Notes discuss the recent theoretical advances in the understanding of open quantum many-body physics in platforms where both dissipative and coherent processes can be tuned and controlled to a high degree. We start by…
We perform quantum simulation on classical and quantum computers and set up a machine learning framework in which we can map out phase diagrams of known and unknown quantum many-body systems in an unsupervised fashion. The classical…
These notes are based on the lectures given by the second author at the School on Optimal Transport on Quantum Structures at Erd\"os Center in September 2022. The focus of the exposition is on two recently introduced approaches on quantum…
Several topics on the implementation of spin qubits in quantum dots are reviewed. We first provide an introduction to the standard model of quantum computing and the basic criteria for its realization. Other alternative formulations such as…
This paper is a slightly reduced and concise version of a course given at Geonet2019 school on New Trends in Mathematical Methods for Physics at IMSP in Rep. of Benin, May 2019. The notes are intended to provide the reader with an…
This introductory text on the basics of quantum mechanics is intended to serve as a kind of travel guide through the quantum world. It starts by asking whether quantum physics is important, or weird, or incomprehensible. It explains why…
These lecture notes aim to provide a self-contained, pedagogical introduction to the physics of local constraints, fractionalisation and topological liquids organised around the Rokhsar-Kivelson quantum dimer model. Topics and phenomena…
This work introduces a novel method for embedding continuous variables into quantum circuits via piecewise polynomial features, utilizing low-rank tensor networks. Our approach, termed Piecewise Polynomial Tensor Network Quantum Feature…
This paper collects and extends the lectures I gave at the "XXIV International Fall Workshop on Geometry and Physics" held in Zaragoza (Spain) August 31 - September 4, 2015. Within these lectures I review the formulation of Quantum…
This is an introductory machine-learning course specifically developed with STEM students in mind. Our goal is to provide the interested reader with the basics to employ machine learning in their own projects and to familiarize themself…
Tensor Networks (TN) are approximations of high-dimensional tensors designed to represent locally entangled quantum many-body systems efficiently. This study provides a comprehensive comparison between classical TNs and TN-inspired quantum…