Introduction to Quantum Computer : Basics and Recent Advances(Tutorials)

Robert H. Ewald

Julian Berberich, Daniel Fink

Quantum computing is a fascinating interdisciplinary research field that promises to revolutionize computing by efficiently solving previously intractable problems. Recent years have seen tremendous progress on both the experimental realization of quantum computing devices and the development and implementation of quantum algorithms. However, realizing the computational advantages of quantum computers in practice remains a widely open problem due to numerous fundamental challenges. Interestingly, many of these challenges are connected to performance, robustness, scalability, optimization, or feedback, all of which are central concepts in control theory.This article provides a tutorial introduction to quantum computing from the perspective of control theory. We introduce the mathematical framework of quantum algorithms ranging from basic elements, including quantum bits and quantum gates, to more advanced concepts, such as variational quantum algorithms and quantum errors. The tutorial only requires basic knowledge of linear algebra and, in particular, no prior exposure to quantum physics. Our main goal is to equip readers with the mathematical basics required to understand and possibly solve (control-related) problems in quantum computing. In particular, beyond the tutorial introduction, we provide a list of research challenges in the field of quantum computing and discuss their connections to control.

Marcus Stephen Edwards

Amr Magdy, Ibrahim Sabek, Moustafa A. Youssef

Quantum computing has shown significant potential for addressing complex optimization and computationally intensive problems across a range of domains. Its adoption in spatial data applications presents substantial opportunities for advancing spatial computing. This tutorial provides an in-depth introduction to quantum computing, covering both the quantum circuit model (gate model) and quantum annealing, and discusses their applications in spatial computing. The tutorial is organized into three parts. The first part introduces fundamental concepts in quantum computing. The second part presents quantum gates, highlighting examples of basic gates and their use in circuits. The third part introduces quantum annealing, including Quadratic Unconstrained Binary Optimization (QUBO) modeling and hybrid solvers that combine the power of Quantum Processing Units (QPUs) with classical CPUs. The tutorial also points readers to key resources at the intersection of quantum computing and spatial computing.

Stefano Olivares

S. E. Rasmussen, K.S. Christensen, Simon Panyella Pedersen +4 more

This tutorial aims at giving an introductory treatment of the circuit analysis of superconducting qubits, i.e., two-level systems in superconducting circuits.It also touches upon couplings between such qubits and how microwave driving and these couplings can be used for single-and two-qubit gates, as well as how to include noise when calculating the dynamics of the system.We also discuss higher-dimensional superconducting qudits.The tutorial is intended for new researchers with limited or no experience with the field but should be accessible to anyone with a bachelor's degree in physics.The tutorial introduces the basic methods used in quantum circuit analysis, starting from a circuit diagram and ending with a quantized Hamiltonian, that may be truncated to the lowest levels.We provide examples of all the basic techniques throughout the discussion, while in the last part of the tutorial we discuss several of the most commonly used circuits for quantum-information applications.This includes both worked examples of single qubits and examples of how to analyze the coupling methods that allow multiqubit operations.In several detailed appendices, we provide the interested reader with an introduction to more advanced techniques for handling larger circuit designs.