Quantum computing comes with the potential to push computational boundaries in various domains including, e.g., cryptography, simulation, optimization, and machine learning. Exploiting the principles of quantum mechanics, new algorithms can be developed with capabilities that are unprecedented by classical computers. However, the experimental realization of quantum devices is an active field of research with enormous open challenges, including robustness against noise and scalabilty. While systems and control theory plays a crucial role in tackling these challenges, the principles of quantum physics lead to a (perceived) high entry barrier for entering the field of quantum computing. This tutorial paper aims at lowering the barrier by introducing basic concepts required to understand and solve research problems in quantum systems. First, we introduce fundamentals of quantum algorithms, ranging from basic ingredients such as qubits and quantum logic gates to prominent examples and more advanced concepts, e.g., variational quantum algorithms. Next, we formalize some engineering questions for building quantum devices in the real world, which requires the careful manipulation of microscopic quantities obeying quantum effects. To this end for N-level systems, we introduce basic concepts of (bilinear) quantum systems and control theory including controllability, observability, and optimal control in a unified frame. Finally, we address the problem of noise in real-world quantum systems via robust quantum control, which relies on a set-membership uncertainty description frequently employed in control. A key goal of this tutorial paper is to demystify engineering aspects of quantum computing by emphasizing that its mathematical description mainly involves linear algebra (for quantum algorithms) and the handling of bilinear control systems (for quantum systems and control theory) but does not require too much detailed knowledge of quantum physics.
Quantum computing comes with the potential to push computational boundaries in various domains including, e.g., cryptography, simulation, optimization, and machine learning. Exploiting the principles of quantum mechanics, new algorithms can be developed with capabilities that are unprecedented by classical computers. However, the experimental realization of quantum devices is an active field of research with enormous open challenges, including robustness against noise and scalabilty. While systems and control theory plays a crucial role in tackling these challenges, the principles of quantum physics lead to a (perceived) high entry barrier for entering the field of quantum computing. This tutorial paper aims at lowering the barrier by introducing basic concepts required to understand and solve research problems in quantum systems. First, we introduce fundamentals of quantum algorithms, ranging from basic ingredients such as qubits and quantum logic gates to prominent examples and more advanced concepts, e.g., variational quantum algorithms. Next, we formalize some engineering questions for building quantum devices in the real world, which requires the careful manipulation of microscopic quantities obeying quantum effects. To this end for N-level systems, we introduce basic concepts of (bilinear) quantum systems and control theory including controllability, observability, and optimal control in a unified frame. Finally, we address the problem of noise in real-world quantum systems via robust quantum control, which relies on a set-membership uncertainty description frequently employed in control. A key goal of this tutorial paper is to demystify engineering aspects of quantum computing by emphasizing that its mathematical description mainly involves linear algebra (for quantum algorithms) and the handling of bilinear control systems (for quantum systems and control theory) but does not require too much detailed knowledge of quantum physics.
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.
Quantum computing, a transformative field that emerged from quantum mechanics and computer science, has gained immense attention for its potential to revolutionize computation. This paper aims to address the fundamentals of quantum computing and provide a comprehensive guide for both novices and experts in the field of quantum computing. Beginning with the foundational principles of quantum computing, we introduce readers to the fundamental concepts of qubits, superposition, entanglement, interference, and noise. We explore quantum hardware, quantum gates, and basic quantum circuits. This study offers insight into the current phase of quantum computing, including the noisy intermediate-scale quantum (NISQ) era and its potential for solving real-world problems. Furthermore, we discuss the development of quantum algorithms and their applications, with a focus on famous algorithms like Shor’s algorithm and Grover’s algorithm. We also touch upon quantum computing’s impact on various industries, such as cryptography, optimization, machine learning, and material science. By the end of this paper, readers will have a solid understanding of quantum computing’s principles, applications, and the steps involved in developing quantum circuits. Our goal is to provide a valuable resource for those eager to embark on their quantum computing journey and for researchers looking to stay updated on this rapidly evolving field.
This textbook provides a comprehensive foundation for the emerging interdisciplinary field of quantum robotics. It systematically addresses the core question of how quantum computational principles can be formulated to address fundamental challenges in robotics: planning, optimization, perception, and control. The work is structured to build a rigorous bridge between the abstract mathematics of quantum information and the concrete computational problems of autonomous systems. The first part establishes the necessary foundations, introducing the computational models of quantum circuits alongside the classical formulations of robotic kinematics, dynamics, and state estimation. The second part is dedicated to quantum algorithmic primitives, with detailed exposition on quantum search, quantum linear algebra, and quantum optimization algorithms. Each algorithmic chapter explicitly maps these primitives to robotic problem classes, such as motion planning, sensor data processing, and trajectory optimization, discussing both potential advantages and current practical constraints. The third part focuses on system integration and forward-looking perspectives. It explores quantum machine learning models for robotic learning, outlines hybrid quantum-classical computer architectures required for real-world applications, and rigorously examines the ethical and societal implications of increasingly capable quantum-optimized autonomous systems. The textbook concludes with practical appendices detailing software tools, benchmark problems, and problem sets. Designed for graduate students and researchers in robotics, computer science, and quantum engineering, this book emphasizes clear problem formulation, realistic resource analysis, and verifiable claims. Its goal is to equip the next generation of scientists and engineers with the principles and critical perspective needed to advance the field beyond theoretical potential into practical, validated technology.
Abstract Effectively manipulating quantum computing (QC) hardware in the presence of imperfect devices and control systems is a central challenge in realizing useful quantum computers. Susceptibility to noise critically limits the performance and capabilities of today’s so-called noisy intermediate-scale quantum devices, as well as any future QC technologies. Fortunately, quantum control enables efficient execution of quantum logic operations and quantum algorithms with built-in robustness to errors, and without the need for complex logical encoding. In this manuscript we introduce software tools for the application and integration of quantum control in QC research, serving the needs of hardware R&D teams, algorithm developers, and end users. We provide an overview of a set of Python-based classical software tools for creating and deploying optimized quantum control solutions at various layers of the QC software stack. We describe a software architecture leveraging both high-performance distributed cloud computation and local custom integration into hardware systems, and explain how key functionality is integrable with other software packages and quantum programming languages. Our presentation includes a detailed mathematical overview of key features including a flexible optimization toolkit, engineering-inspired filter functions for analyzing noise susceptibility in high-dimensional Hilbert spaces, and new approaches to noise and hardware characterization. Pseudocode is presented in order to elucidate common programming workflows for these tasks, and performance benchmarking is reported for numerically intensive tasks, highlighting the benefits of the selected cloud-compute architecture. Finally, we present a series of case studies demonstrating the application of quantum control solutions derived from these tools in real experimental settings using both trapped-ion and superconducting quantum computer hardware.
Unlock the future of quantum technology with this comprehensive guide that bridges the gap between complex quantum theory and real-world applications, giving you the practical edge needed to solve the next generation’s toughest scientific and industrial problems. At its core, quantum computing leverages the principles of quantum mechanics to process information in fundamentally different ways from classical computing. As physical limits constrain the continued scaling of classical technologies, quantum computing offers a fundamentally new pathway toward solving complex problems in science, engineering, and industry. This book is a comprehensive guide designed to bridge the gap between theoretical principles and real-world quantum computing applications. It explores quantum information theory, a cornerstone of quantum computing, to explain how information is encoded, manipulated, and measured in a quantum system. Topics such as quantum gates, circuits, and the Bloch sphere representation are covered in detail, offering readers a solid grounding in the mechanics of quantum operations. With a focus on practical implementation, this book is tailored for students, researchers, and professionals seeking to delve into the transformative world of quantum computing, where the boundaries of classical computation are redefined. Readers will find the book: Uses step-by-step guides and hands-on tutorials for building quantum circuits and running algorithms; Explores core algorithms through detailed walkthroughs of quantum algorithms, including Shor’s, Grover’s, and Quantum Fourier Transform; Provides hands-on learning through exercises, coding challenges, and projects to reinforce practical skills. Audience Academics, researchers, quantum software developers and hardware engineers, data scientists, AI specialists, and security experts focused on the study and implementation of quantum systems and processors.
Quantum computing represents a transformative shift in computational technology, leveraging the principles of quantum mechanics to process information in ways that surpass the limits of classical systems.By exploiting qubits, superposition, entanglement, and quantum parallelism, quantum computers offer the potential to solve certain classes of problems-such as optimization, cryptography, molecular simulation, and complex machine learning tasks-significantly faster than classical algorithms.With rapid advancements in quantum hardware and the emergence of Noisy Intermediate-Scale Quantum (NISQ) devices, quantum computing has evolved from a theoretical concept to a practical field with growing industrial and scientific relevance.Although current systems face challenges related to error rates, decoherence, and scalability, ongoing developments in quantum error correction, hybrid quantum-classical algorithms, and software frameworks like Qiskit, Cirq, and PennyLane continue to push the field forward.This paper provides an introductory overview of quantum computing, outlining its foundational principles, current technological landscape, key algorithms, and future research directions.The goal is to offer a clear understanding of how quantum computing is poised to reshape the future of computation.