Fundamentals of Quantum Computing: Theory and Practice

Hafiz Md. Hasan Babu

Vishal Kumar Jaiswal, Sam Goundar, Gurram Sunitha +3 more

Quantum computing is an emerging technology around the world. Even though it is limited to theory in most cases, it can break today’s encryption in seconds, unlike classical computers, which could take some years; however, quantum computers’ limited qubits stop them from being widely used in real-world situations, where they can demonstrate their superior efficiency. A lot of complex real-world problems have been solved using the fundamental concepts. So, unlike other books on quantum computing and quantum mechanics, this chapter aims to combine quantum mechanics and quantum computing to make sense of quantum computing efficiently. In this chapter, we will discuss the fundamental concepts of quantum computing, like qubits, as well as practical applications and error corrections. Along with this, it will provide insights into the latest evolution of quantum computing by major companies working on quantum computing. Finally, this chapter will not discuss pure theory but mostly focus on the fundamentals and their applications and their limitations. At the end, there are some open questions to encourage future research opportunities in quantum computing.

Marek Kuś

Shengyu Hung

Building on the fundamental principles of quantum computing, this paper sequentially presents the development of quantum computing and its associated application domains. We also analyze and compare the differences between quantum and classical computing, highlighting the benefits of quantum computing for specific problems. To comprehend the advantages of quantum computing in particular fields, extensive research has been conducted in three areas: cryptography, chemistry, and artificial intelligence. We also discuss the wider applications of this emerging technology for future investigation, considering the current state of quantum computing development and anticipated trends.

Jincheng Zhang

This paper investigates the potential of quantum computation to revolutionize numerical simulation of quantum systems. Traditional numerical methods often struggle to accurately capture the complexities of quantum phenomena, necessitating the development of novel approaches. We propose a new dynamic variable field theory, leveraging quantum computation's inherent parallelism and superposition properties to provide a fundamentally different approach to simulating quantum behavior. This theory offers the promise of enhanced accuracy, speed, and the ability to predict quantum system evolution, potentially surpassing the limitations of existing numerical methods. The core of our work centers around a quantum-enhanced dynamic variable field formulation, emphasizing the interplay between quantum states and system evolution. The theoretical foundations and initial implementation demonstrate a robust framework for simulating fundamental quantum systems, offering a significant step towards practical quantum simulation.

Venkateswaran Kasirajan