In 1981, Richard Feynman proposed a device called a "quantum computer" to take advantage of the laws of quantum physics to achieve computational speed-ups over classical methods. Quantum computing promises to revolutionize how and what we compute. Over the course of three decades, quantum algorithms have been developed that offer fast solutions to problems in a variety of fields including number theory, optimization, chemistry, physics, and materials science. Quantum devices have also significantly advanced such that components of a scalable quantum computer have been demonstrated; the promise of implementing quantum algorithms is in our near future. I will attempt to explain some of the mysteries of this disruptive, revolutionary computational paradigm and how it will transform our digital age.
In 1981, Richard Feynman proposed a device called a "quantum computer" to take advantage of the laws of quantum physics to achieve computational speed-ups over classical methods. Quantum computing promises to revolutionize how and what we compute. Over the course of three decades, quantum algorithms have been developed that offer fast solutions to problems in a variety of fields including number theory, optimization, chemistry, physics, and materials science. Quantum devices have also significantly advanced such that components of a scalable quantum computer have been demonstrated; the promise of implementing quantum algorithms is in our near future. I will attempt to explain some of the mysteries of this disruptive, revolutionary computational paradigm and how it will transform our digital age.
Quantum computing promises to revolutionize several scientific and technological domains through fundamentally new ways of processing information. Among its most compelling applications is digital quantum simulation, where quantum computers are used to replicate the behavior of other quantum systems. This could enable the study of problems that are otherwise intractable on classical computers, transforming fields such as quantum chemistry, condensed matter physics, and materials science. Despite this potential, realizations of practical quantum advantage for relevant problems are hindered by imperfections of current devices. This also affects quantum hardware based on superconducting circuits which is among the most advanced and scalable platforms. The envisaged long-term solution of fault-tolerant quantum computers that correct their own errors remains out of reach mainly due to the associated qubit number overhead. As a result, the field has developed strategies that combine quantum and classical resources, exploit hardware-native operations, and employ error mitigation techniques to extract meaningful results from noisy data. This doctoral thesis contributes to this broader effort by exploring methods for advancing quantum simulation across the full computational stack, including hardware-level innovations, refined techniques for noise modeling and error mitigation, and algorithmic improvements enabled by efficient measurement processing.
This volume explores the potential of quantum technologies. The book features insightful perspectives on quantum mechanics, computational paradigms, and practical applications, and it explores key concepts such as quantum entanglement, adiabatic computing, and quantum algorithms. Readers will discover how quantum systems are revolutionizing fields like cryptography, materials science, and artificial intelligence, promising faster computations and significant advances. Through a blend of theoretical exploration and practical insights, this book navigates the complexities of quantum communication, error correction, and the development of scalable quantum architectures. Ideal for researchers, students, and enthusiasts alike, it offers a gateway to understanding the current capabilities and future directions of quantum computing, demonstrating its potential for transforming technical developments and pushing scientific frontiers.
Quantum physics is a fascinating area from a computational viewpoint. The features that make quantum systems prohibitively hard to simulate classically are precisely the aspects exploited by quantum computation to obtain exponential speedups over classical computers. In this talk I will survey our current understanding of the power (and limits) of quantum computers, and prospects for experimentally realizing them in the near future. I will also touch upon insights from quantum comuptation that have resulted in new classical algorithms for efficient simulation of certain important quantum systems.
Commercial applications of quantum computation have become viable due to the rapid progress of the field in the recent years. Efficient quantum algorithms are discovered to cope with the most challenging real-world problems that are too hard for classical computers. Manufactured quantum hardware has reached unprecedented precision and controllability, enabling fault-tolerant quantum computation. Here, I give a brief introduction on what principles in quantum mechanics promise its unparalleled computational power. I will discuss several important quantum algorithms that achieve exponential or polynomial speedup over any classical algorithm. Building a quantum computer is a daunting task, and I will talk about the criteria and various implementations of quantum computers. I conclude the talk with near-future commercial applications of a quantum computer.
Quantum computing, a revolutionary paradigm shift in computation, leverages the principles of quantum mechanics to perform tasks beyond the capabilities of classical computers. By harnessing the power of quantum bits (qubits), which can exist in superpositions of states and exhibit entanglement, quantum computers offer the potential to revolutionize fields such as chemistry, materials science, cryptography, and artificial intelligence. This paper delves into the fundamental concepts of quantum computing, including superposition, entanglement, and quantum gates. We explore the development of quantum hardware, encompassing various technologies like superconducting qubits, ion traps, and photonic qubits. Additionally, we discuss the limitations and challenges faced in building scalable and error-corrected quantum computers, such as decoherence and noise. The potential applications of quantum computing are vast and far-reaching. In the realm of quantum chemistry and materials science, quantum computers can simulate complex molecular systems, enabling the design of novel materials and drugs. In the field of cryptography, quantum computers pose a significant threat to classical cryptographic algorithms, necessitating the development of quantum-resistant cryptographic techniques. Furthermore, quantum machine learning holds the promise of accelerating AI advancements by enabling the development of powerful quantum algorithms.
Many important physical and mathematical problems are difficult to solve on classical computers, resulting in difficulty in finding new advanced materials, simulating quantum field theories and solving large combinatorial optimisation tasks. Quantum computers have shown great promise in being able to solve these (and many other) problems faster than their classical counterparts, and therefore should be thoroughly investigated as a significant tool for enabling the acceleration of scientific progress. This work develops methods to tackle several problems across the spectrum of quantum algorithms, providing methods suitable for the near-term hardware, to the future where large fault-tolerant quantum computers exist. Therefore, the works in this thesis range from efficiently making use of limited quantum hardware to taking advantage of hardware benefits (e.g. excess qubits) as quantum computation advances. Covered topics include: an alternative paradigm for the optimisation of variational circuits and quantum neural networks; techniques for improving energy estimation of quantum states through the collection and processing of large amounts of randomised measurement data; the use of entanglement in guiding the automatic discovery of quantum circuits; investigating the role of symmetries in adiabatic state preparation of molecules and the large scale parallelisation of a common fault-tolerant subroutine, potentially producing large runtime speed-ups for the simulation of chemistry on quantum computers. Although there are many challenges remaining from both hardware and algorithms perspectives before the large-scale utility of quantum computers can be demonstrated, the contributions of this work make steps towards the efficient utilisation of quantum hardware that will be available in the coming years.