Author(s): Schmitz, Timothy | Advisor(s): Barrett, Jeffrey A | Abstract: Our epistemic limits depend on the nature of the physical world we inhabit and the ways in which we can observe and manipulate it. This dissertation examines these limits in the realm of physical computation. It focuses on quantum computing and particularly computing in GRW quantum mechanics, although it has implications for both quantum computing in particular and physical computation more broadly. By rigorously investigating the conceptual issues that arise when looking at computation in GRW, we see how the conceptual issues in the foundations of quantum mechanics and our solutions to these issues determine what models of quantum computation can be realized and what quantum computing can achieve. More broadly, we see how grounding our discussions of physical computation in precise physical theories informs our understanding of computational and epistemic limits and illustrates the challenges and nuances involved in the work of developing a rigorous understanding of what is physically computable.
Author(s): Schmitz, Timothy | Advisor(s): Barrett, Jeffrey A | Abstract: Our epistemic limits depend on the nature of the physical world we inhabit and the ways in which we can observe and manipulate it. This dissertation examines these limits in the realm of physical computation. It focuses on quantum computing and particularly computing in GRW quantum mechanics, although it has implications for both quantum computing in particular and physical computation more broadly. By rigorously investigating the conceptual issues that arise when looking at computation in GRW, we see how the conceptual issues in the foundations of quantum mechanics and our solutions to these issues determine what models of quantum computation can be realized and what quantum computing can achieve. More broadly, we see how grounding our discussions of physical computation in precise physical theories informs our understanding of computational and epistemic limits and illustrates the challenges and nuances involved in the work of developing a rigorous understanding of what is physically computable.
The field of quantum computing has emerged as a promising frontier in information technology, harnessing the counterintuitive principles of quantum mechanics to revolutionize the way we process and manipulate information. This paper delves into the fundamentals of quantum computing, exploring its theoretical underpinnings, physical realizations, and potential applications. By examining the principles of quantum superposition, entanglement, and quantum parallelism, we shed light on the remarkable capabilities of quantum computers and their ability to tackle complex computational problems that are intractable for classical computers. The paper also investigates the various physical platforms being explored for the realization of quantum computing, including superconducting circuits, trapped ions, and topological systems. Additionally, we discuss the current state of quantum computing hardware, highlighting the challenges and progress in areas such as qubit scalability, error correction, and quantum supremacy. Finally, we explore the potential applications of quantum computing across diverse fields, ranging from cryptography and optimization to quantum simulation and machine learning. Through a comprehensive analysis of theoretical frameworks, experimental findings, and technological developments, this paper aims to provide a comprehensive understanding of the quantum computing landscape and its vast implications for the future of information processing. Keywords: Quantum Computing, Information Processing, Quantum Mechanics, Superposition, Entanglement, Computation, Theoretical Foundations, Qubit, Quantum Gates, Quantum Computing Models, Circuit Model, Adiabatic Model, Quantum Error Correction, Decoherence.
Decoherence is the physical process by which the classical world - the world of common sense - emerges from its quantum underpinnings. This physical process refers to the loss of phase coherence between the parts of a quantum system, because of the interaction of the system with the environment. This text with contributions from the Advanced Research Workshop (ARW) provides an in-depth discussion of this physical process and of its relevance in understanding and interpreting quantum mechanics, with special emphasis given to its implications in implementing the practical aspects of quantum computation and information transfer. The ARW brings together scientists in diverse fields such as mathematical physics, quantum logic, and quantum computing for an intense, interdisciplinary discussion of decoherence and its practical implications in quantum computing. Quantum computing represents possibly the epitome of the technological impact that quantum mechanics can have on technological developments in the foreseeable future. Its realization would allow the performance of tasks that are practically unthinkable in terms of classical physics. Such exotic occurrences as breaking hitherto unbreakable codes, searching enormous lists for specific entries, and communicating with messages that betray the presence of eavesdropping would fall within reach. These wonders are possible when one exploits the logical consequences of the laws that govern natural phenomena at the most fundamental level, namely, the laws of quantum mechanics standing squarely in the way of these developments is decoherence. The aim of the workshop was to provide an in-depth discussion of the state of affairs regarding the progress that is being made in understanding the effects of decoherence in quantum computation and information transfer and in getting around it. The present is a particularly fitting time for discussions of an interdisciplinary nature, encompassing quantum logic, mathematics and physics, addressing these issues. The invited speakers have been chosen among those who continue to make significant contributions in this domain of science and we expect lively and informative presentations and discussions. Also invited were those who are expected to benefit greatly from exposure to the issues under consideration and who will carry developments further as their own scientific career unfolds.
Abstract This chapter examines several fundamental quantum issues. Although not strictly needed for quantum information science (QIS) and quantum computing (QC), these issues help the reader understand why QC provides capabilities that go far beyond those of classical computers. The chapter begins with a look at a specific instantiation of Bell’s theorem and why, nearly 60 years after its publication, it continues to roil discussions about the foundations of quantum mechanics and the implications for what we can say about the physical nature of the world. Equally controversial, at the foundational level, is the problem of describing quantum measurements and their probabilistic results. The discussion shows that entanglement issues lie at the core of many of the debates about measurement and that correlations among measurement outcomes can reveal entanglement. Finally, the fragility of actual quantum systems that could interact with their environments causes decoherence. While this is a problem for QC, it could be useful in quantum sensing.
The physics and the mathematics of computation are examined to provide a foundation and perspective for the investigation of the quantum mechanics of computation. Our purpose is to explore the fundamental limits and constraints imposed on computation by Nature through the laws of physics and the mathematics of computational complexity. Inasmuch as information storage and transmission are an integral part of computation, their physical bounds are considered. The computer is viewed both physically and mathematically as a dynamical system, and is depicted in terms of the basic Turing machine paradigm. Three fundamental classes of the Turing machine are defined; the deterministic, stochastic and quantum Turing machines. Hamiltonian models and physical realizations of quantum computing are described. Quantum computers can perform some tasks which have no classical analogue, but they cannot compute functions that are non-computable by classical means. Some classically intractable problems can be solved with quantum computers.
This special issue of Journal of Physics A: Mathematical and Theoretical entitled 'The Quantum Universe' is dedicated to Professor Giancarlo Ghirardi on the occasion of his 70th birthday. Giancarlo Ghirardi has made many important contributions to the foundations of quantum mechanics including the celebrated Ghirardi–Rimini–Weber (GRW) model of spontaneous wavefunction collapse. However, although Professor Ghirardi's birthday is the inspiration for this issue, it has a much broader scope than the area traditionally known as Foundations of Quantum Mechanics. All invited authors are experts in areas of physics in which quantum theory is fundamental: non relativistic quantum mechanics, quantum computation and information, quantum field theory, quantum gravity, quantum cosmology and philosophy of science. The issue was conceived as an opportunity for workers in these diverse areas to share with the widest possible readership their views on quantum theory. Authors were encouraged to give their personal assessment of the role of quantum theory in their work particularly as it pertains to a vision of the global aims of their research. The articles are accessible to any physicist with a solid knowledge of quantum mechanics, and many contain an emphasis on conceptual developments, both those achieved and those hoped for. One theme that runs throughout Giancarlo Ghirardi's contributions to science is the unity of physics: the development of the GRW model itself was motivated by the conviction that the same physics should govern microscopic and macroscopic systems. However, readers of this special issue will clearly see that there is no unity as yet in the views of workers on fundamental quantum theories. Indeed the diversity of the articles, ranging from technical developments in well defined approaches, to new proposals for interpretations of quantum mechanics, indicates the state of fundamental physics: healthily active and yet lacking the consensus we seek in science. Much work clearly remains and this volume has the potential to be a lasting reference recording the achievements of, and crucial further challenges for, our quantum community.