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Control and Verification of Quantum Mechanical Systems

Dvir Kafri

Published Jan 1, 2015• 0 citations
Publisher

Abstract

Quantum information science uses the distinguishing features of quantum mechanics for novel information processing tasks, ranging from metrology to computation. This manuscript explores multiple topics in this field. We discuss implementations of hybrid quantum systems composed of trapped ions and superconducting circuits, protocols for detecting signatures of entanglement in small and many-body systems, and a proposal for ground state preparation in quantum Hamiltonian simulators.

DOI
10.13016/m2v34z

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Quantum information science uses the distinguishing features of quantum mechanics for novel information processing tasks, ranging from metrology to computation. This manuscript explores multiple topics in this field. We discuss implementations of hybrid quantum systems composed of trapped ions and superconducting circuits, protocols for detecting signatures of entanglement in small and many-body systems, and a proposal for ground state preparation in quantum Hamiltonian simulators.
Quantum information science is an emerging and multidisciplinary field whose ultimate goal is to take advantage of quantum phenomena, such as superposition and entanglement, in order to improve the information storage, commmunication and computation. Among all the disciplines spanned by QIS, quantum computing and quantum simulations have attracted a great deal of attention, as they aim to solve problems which are nowadays impossible to access with classical computers. There exist several proposals for implementing both quantum computers and quantum simulators, all of them based on different physical systems. Trapped ions, ultracold atoms, NMR systems, quantum dots or superconducting circuits are some examples of quantum simulators. Indeed, superconducting circuits are particularly suitable for implementing those devices, since they posess strong interactions, it is straightforward to scale them up, and are easily controllable..
Direct experimental access to some of the most intriguing quantum phenomena is not granted due to the lack of precise control of the relevant parameters in their naturally intricate environment. Their simulation on conventional computers is impossible, since quantum behaviour arising with superposition states or entanglement is not efficiently translatable into the classical language. However, one could gain deeper insight into complex quantum dynamics by experimentally simulating the quantum behaviour of interest in another quantum system, where the relevant parameters and interactions can be controlled and robust effects detected sufficiently well. Systems of trapped ions provide unique control of both the internal (electronic) and external (motional) degrees of freedom. The mutual Coulomb interaction between the ions allows for large interaction strengths at comparatively large mutual ion distances enabling individual control and readout. Systems of trapped ions therefore exhibit a prominent system in several physical disciplines, for example, quantum information processing or metrology. Here, we will give an overview of different trapping techniques of ions as well as implementations for coherent manipulation of their quantum states and discuss the related theoretical basics. We then report on the experimental and theoretical progress in simulating quantum many-body physics with trapped ions and present current approaches for scaling up to more ions and more-dimensional systems.
Abstract This comprehensive and self-consistent textbook presents quantum information science, a rapidly evolving interdisciplinary scientific field that will change modern computer science. The book is divided into four parts. The first part starts with a gentle introduction to some important mathematical concepts, followed by a discussion of computational models, linear algebra, and quantum mechanics. The second part explains more advanced topics of quantum mechanics, which are necessary to describe the decoherence of quantum states. The third part includes a presentation of entanglement, early quantum algorithms and quantum simulation, focussing on computational problems that quantum computers can solve faster than classical machines. The last part presents superconducting devices, a promising architecture for the implementation of quantum computers. With more than 200 figures and 100 exercises (with solutions), this book is ideal for a master’s course on quantum information processing. Readers starting a master’s program or a graduate course in physics, computer science, mathematics or quantum engineering will develop a good understanding of the fundamental concepts of the field.
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.