Quantum Foundations And Open Quantum Systems: Lecture Notes Of The Advanced School

Lecture Notes of the Advanced School

Theo M Nieuwenhuizen, Claudia Pombo, Claudio Furtado, Andrei Yu Khrennikov, Inácio A Pedrosa, Václav Špička

• Publisher: WSPC
• Year: 2014
• eBook ISBN: 9789814616744
• Topic: Biological Sciences
• Subtopic: Science General
• Index: Biological Sciences

The Advanced School on Quantum Foundations and Open Quantum Systems was an exceptional combination of lectures. These comprise lectures in standard physics and investigations on the foundations of quantum physics.

On the one hand it included lectures on quantum information, quantum open systems, quantum transport and quantum solid state. On the other hand it included lectures on quantum measurement, models for elementary particles, sub-quantum structures and aspects on the philosophy and principles of quantum physics.

The special program of this school offered a broad outlook on the current and near future fundamental research in theoretical physics.

The lectures are at the level of PhD students.

Contents:

• The Physics of Quantum Computation (Giuseppe Falci and Elisabetta Paladino)
• Quantum Information in Communication and Imaging (David S Simon, Gregg Jaeger and Alexander V Sergienko)
• Electron Systems Out of Equilibrium: Nonequilibrium Green's Function Approach (Václav Špička, Bedřich Velický and Andĕla Kalvová)
• A Geometric Approach to Dislocation Densities in Semiconductors (Knut Bakke and Fernando Moraes)
• Quantum Transport: A Unified Approach via a Multivariate Hypergeometric Generating Function (Ailton F Macedo-Junior and Antonio M S Macêdo)
• Time-Dependent Coupled Harmonic Oscillators: Classical and Quantum Solutions (Diego Ximenes Macedo and Ilde Guedes)
• Event-Based Simulation of Quantum Physics Experiments (Kristel Michielsen and Hans De Raedt)
• Lectures on Dynamical Models for Quantum Measurements (Theo M Nieuwenhuizen, Martí Perarnau-Llobet and Roger Balian)
• Towards a Wave Resolution of the Wave-Particle Duality (Andrei Yu Khrennikov)
• Emergence of Quantum Mechanics from a Sub-Quantum Statistical Mechanics (Gerhard Grössing)
• The Zero-Point Field and the Emergence of the Quantum (Luis de la Peña, Ana Maria Cetto and Andrea Valdés-Hernándes)
• Kerr-Newman Electron as Spinning Soliton (Alexander Burinskii)
• Elements for the Development of a Darwinian Scheme Leading to Quantum Mechanics (Carlos Baladrón)
• Reality, Causality, and Probability, from Quantum Mechanics to Quantum Field Theory (Arkady Plotnitsky)

Chapter 1

The Physics of Quantum Computation

Giuseppe Falci* and Elisabette Paladino^†

Dipartimento di Fisica e Astronomia, Università degli Studi Catania & CNR-IMM MATIS, Consiglio Nazionale delle Ricerche &
Istituto Nazionale di Fisica Nucleare, Sezione di Catania
Via Santa Sofia 64, 95123 Catania, Italy

Quantum Computation has emerged in the past decades as a consequence of down-scaling of electronic devices to the mesoscopic regime and of advances in the ability of controlling and measuring microscopic quantum systems. QC has many interdisciplinary aspects, ranging from physics and chemistry to mathematics and computer science. In these lecture notes we focus on physical hardware, present day challenges and future directions for design of quantum architectures.

1.Preliminary concepts

The field of quantum computation¹ has emerged in the past decades as a consequence of down-scaling of electronic devices to the mesoscopic regime and of advances in the ability of controlling and measuring microscopic quantum systems. The question emerges whether there is any fundamental gain in resorting to new computational paradigms where quantum mechanical properties of physical objects are fully exploited. Positive answers came from Richard Feynman² who showed that quantum systems may be efficiently simulated only by other quantum systems, i.e. an analog Quantum Computer (QC), and from the Shor’s breakthrough discovery of an efficient factoring algorithm on a digital QC.³ This has motivated theoretical and experimental investigation on the implementation of Digital QCs, which will be mainly addressed in this article, although the scenario of Quantum Information is much wider, and present efforts are mainly focused on analog QCs.⁴

QC has many interdisciplinary aspects, ranging from physics and chemistry to mathematics and computer science. It also plays, in our opinion, a central role in the field of foundations of Quantum Mechanics (QM). However for the sake of clarity we will adopt here a totally different point of view, presenting QC as an application of QM and addressing the topic of quantum hardware. On the other hand, quite often people use the Copenhagen interpretation as an efficient tool to teach the how-to of QM. Despite of our choice it is worth stressing that ultimate answers on fundamental questions may critically depend on subtle hardware problems, as in the case of the violation of Bell inequalities.⁵ Improvement in hardware as sources and detectors, and in the ability of faithful production of highly entangled states, belong indeed to the realm of Quantum Information and certainly will trigger new insight and provide new tools for fundamental physics studies.

In these lecture notes we focus on physical hardware, present day challenges and future directions for design of quantum architectures. An exhaustive but condensed review on the subject has been published by Ladd et al. few years ago.⁶ We will first describe the main issues of digital QC^a from which naturally emerges a set of requirements a quantum system should satisfy to be a good candidate for the implementation of a quantum computer, known as Di Vincenzo criteria.⁷ Recent experimental progresses have dealt with the central problem of decoherence, showing that it can be challenged to a certain extent. Also it emerged that a key concept for quantum computation is scaling, which is referred to several aspects of the problem as quantum algorithms, fabrication of “fault tolerant” (protected from decoherence/defects and reliable) hardware, number of elementary control pulses required for preparation, manipulation and interaction of quantum bits. This has lead to a more mature reformulation of the physical criteria for the implementation of quantum architectures.^6,8

1.1.From miniaturization to quantum technologies

Although microscopic systems are a natural hardware for Quantum Information, the strong motivation triggering this field comes from the quest for faster and low consuming “classical” computers (ClC), which is achieved by using smaller and smaller devices in the mesoscopic regime.⁹ As for the technological roadmap to down-scaling, also fundamental studies in Condensed Matter Physics follow a “top-down” approach for the description of solid-state phenomena. This approach is sort of “adaptive”: The underlying quantum nature is introduced judiciously, starting from phenomena related to quantization and then to coherence, which appears as long as macroscopic (semiclassical) physical systems shrink to become mesoscopic (see Fig. 1).

1.1.1.Semiclassical electrons in electronic devices

The golden era of semiconductor electronics started about sixty years ago with the invention of the bipolar transistor, and then with the discovery that also resistors and capacitors can be made out of silicon, yielding the integrated circuit. The development of planar technology has allowed to reach integration levels from several thousands of transistor per unit chip area since 1970 to several billions nowadays. This trend has been empirically described by the Moore’s law^b (1965), which states that the number of transistor on a chip doubles roughly every two years. Scaling down the size of integrated circuits, keeping a much slower increase of costs per unit area, has been the main subject of microelectronics technologies in the last two decades, and has required enormous progresses in manufacturing.⁹ Ideally it would allow to build larger and faster computers, with the same volume and price. However even in this scenario there are fundamental limitations to miniaturization. One of these is related to the so called Landauer principle¹⁰ (see Sec. 1.2), other limitations being due to stray quantum effects coming into play, leading to malfunctioning of standard logic devices.⁹ As we will see quantum computation leverages on these two issues to propose a new paradigm for information processing.

Fig. 1. Synoptic scheme of the roadmap from semiclassical to quantum coherent regimes in solid-state systems. New phenomena related to the quantum nature, in particular quantization and coherence, appear as long as macroscopic (semiclassical) physical systems shrink to become microscopic. In the intermediate mesoscopic regime, explored by Nanophysics, effects as quantum coherence in atoms survive on much larger time and space scales.

From the point of view of transport the regime of microelectronics is referred as semiclassical since, even if QM properties are crucial in explaining thermodynamics and even the very existence of solids, electrons move as classical particles, with a number of peculiarities which do not prevent the use of classical Boltzmann equation as the main investigation tool for computational electronics. Also electromagnetic fields used to address optoelectronic microdevices are semiclassical. In particular laser light, is a phase coherent classical radiation, i.e. containing many many photons, even if phenomena involved in the physics of laser sources is exquisitely “quantum incoherent”.

1.1.2.Incoherent nanophysics

The quantum signature appearing when devices are do...

Table of contents

• Cover Page
• Title
• Copyright
• Preface
• Contents
• 1. The Physics of Quantum Computation
• 2. Quantum Information in Communication and Imaging
• 3. Electron Systems Out of Equilibrium: Nonequilibrium Green’s Function Approach
• 4. A Geometric Approach to Dislocation Densities in Semiconductors
• 5. Quantum Transport: A Unified Approach via a Multivariate Hypergeometric Generating Function
• 6. Time-Dependent Coupled Harmonic Oscillators: Classical and Quantum Solutions
• 7. Event-Based Simulation of Quantum Physics Experiments
• 8. Lectures on Dynamical Models for Quantum Measurements
• 9. Towards a Wave Resolution of the Wave-Particle Duality
• 10. Emergence of Quantum Mechanics from a Sub-Quantum Statistical Mechanics
• 11. The Zero-Point Field and the Emergence of the Quantum
• 12. Kerr-Newman Electron as Spinning Soliton
• 13. Elements for the Development of a Darwinian Scheme Leading to Quantum Mechanics
• 14. Reality, Causality, and Probability, from Quantum Mechanics to Quantum Field Theory