Universal Quantum Computing: Supervening Decoherence - Surmounting Uncertainty

Supervening Decoherence — Surmounting Uncertainty

Richard L Amoroso

• Publisher: WSPC
• Year: 2017
• eBook ISBN: 9789813146013
• Topic: Physical Sciences
• Subtopic: Computer Science General

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This breakthrough volume touts having dissolved the remaining barriers to implementing Bulk Universal Quantum Computing (UQC), and as such most likely describes the most advanced QC development platform. Numerous books, hundreds of patents, thousands of papers and a Googolplex of considerations fill the pantheon of QC R&D. Of late QC mathemagicians claim QCs already exist; but by what chimeric definition. Does flipping a few qubits in a logic gate without an algorithm qualify as quantum computing? In physics, theory bears little weight without rigorous experimental confirmation, less if new, radical or a paradigm shift. This volume develops quantum computing based on '3rd regime' physics of Unified Field Mechanics (UFM). What distinguishes this work from a myriad of other avenues to UQC under study? Virtually all R&D paths struggle with technology and decoherence. If highly favored room-sized cryogenically cooled QCs ever become successful, they would be reminiscent of the city block-sized Eniac computer of 1946. The QC prototype proposed herein is room temperature and tabletop. It is dramatically different in that it is not confined to the limitations of quantum mechanics; since it is based on principles of UFM the Uncertainty Principle and Decoherence no longer apply. Thus this QC model could be implemented on any other quantum platform!

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Contents: From Concept to Conundrum;Cornucopia of Quantum Logic Gates;Multiverse Cosmology — A New Basis of Reality;A Revolution in the Conception of Matter;From Qubits to Relativistic (R-Qubits);Utility of Unified Field Mechanics;Surmounting Uncertainty Supervening Decoherence;Measurement with Certainty;Topological Quantum Field Theory;Topological Quantum Computing;A New Group of Transformations;Ontological-Phase Topological Field Theory;New Classes of Quantum Algorithms;Class II Mesoionic Xanthines as Potential Ten Qubit Substrate Registers;Universal Quantum Computing Prototype Modeling; --> -->
Readership: Graduate students and researchers interested in quantum computing or quantum information.
-->Decoherence, Quantum Computing, Qubit, Uncertainty Principle

• Unique in solving remaining problem of decoherence
• Introduces relativistic qubit model with additional degrees of freedom
• Operationally surmounts the Quantum Uncertainty Principle

Chapter 1

From Concept to Conundrum

“… Trying to find a computer simulation of physics, seems … an excellent program to follow … I’m not happy with all the analyses that go with just the classical theory, because nature isn’t classical, … and if you want to make a simulation of nature, you’d better make it quantum mechanical …”, R. Feynman [1].

The concept of quantum computing (QC) is generally credited to ratiocination by Nobelist Richard Feynman during the 1980’s, who saw ‘nothing in the laws of physics that precluded their development’. During the ensuing decades accelerating progress has been made in the ongoing development of quantum logic gates, a variety albeit dearth of algorithms and most assuring a plethora of potentially viable substrates for QC implementation. Proponents generally consider the remaining hurdle preventing bulk universal QC centers on problems associated with decoherence. In this chapter for the purpose of bringing the reader up to speed and a semblance of self-containment, a precis of the dominant platforms under development is given; each platform is unique in substrate technology, implementation format and scaling challenges. This also prepares the reader for later chapters where we move from qubits to a new class of relativistic qubits (r-qubits) whereby additional degrees of freedom are deemed essential for crossing the ‘semi-quantum limit’ into the realm of Unified Field Mechanics (UFM) allowing routine violation of the Quantum Uncertainty Principle and thereby supervening decoherence.

1.1Preamble – Bits, Qubits and Complex Space

A classical Turing bit (short for binary digit) is the smallest unit of digital data and is limited to the two discrete binary states, 0 and 1; but a quantum bit (qubit) can additionally enter an entangled superposition of states, in which the qubit is effectively in both states simultaneously. While a classical register made up of n binary bits can contain only one of 2ⁿ possible numbers, the corresponding quantum register can contain all 2ⁿ numbers simultaneously. Thus in theory, a QC could operate on seemingly infinite values simultaneously in parallel, so that a 30-qubit QC would be comparable to a digital computer capable of performing 10¹³ (trillion) floating-point operations per second (TFLOPS) which is comparable to currently fastest supercomputers.

Fig. 1.1. Geometrical qubit representations. a) The qubit resides on the complex circle in the Hilbert space of all possible orientations of

. The complex unit circle is called the Hilbert space representation. In the logical basis, the two degrees of freedom of the qubit are expressed as two angles geometrically interpreted as Euler angles. b) The Bloch sphere in spin space showing the geometric representation of a qubit where

for orthogonal eigenstates

and

of a single qubit on opposite poles, with superpositions located on the sphere’s surface. Adapted from [2].

The qubit, a geometrical representation of the pure state space of a 2-level quantum mechanical system, is described in Dirac’s ‘bra-ket notation’ by the state

where α and β are complex numbers satisfying the absolute value parameter |α|²+|β|² = 1; such that measurement would result in state

with probability

and

with probability

. Formally, a qubit is represented in the 2D complex vector space, ℂ² where the

can be represented in the standard orthonormal basis as

for the ground state or

for the excited state, or on the Bloch sphere as in Fig. 1.1b.

A qubit is shown in Fig. 1.1 in both its SU(2) Hilbert space representation (top), and the same qubit on the Bloch sphere in its O(3) representation (bottom). The SU(2) and O(3) representations are homomorphic, i.e. mapping preserves form between the two structures.

Vincenzo itemized what he felt were the major requirements for implementing practical bulk QC [3]:

•Physically scalable, allowing the number of qubits to be sufficiently increased for bulk implementation.

•Qubits must be able to be initialized to arbitrary values.

•Quantum gates that operate faster than the decoherence time.

•A universal gate set for running quantum algorithms.

•Qubits that can be easily read correctly.

None of Vincenzo’s requirements are yet fulfilled; some are further along than others; system decoherence is among the most challenging aspects remaining. Recently, the fundamental basis of quantum information systems is undergoing an evolution in terms of the nature of reality with radical changes in the nature of the measurement problem. The recent introduction of parameters for relativistic information processing (RIP), including relativistic r-qubits, has brought into question the historical sacrosanct basis of ‘locality and unitarity’ in terms of Bell’s inequalities, overcoming the no-cloning theorem [4,5]. The epistemic view of the Copenhagen Interpretation is challenged by ontic considerations of objective realism and additionally as merged by W. Zurek’s epi-ontic blend of quantum redundancy in quantum Darwinism [6].

1.2Panoply of QC Architectures and Substrates – Limited Overview

The following list represents many prominent QC architectures and substrates currently under development. It seems useful to briefly review the challenges and merits of each system as distinguished by the computing model and physical substrates used to implement qubits.

•Quantum Turing Machine

•Quantum Circuit Quantum Computing Model

•Measurement Based Quantum Computing

•Adiabatic Quantum Computing

•Kane Nuclear Spin Quantum Computing

•QRAM Models of Quantum Computation

•Electrons-On-Helium Quantum Computers

•Fullerene-Based ESR Quantum Computer

•Superconductor-Based Quantum Computers

•Diamond-Based Quantum Computer

•Quantum Dot Quantum Computing

•Transistor-Based Quantum Computer

•Molecular Magnet Quantum Computer

•Bose–Einstein Condensate-Based Quantum Computer

•Rare-Earth-Metal-Ion-Doped Inorganic Crystal Quantum Computers

•Linear Optical Quantum Computer

•Optical Lattice Based Quantum Computing

•Cavity Quantum Electrodynamics (CQED) Quantum Computing

•Nuclear Magnetic Resonance (NMR) Quantum Computing

•Topological Quantum Computing

•Unified Field Mechanical Quantum Computing

1.2.1Quantum Turing Machine

The quantum Turing machine (QTM) generalizes the classical Turing machine (CTM); the internal states of a CTM are replaced by pure or mixed states in a Hilbert space; The QTM is an idealistic platform not currently being developed. A QTM is a simple universal quantum computer used for modeling all the powerful parameters of quantum computing.

The QTM was proposed by Deutsch where he suggested that quantum gates could function similarly to traditional binary digital logic gates [7]. QTMs are not usually used for analyzing quantum computation; the quantum circuit model (QCM) is a more commonly used for such purposes.

1.2.2Quantum Circuit Computing Model

The quantum circuit model (QCM) computes sequences of quantum gates which are reversible transformations on a quantum mechanical analog of a classical n-bit register. The QCM has only two observables, preparation of the initial state and observation of the final state in the same basis for the same variable at the end of the computation [8].

Fig. 1.2. Quantum circuit for 3 qubits using Hadamard gates.

1.2.3Measurement Based Quantum Computing

The measurement based quantum computer (MBQC) model is...

Table of contents

• Cover Page
• Title
• Copyright
• Contents
• Preface
• Dedication
• Chap 1 From Concept to Conundrum
• Chap 2 Cornucopia of Quantum Logic Gates
• Chap 3 Multiverse Cosmology: A New Basis of Reality
• Chap 4 A Revolution in the Conception of Matter
• Chap 5 From Qubits to Relativistic (R-Qubits)
• Chap 6 Utility of Unified Field Mechanics
• Chap 7 Surmounting Uncertainty Supervening Decoherence
• Chap 8 Measurement with Certainty
• Chap 9 Topological Quantum Field Theory
• Chap 10 Topological Quantum Computing
• Chap 11 A New Group of Transformations
• Chap 12 Ontological-Phase Topological Field Theory
• Chap 13 New Classes of Quantum Algorithms
• Chap 14 Class II Mesoionic Xanthines as Potential Ten Qubit Substrate Registers
• Chap 15 Universal Quantum Computing Prototype Modeling
• Index