Brief Primer on the Fundaments of Quantum Computing Richard L Amoroso [email protected] Abstract . 4 Preface . 4 PART 1 From Concept to Conundrum 1.1 Preamble – Bits, Qubits and Complex Space . 8 1.2 Panoply of QC Architectures and Substrates – Limited Overview . .9 1.2.1 Quantum Turing Machine . .10 1.2.2 Quantum Circuit Computing Model . 10 1.2.3 Measurement Based Quantum Computing . .11 1.2.4 Adiabatic Quantum Computer . .12 1.2.5 The Kane Nuclear Spin QC . 13 1.2.6 QRAM Models of Quantum Computation . 14 1.2.7 Electrons-On-Helium Quantum Computers . 14 1.2.8 Fullerene-Based ESR Quantum Computer . 15 1.2.9 Superconductor-Based Quantum Computers . 16 1.2.9.1 SQUID-BASED SUPERCONDUCTOR QC . 16 1.2.9.2 TRAPPED ION-BASED SUPERCONDUCTOR QC . 17 1.2.10 Diamond Based Quantum Computers . 18 1.2.11 Quantum Dot Quantum Computer . 19 1.2.12 Transistor-Based Quantum Computer . .20 1.2.13 Molecular Magnet Quantum Computer . .21 1.2.14 Bose–Einstein Condensate-Based Quantum Computer . .22 1.2.15 Rare-Earth-Metal-Ion-Doped Inorganic Crystal QC . 22 1.2.16 Linear Optical Quantum Computer (LOQC) . .23 1.2.17 Optical Lattice Based Quantum Computing (OLQC) . 24 1.2.18 Cavity Quantum Electrodynamics Quantum Computing. 25 1.2.19 Nuclear Magnetic Resonance (NMR) Quantum Computing. 26 Richard L Amoroso – Fundaments of Quantum Computing 1.2.19.1 LIQUID-STATE NMRQC . 26 1.2.19.2 SOLID-STATE NMRQC. 27 1.2.20 Topological Quantum Computing (TQC) . 28 1.2.21 Unified Field Mechanical Quantum Computing . 29 1.3 Concept. .29 1.4. Conundrum - Hypotheses non Fingo. 30 1.4.1 The Church-Turing Hypothesis . .30 1.4.2 The Church-Turing-Deutsch Thesis. .31 1.4.3 Perspicacious Perspicacity – Who Has it? Where can I get Some? . .31 References. .. .32 PART 2 Cornucopia of Quantum Logic Gates 2.1 Fundamental Properties of Gate Operations. .35 2.2 Unitary Operators as Quantum Gates. .36 2.3 Some Fundamental Quantum Gates . .37 2.5 Rotation Gate Quantum Multiplexer. 43 References. .. .44 PART 3 Surmounting Uncertainty Supervening Decoherence 3.1 Phenomenology Versus Ontology . 45 3.2 The Turing Paradox and Quantum Zeno Effect . 50 3.3 From the Perspective of Multiverse Cosmology. 51 3.4 Micromagnetics LSXD Topological Charge Brane Conformation. 54 3.5 Catastrophe Theory and the M-Theoretic Formalism. .59 3.6 Protocol for Empirically Testing Unified Theoretic Cosmology. .63 3.7 Introduction to a P 1 Experimental Design. 65 3.8 Conclusions . .. .72 References . .. 73 PART 4 Measurement With Certainty 4.1 Introduction – Summary of Purpose. .. .77 4.2 The Principle of Superposition. .. .79 4.3 Oscillatory Rabi NMR Resonance Cycles . 80 4.4 The Problem of Decoherence . .81 2 Richard L Amoroso – Fundaments of Quantum Computing 4.5 Insight into the Measurement Problem . 82 4.6 New Physics from Anthropic Cosmology. 84 4.6.1 Spacetime Exciplex - UF Noeon Mediator. .86 4.6.2 Quantum Phenomenology Versus Noetic UFM Field Ontology . 87 4.7 The Basement of Reality - Through the Glass Ceiling . .89 4.8 Empirical Tests of UFM Cosmology Summarized . 91 4.8.1 Summary of Experimental Protocols . .92 4.8.2 Review of Key Experimental Details. 93 4.9 Unified Field Mechanical (UFM) Précis - Required Parameters. 96 4.10 Formalizing the Noeon, New Physical Unit Quantifying UFM Energy . 97 4.11 Quarkonium Flag Manifold Topology. .99 4.12 Singularities, Unitary Operators and Domains of Action . .100 4.12.1 Semi-Classical Limit . 101 4.12.2 Semi-Quantum Limit . 101 4.13 Measurement . 101 4.14 The No-Cloning Theorem (NCT) . .103 4.14.1 Proof of the Quantum No-Cloning Theorem (NCT) . .104 4.14.2 Quantum No-Deleting Theorem. .105 4.15 The Tight-Bound State Protocol . 105 4.16 Indicia of the UFM Tight Bound State CQED Model. .106 4.17 Building the UFM TBS Experimental Protocol . .108 4.18 Issues of Experimental Design . 117 References. .. 120 PART 5 New Classes of Quantum Algorithms 5.1 Introduction - From al-Khwarizmi to Unified Field-Gorhythms . .125 5.2 The Church-Turing Hypothesis . .126 5.3 Algorithms Based on the Quantum Fourier Transform . .126 5.4 Exponential Speedup by Quantum Information Processing . .127 5.5 Classical Holographic Reduction Algorithms . 129 5.6 Ontological-Phase UFM Holographic Algorithms .. 130 5.7 The Superimplicate Order and Instantaneous UQC Algorithms .. 132 5.8 Some Ontological-Phase Geometric Topology. 135 5.9 Summation. .138 References . .139 3 Richard L Amoroso – Fundaments of Quantum Computing This QC primer is based on excerpts from the breakthrough volume Universal Quantum Computing (ISBN: 978-981-3145-99-3) which 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 the currently highly favored room-sized cryogenically cooled quantum Hall anyon bilayer graphene QCs ever become successful, they would be reminiscent of the city block-sized Eniac computer of 1946. In 2017 quantum Hall techniques experimentally discovered additional dimension, said to be inaccessible and were called ‘artificial’. This scenario will not last long; the floodgates will open momentarily. Then we will have actual QCs! 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! Preface – From the Volume The breakthrough volume, from which the following excerpts come - (ISBN: 978-981-3145-99-3 print; ISBN: 978-981-3146-01-3 electronic) touts having conceptually dissolved the remaining barriers for immediate implementation of Bulk Universal Quantum Computing (UQC), and as such most likely describes the most advanced basis for developing Quantum Information Processing (QIP). Numerous books, many 100s of patents, 1,000s 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 qualify as quantum computing? In physics, theory bears little weight until it is supported by rigorous experimental confirmation, less if new, radical or an untested paradigm shift. This volume develops quantum computing based on ‘3rd regime’ physics of Unified Field Mechanics (UFM). What distinguishes this work from myriad other avenues to UQC under study? Virtually all R&D paths struggle with refining technology and decoherence. If the highly favored room-sized cryogenically cooled QCs ever become successful, they would be reminiscent of the 1946 city block-sized Eniac computer that contained 17,468 vacuum tubes. Does the proposed by-pass of that step retard acceptance of the UFM model; maybe, maybe not as UFM modeling also puts an end to the need for large supercolliders like the CERN LHC. The QC prototype proposed herein is room temperature, tabletop, surmounts uncertainty and supervenes decoherence during.