Universal Quantum Computing

The following sections are included:

• Preface
• Dedication
• Contents

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.

A logic gate is the elementary building block of a computing circuit or algorithm practically applying the concept of binary Boolean bits to circuits using combinational logic. Logic gates are of recent origin. From the time that Leibniz refined binary numbers and showed that mathematics and logic could be combined in 1705, it took well over a hundred years before Babbage devised geared mechanical logic gates in 1837 for use in his proposed Analytical Engine. Another sixty years passed before the first electronic relays appeared in the late 1890s. Then it wasn’t until the 1940s that the first working computer was built. Now, with the arrival of quantum logic gates the evolution continues; and universal quantum computers (UQC) wait in the wings while finishing the absorption of required remaining discovery in physics.

The cosmological term Multiverse refers to the set of finite and infinite types of possible interconnected universes. Since the study of physical systems is typically to isolate and restrict the principle under investigation to the smallest domain feasible, why should issues of cosmology enter into a discussion of Quantum Information Processing (QIP)? As we hope to adequately demonstrate in this volume, the situation has dramatically changed recently; QIP has not and cannot be achieved beyond a few qubits by continuing to utilize the nonphysical mathematical representation of qubits on a Bloch sphere in Hilbert space as its basis. One might do better to define a qubit as a ‘realiton’, a complete microcosm of reality itself; and emphatically, since reality can no longer be considered fundamentally quantum, that microcosm must encompass whatever a localized segment of the multiverse entails in order to holistically process information! Therefore, an operationally sufficient understanding of the penultimate basis of reality (cosmology) appears mandatory in order to incorporate the newly perceived requirements of relativistic information processing and topological QC from the point of view of Unified Field Mechanics (UFM).

Physics, simplistically, is the study of matter and energy; or as Einstein called it, ‘extension and duration’. A hundred and twenty years ago, our understanding of the physical world was described by the Newtonian Classical Mechanical belief in indivisible billiard ball-like atoms as the fundamental building blocks of matter. Discovery of the electron in 1897 by J.J. Thompson demonstrated that atoms are not indivisible, ushering in modern atomic theory. The advent of quantum mechanics showed that matter had wave properties. Now on the brink of discovering additional dimensions (XD) another advance beckons; extending our understanding of the structure of matter to include Calabi-Yau mirror symmetric topological brane phenomena hidden until now behind the veil of the uncertainty principle in a 3^rd regime of Unified Field Mechanics (UFM). Classical observation seemingly straight forward, became compounded by uncertainty in quantum mechanics. Just as infinities in the Raleigh-Jeans Law were an indicia of quantum theory; likewise, the renormalization problem of infinite self-energy of a charged point particle in both classical and quantum theory are deemed inconsistencies, certainly suggesting incompleteness, that point the way to a new horizon of additional physics that can be accessed by utilizing a new class of HD commutation rules allowing the uncertainty principle to be ontologically overcome.

Quantum Computing (QC) has remained elusive beyond a few qubits. One of Feynman’s initial premises was to recommend the use of a “synchronization backbone” for achieving the bulk implementation of Universal Quantum Computing (UQC); unfortunately, that has generally been abandoned as intractable; a conundrum we believe arises from limitations imposed by the standard Copenhagen Interpretation of Quantum Theory (QT) and current incomplete models of Cosmology. In this work it is proposed that not only can Feynman’s synchronization backbone model be utilized, but in fact it is a required key element for implementing UQC if done with the addition of valid higher dimensional (HD) extensions of QT and cosmology. Requisite additional degrees of freedom are introduced by defining a relativistic basis for the qubit (rqubit) in an HD conformal invariant context, and by defining a new anticipatory based cosmology (cosmology itself cast as a hierarchical form of complex self-organized system) making correspondence to dual 3-tori 6D Calabi-Yau mirror symmetries in M-Theory. An additional control parameter required by Unified Field Mechanics (UFM) is added bringing dimensionality to 12 (12D). The causal structure of these conditions reveal an inherent new UFM ‘action principle’ (not a 5^th force, but an ontological ‘force of coherence’ of the UF) driving self-organization and providing a basis for applying Feynman’s synchronization backbone principle. Attempts by the few researchers for a synchronization backbone, should at best be called ‘bi-local’; when as we shall show the symmetry for synchrony is an inherent component of HD brane topology. Operationally a new set of transformations (beyond the standard Galilean/Lorentz- Poincairé) ontologically describe how to surmount the quantum condition, (supervening decoherence during both initialization and measurement) by an acausal energyless topological brane interaction.

At one time, Classical Mechanics governed our whole understanding of the physical universe; then a 2^nd regime of reality Quantum Mechanics was discovered, giving insight into the microscopic realm. Now we prepare to pragmatically enter a 3^rd regime of natural science, Unified Field Mechanics (UFM). A 4^th regime, beckoning just beyond our reach, is also postulated that will take us experimentally from Universe to Multiverse (infinite number of nested Hubble Spheres, each with their own fine-tuned laws of physics); but this 4^th regime is beyond the scope of this monograph. In this chapter we introduce some of the, putative at this time, aspects of UFM deemed essential for Universal Quantum Computing (UQC).

Eliminating ensemble decoherence time and uncertainty in the operation and measurement process of Quantum Information Processing (QIP) systems are remaining problems considered to be of paramount importance in the task of implementing viable bulk scalable Universal Quantum Computing (UQC). Most teams currently attempt to supervene decoherence by utilizing multimillion dollar room sized cryogenic apparatus. If our model is correct, it will allow tabletop room temperature UQC. We theoretically illustrate (in a manner empirically testable) that these conditions essentially become irrelevant in terms of the radical new Unified Field Mechanical (UFM) approach to QIP introduced here. It should be noted that the recent relativistic restrictions the QC research community has imposed on QIP point the way to our model. The additional degrees of freedom obtained by leaving the 3D realm of Euclidean space associated with Newtonian Classical Mechanics and entering the 4D domain of Minkowski 4-space had a profound effect on physics during the last century. Now as we enter a 12D M-Theoretic (String Theory) dual Calabi-Yau mirror symmetric 3-torus 3^rd regime associated with UFM, more surprises like the ability to surmount the quantum uncertainty principle are proffered. In this chapter we review a UFM protocol for allowing uncertainty and decoherence to be routinely surmounted and supervened respectively, 100% of the time with probability, P ≡ 1. We begin with a discussion of Interaction-Free Measurement (IFM), an interesting 4D precursor providing another indicium of the 12D brane topology model introduced here. IFM is a novel quantum mechanical procedure for detecting the state of an object without an interaction occurring with the measuring device. What we propose is a radical extension of the various experimental protocols spawned by the recent Elitzur-Vaidman IFM thought experiment.

Because of what Unified Field Mechanics (UFM) appears to tell us about the fundamental basis of matter (albeit a preliminary foray); it is postulated that a bulk UQC cannot be built without utilizing UFM parameters with an inherent ability to supervene the quantum uncertainty principle. Although no attempt has been made yet to make correspondence with MTheoretic supersymmetry, since it remains sufficiently unfinished; the topological order envisioned for UFM additions to the structure of matter can probably readily be made to do so. Concepts required to supervene uncertainty, such as a Dirac polarized vacuum, the de Broglie-Bohm causal interpretation and Cramer’s transactional interpretation are already well-known to physics, but generally ignored. Concepts like Large-Scale Additional Dimensions (LSXD), brane topology and the vision that spacetime is not fundamental, but emergent, are already known and under ongoing development. The three main additions we apply are the discovery of a manifold of uncertainty (MOU) with finite radius, to which the unified field provides an ontological force of coherence (not 5^th force) and that the underlying bulk hidden behind the ‘veil of uncertainty’ is a tessellation of ‘Least Cosmological Units’ (LCU) annihilated and recreated with a cyclic beat frequency. May it become obvious, that this inherent LCU beat frequency is the key factor in supervening uncertainty for measurement with certainty.

Among the dozens of theoretical elements and substrates proposed for Universal Quantum Computing (UQC), Topological Quantum Computing (TQC) is considered a leading contender. This is primarily because of the putative utility of fractional quantum Hall effect superconductors on 2D quasiparticles defined as non-Abelian anyons, whose world lines cross forming topological braids of quantum states which for all practical purposes are securely isolated from the environment and do not decohere. TQC is highlighted in this volume because many of its topological parameters are like a ‘shadow’ or lower dimensional (LD) ‘toy model’ of the higher dimensional (HD) Unified Field Mechanical QC model introduced in this monograph. However, the anyon TQC must operate at cryogenic temperatures, whereas our UFM model is designed to be tabletop and operate at room temperature. Topological Quantum Field Theory (TQFT) is quantum field theory based on topological invariants, which is a property of topological space invariant under homeomorphisms. Topological invariants are distinctly different from the unitary operators generally used in most other types of QC models under study. All known topological field theories are either the Schwarz-type TQFTs or the Witten-type TQFTs, which are sometimes referred to as cohomological field theories. A TQC précis is given as foundation for coming discussion.

Topological Quantum Computation (TQC) is generally being studied with topologically protected non-Abelian anyons realized in 2D fractional quantum Hall quasiparticle states. Elementary qubits tested are being constructed by localizing Ising-model anionic excitations in films of super-cooled liquid helium on fractional quantum Hall antidots and various quantum gates where quantum information processing (QIP) in such multi-qubit register arrays are putatively implemented by the exchange or braiding of these non-Abelian anyons. While anyonic braiding promises unprecedented protection for QIP, the quantum states are currently so well ‘hidden’ that they are operationally inaccessible, raising concerns that the quantum non-cloning and quantum non-erasure theorems cannot be easily overcome if applicable in this case. The hope of TQC developers is that techniques like ‘experimentally’ detecting the signature of non-Abelian anyons in Coulomb blockaded quantum Hall islands could eventually be realized. We highlight TQC in this volume because we see it as a toy model precursor to our UFM model for UQC.

Just as infinities in the Rayleigh-Jeans Law pointed the way to quantum mechanics; now infinities in the renormalization of quantum field theory provide indicia for the next age of discovery. Additionally, this imminent paradigm shift demands that the observational frame of reference be radically adjusted! Just as Copernicus (and Greek astronomer/ mathematician Hipparchus 2,200 years prior), caused the switch to heliocentric cosmology (after a 150-year struggle to gain general acceptance); for natural science to observe the 3^rd regime of reality (CM → QM →UFM) we must no longer consider Euclidean 3-space as the fundamental frame of reference. We hope the ‘update’ does not take 150 years this time. Physicists, so demanding of the utility of rigor in scientific method and principles, are often quite rigid in their belief system. Two contemporary examples are: 1) In the 2014 Hollywood biographical film, “The Theory of Everything”, Stephen Hawking says – “Who is God to tell me how to write my equation?”. 2) The field of Cognitive Science unscientifically tells its fundamental question, “What processes in the brain give rise to awareness”, how to answer itself; the question should simply be posed, ‘What processes give rise to awareness?’. The Observer continues to plague measurement theory. A frame of reference is typically a set of three orthogonal measuring rods with an associated clock to which a metric is attached for observing entities such as position, displacement, motion or energy. The frame of reference and observer or apparatus cannot be separated. We have come to the point of requiring another set of transformations beyond the Galilean, Lorentz-Poincairé to observe the UFM regime. This 3^rd regime reveals an inherent new unified field ‘action principle’ driving self-organization, in a manner corresponding to a de Broglie-Bohm ‘super-quantum potential. Operationally this new set of transformations allows one to ontologically surmount the quantum condition, by an acausal, energyless topological interaction.

The following sections are included:

• Abductive a Priori a Posteriori Tautology
• The Phasor (Phase Vector) Complex Probability Amplitude
  • Complex Phase Factor
  • Geometric Phase - Berry Phase
  • The Toric Code
• Transitioning from TQFT to OPTFT
  • The A and B-Models of Topological Field Theory
  • Dualities Between Topological String Theories (TSTs)
  • The Holomorphic Anomaly
• Topological Vacuum Bubbles by Anyon Braiding
• Topological Switching – Key to Ontological-Phase
• Dual Amplituhedron Geometry and ‘Epiontic’ Realism
• References

Quantum algorithm research and development remains in its infancy, because although a fair number of quantum gates and qubit technology platforms exist, it is safe to say that until an actual Universal Quantum Computer (UQC) implementation capable of bulk operation occurs, a complete conception of what sufficient quantum algorithms are seems unlikely; especially if much of the novel new parameters proposed in this monograph are required. Meaning for example, that the first bulk quantum computing system might in actuality be scalable, but there may be a dearth of quantum algorithms to implement sufficient quadratic speedup for practical utility beyond classical computing. We propose a new class of unified field mechanical (UFM) based holographic quantum algorithms with asymptotic speedup beyond the purely classical holographic reduction algorithmic process currently under development even to the point of a new class of instantaneous algorithms. There is recent talk of an end to locality and unitarity as a new basis for QC, along with the new field relativistic information processing (RIP); these scenarios may cause dramatic changes in QC research.

Class II mesoionic xanthines such as anhydro-(8-hydroxyalkyl-5- hydroxy-7-oxothia-zolo[3,2-a]pyrimidinium hydroxides) are unique, small atomic weight, stable crystalline organic compounds that can be represented as a combination of ten different resonance structures for each simple xanthine molecule. Each resonance structure contributes a certain percentage to the total resonance of the molecule. This unique resonance represents ten different quantum states of the entire molecule and can thus be exploited as a potential substrate for a ten-qubit register. The number of possible superposition states for such a register in a single molecule is potentially as high as 2ⁿ states or (in this case where n = 10) 1,024 complex numbers. In solution the least-unit of this mesoionic crystalline structure is scalable suggesting putative utility for bulk NMR quantum computing. It will be shown that these ten-qubit registers are amenable to standard Deutsch-Jozsa, Shor and Grover algorithms. Additionally, we attempt to formalize I/O techniques for our Class II mesoionic xanthines based on a coherent control rf-process of cumulative resonant interaction where by utilizing additional degrees of freedom pertinent to a relativistic basis for the qbit (r-qbit) new HD commutation rules allow decoherence to be ontologically overcome.

Quantum Computing (QC) has remained elusive beyond a few qubits. Feynman’s recommended use of a “synchronization backbone” for achieving bulk implementation has generally been abandoned as intractable; a conundrum we believe arises from limitations imposed by the standard models of Quantum Theory (QT) and Cosmology. It is proposed that Feynman’s model can be utilized to implement Universal Quantum Computing (UQC) with valid extensions of QT and cosmology. Requisite additional degrees of freedom are introduced by defining a relativistic basis for the qubit (r-qubit) in a higher dimensional (HD) conformal scale-invariant context and defining a new anticipatory based cosmology (cosmology itself cast as a hierarchical form of complex selforganized system) making correspondence to 12D Calabi-Yau mirror symmetries in extended M-Theory. The causal structure of these conditions reveal an inherent new ‘action principle’ driving selforganization and providing a basis for utilizing Feynman’s synchronization backbone principle. Operationally a new set of transformations (beyond the standard Galilean / Lorentz-Poincairé) ontologically surmount the quantum condition, by an acausal, energyless topological interaction. Utilizing ontological phenomenology of the HD regime requires new commutation rules and corresponding I/O techniques based on a coherent control process of cumulative interaction to manipulate applicable cyclic modes of HD brane manifolds as a spinexchange continuous-state spacetime resonance hierarchy.

The following section is included:

• Index