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Stealthy orbitals hypothesis: quantum gates and singularities

Jean-Yves Boulay

Published Apr 1, 2024• 0 citations
Publisher

Abstract

The graphic charting of atomic orbitals into the form of chevrons suggests the existence of stealth orbitals occupying the quantum vacant space of the various electronic shells. It is proposed here, the hypothesis that these quantum gates allow transit of electrons from orbital to another, and that these gates can be accesses to quantum singularities without space-time. Singular arithmetic arrangements in the distribution of real and stealthy orbitals of certain genetic code components reinforces the hypothesis to existence of these quantum gates.

DOI
10.5281/zenodo.17701065

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The graphic charting of atomic orbitals into the form of chevrons suggests the existence of stealth orbitals occupying the quantum vacant space of the various electronic shells. It is proposed here, the hypothesis that these quantum gates allow transit of electrons from orbital to another, and that these gates can be accesses to quantum singularities without space-time. Singular arithmetic arrangements in the distribution of real and stealthy orbitals of certain genetic code components reinforces the hypothesis to existence of these quantum gates.
It is proposed here to represent the quantum distribution of atomic orbitals in an unprecedented table where the quantum shells and subshells are drawn in the form of chevrons whose vertices are occupied by orbitals with the magnetic quantum number m = 0. This new representation visually shows, much better than a classic linear chart, the relationship between the number of quantum shells and the number of orbitals. Also, this new visual model can be easily used in the individual quantum depiction of the atoms represented alone or into molecules and can find its place in illustration of some two-dimensional space-time quantum theories. Finally, this graphic representation allows to introduce the hypothesis of the existence of stealth orbitals, quantum gates opening towards singularities.
To this point only quantum gates derived from invertible digital counterparts or general invertible Boolean functions have been considered. Here we introduce a number of quantum gates without digital equivalents. In particular, we consider the Pauli gates, the https://www.w3.org/1998/Math/MathML" display="inline"> n o t https://www.w3.org/1999/xlink" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003264569/7139ce19-0d58-4a0c-820f-b76fb033e438/content/math21_1.tif "/> gate, the phase-shift gate and the Hadamard gate, some of which occur in quantum algorithms introduced later. These gates impart additional power to quantum computation.
Quantum computing has been attracting tremendous efforts in recent years. One prominent application is to perform programmable quantum simulations of electron correlations in large molecules and solid-state materials, where orbital degrees of freedom are crucial to quantitatively model electronic properties. Electron orbitals unlike quantum spins obey crystal symmetries, making the atomic orbital in optical lattices a natural candidate to emulate electron orbitals. Here, we construct an atom-orbital qubit by manipulating sss and ddd orbitals of atomic Bose-Einstein condensation in an optical lattice. Noise-resilient single-qubit gates are achieved by performing holonomic quantum control, which allows geometrical protection. We find it is critical to eliminate the orbital leakage error in the system. Our work opens up wide opportunities for atom-orbital-based quantum information processing, of vital importance to programmable quantum simulations of multiorbital physics in molecules and quantum materials.
The nature of quantum mechanics has various interpretations. In this paper we consider the hypothesis of quantum Darwinism. Quantum theory is closely connected with the concept of information. Perhaps there is an analogue of the genetic code for quantum Darwinism. Here the attempt of the genetic formulation of quantum gravity. It is based on the idea of the quantum genetic spiral the space-time, directed along the time axis. Such a mathematical form exists in braid theory. Matter how information is coded in the genetic structure of space-time. Natural and artificial selection of quantum Darwinism leads to the collapse of the wave function and the identification of a dominant gene.
Discretizing electronic degrees of freedom into atomic orbitals is the default choice to accurately model electrons in molecules in a compact and flexible way. We consider the task of simulating such electronic structure models on a quantum computer for NNN orbitals, keeping the number of orbitals per atom constant. Atomic orbitals give rise to Hamiltonians with potentially up to O(N4)\mathcal{O}(N^4)O(N4) terms and little structure, which made it challenging to match the complexity of methods based on plane waves and real-space grids. In this work, we show that a Trotter step for atomic orbitals can be implemented in depth O(polylog(N))\mathcal{O}(\mathrm{polylog}(N))O(polylog(N)) without ancillas by combining a rigorous treatment of orbital localization, a hierarchical Hamiltonian decomposition based on the Fast Multipole Method, and shallow quantum Fourier arithmetic circuits. By bounding the Trotter error, we obtain sublinear simulation depth, and our total gate count N5/3+o(1)N^{5/3 + o(1)}N5/3+o(1) matches the best scaling known for any basis.