http://popups.lib.uliege.be/1373-5411/index.php?id=711 Index terms fr 0 http://popups.lib.uliege.be/1373-5411/index.php?id=4546 The universal Turing machine is an anticipatory theory of computability by any digital or quantum machine. However the Church-Turing hypothesis only gives weak anticipation. The construction of the quantum computer (unlike classical computing) requires theory with strong anticipation. Category theory provides the necessary coordinate-free mathematical language which is both constructive and non-local to subsume the various interpretations of quantum theory in one pullback/pushout Dolittle diagram. This diagrame can be used to test and classify physical devices and proposed algorithms for weak or strong anticipation. Quantum Information Science is more than a merger of Church-Tirring and quantum theories. It has constructively to bridge the non-local chasm between the weak anticipation of mathematics and the strong anticipation of physics , Mon, 14 Oct 2024 10:51:06 +0200 Mon, 14 Oct 2024 12:59:33 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=4546 http://popups.lib.uliege.be/1373-5411/index.php?id=4540 The universal Turing machine is an anticipatory theory of computability by any digital or quantum machine. However the Church-Turing hypothesis only gives weak anticipation. The construction of the quantum computer (unlike classical computing) requires theory with strong anticipation. Category theory provides the necessary coordinate-free mathematical language which is both constructive and non-local to subsume the various interpretations of quantum theory in one pullback/pushout Dolittle diagram. This diagrame can be used to test and classify physical devices and proposed algorithms for weak or strong anticipation. Quantum Information Science is more than a merger of Church-Tirring and quantum theories. It has constructively to bridge the non-local chasm between the weak anticipation of mathematics and the strong anticipation of physics , Mon, 14 Oct 2024 10:47:39 +0200 Mon, 14 Oct 2024 12:58:47 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=4540 http://popups.lib.uliege.be/1373-5411/index.php?id=3716 We introduce an anticipatory approach to Universal Quantum Computing (UQC) utilizing a variety of extended theoretical parameters. Thu, 26 Sep 2024 11:15:12 +0200 Tue, 08 Oct 2024 13:41:31 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=3716 http://popups.lib.uliege.be/1373-5411/index.php?id=3744 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 often 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 2' 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 VO 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 Thu, 26 Sep 2024 12:21:53 +0200 Tue, 08 Oct 2024 13:38:13 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=3744 http://popups.lib.uliege.be/1373-5411/index.php?id=564 Coherent wavelets form a unified basis of the multichannel perfect reconstruction analysis-synthesis filter bank of high resolution radar imaging and clinical magnetic resonance imaging (MRI). The filter bank construction is performed by the Kepplerian temporospatial phase detection strategy which allows for the stroboscopic and synchronous cross sectional quadrature filtering of phase histories in local frequency encoding multichannels with respect to the rotating coordinate frame of reference. The Kepplerian strategy and the associated filter bank construction take place in symplectic affine planes which are immersed as coadjoint orbits of the Heisenberg two-step nilpotent Lie group G into the foliated three-dimensional real projective space P(R x Lie(G)). Due to the factorization of transvections into affine dilations of opposite ratio, the Heisenberg group G under its natural sub-Riemannian metric acts on the line bundle realizing the projective space P(R x Lie(G)). Its elliptic non-Euclidean geometry without absolute quadric, associated to the unitary dual G, governs the design of the coils inside the bore of the MRI scanner system. It determines the distributional reproducing kernel of the tracial read-out process of quantum holograms excited and coexisting in the MRI scanner system. Thus the pathway of this paper leads from Keppler's approach to projective geometry to the Heisenberg approach to the sub-Riemannian geometry of quantum physics, and finally to the enormously, appealing topic of ensemble quantum computing. Fri, 28 Jun 2024 09:00:50 +0200 Fri, 28 Jun 2024 17:14:56 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=564 http://popups.lib.uliege.be/1373-5411/index.php?id=520 We begin with a brief review of the basic notions of classical computability theory and the Turing machine. The concept of decidability and computability, as well as the Church-Turing thesis are also introduced. The recently formalized foundations of quantum computability theory are surveyed next. Included are such topics as the universal quantum computer; the use of quantum parallelism in computation; and the Church-Turing principle. We highlight some avenues of research for new computational paradigms and suggest that underlying the new advances in both the theory and practical aspects (actual devices), is a new conceptual basis for interpreting the interactions that produce complex and partially understood processe. Thu, 27 Jun 2024 13:45:14 +0200 Fri, 28 Jun 2024 17:09:33 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=520