Nonlocal Quantum Computing Theory and Spherical Time Crystals

Four new fundamental nonlocal quantum computing operator-state diagonal relations are derived for a model entangled atomic chain. Those relations lead directly to four interacting quasi-planar time crystals with the same Poincare cycle and the crystals are predicted to be only half-observable. But birth-and-death of the time crystals can exist at other part of a long chain that is beyond the perpetual motion of the time crystals. Quantized condition for quantum teleportation distance is provided. The rotational symmetry breaking leads to the existence of spherical time crystals, where time axis can be curved. Quantum computing are thus rule-based and not logic-gate based. That is a great departure on the starting point of quantum computing. Geometry, physical process and the nature of computing involved are triangularily related. Quantum processor, man-made or in nature, possesses intrinsic interconnection lengths just like molecular bondings. Different interconnections alter the geometry and hence the nature of computing. But general-purpose quantum computing has to be singularly Euclidean based while the rest are not. Rules for general-purpose (man-made), biological (where consciousness is based) and entangled atomic chain of natural phase computing are presented.