Flatland/rev II

On New Year's Eve, the Square dreams of a visit to a one-dimensional world, "Lineland", inhabited by men, who are lines, while the women are "lustrous points". These points and lines are unable to see the Square as anything other than a set of points on a line. 

The plot thickens ...

Following this vision, the Square is visited by a sphere. Similar to the "points" in Lineland, he is unable to see the three-dimensional object as anything other than a circle (more precisely, a disk). The Sphere then levitates up and down through Flatland, allowing the Square to see the circle expand and contract between a great circle and small circles. The Sphere then tries further to convince the Square of the third dimension by dimensional analogies (a point becomes a line, a line becomes a square). 

In quantum mechanics and computing, the Bloch sphere is a geometrical representation of the pure state space of a two-level quantum mechanical system (qubit), named after the physicist Felix Bloch.

The Bloch sphere, has an inner reality along with a clearly defined surface, just like the sphere in Constructive Solid Geometry, a primitives based 3D environment created by Philip Mittleman in 1966, twenty years after Felix Bloch conceptualized his Bloch Sphere.

After the war, Bloch concentrated on investigations into nuclear induction and nuclear magnetic resonance, which are the underlying principles of MRI.[10][11][12] In 1946, he proposed the Bloch equations, which determine the time evolution of nuclear magnetization. 

Felix Bloch

The story of MAGI Mathematical Applications Group Incorporated began with the “simple” question, “What paths would radiation take when a 20 megaton nuke goes off? Hypothetical target? NYC." 

SG objects can be represented by binary trees, where leaves represent primitives, and nodes represent operations. In this figure, the nodes are labeled ∩ for intersection, ∪ for union, and — for difference.

1966: MAGI answered the question by inventing ray tracing to track the radiation paths of the nuke’s blast to the environment but also to apply the same technique to imaging as a nuke is a single energy source like a light bulb and blast and light rays propagate exactly the same but with the difference being light rays nondestructively intersect with objects and react according to the kind of characteristics the objects in question may possess like color, texture, transparency and reflectivity, using the laws of physics to generate an accurate 3D rendering of the scene in question. CSG, with B-Rep (boundary conditions defining volume), provides the accuracy needed to do scientifically accurate ray tracing by generating 3D objects complete with physical characteristics like density, transparency and reflectivity along with the creation of mathematically correct shadows as needs warrant, qualities not possessed by polygonal based modeling. 

Ray tracing

Lastly - The physics ...

1981 (The Computing Paradigm): Richard Feynman delivered his famous lecture, "Simulating Physics with Computers". His core thesis was that classical computers—which operate on flat, binary, linear logic—cannot accurately simulate the physical universe because the universe is not classical. He recognized that quantum systems could potentially solve problems exponentially faster than classical computers, establishing the theoretical motivation for developing quantum computing technology. He realized you cannot use 2D math to calculate a 3D physical reality; you have to use the physical reality itself.

The problem ... As seen by the Bloch Sphere, Quantum Computers are 3D analog systems so ... why do researchers continue to work with 3D environments with 2D logic? A Square, in Flatland, could not understand Sphere so it stands to reason why a QC 3D construct does not understand 2D math. 

It's akin to trying to fit a square peg into a round hole does it not?

History lesson 

The true architecture of QC wasn't born in a Silicon Valley server farm or a corporate boardroom. It was born in the minds of the physicists who were tearing apart the fundamental nature of reality long before a microchip ever existed.

The founders of modern physics

A. Piccard, E. Henriot, P. Ehrenfest, E. Herzen, Th. De Donder, E. Schrödinger, J.E. Verschaffelt,
W. Pauli, W. Heisenberg, R.H. Fowler, L. Brillouin; P. Debye, M. Knudsen, W.L. Bragg, H.A. Kramers, P.A.M. Dirac, A.H. Compton, L. de Broglie, M. Born, N. Bohr; I. Langmuir, M. Planck, M. Skłodowska-Curie, H.A. Lorentz, A. Einstein, P. Langevin, Ch. E. Guye, C.T.R. Wilson, O.W. Richardson

Fifth conference participants, 1927. Institut International de Physique Solvay in Leopold Park.

The QC founders with Max Planck as start point as he discovered Quantum Mechanics.

Key insight: The hardware evolved over decades, but the underlying 3D physics
—the "round hole"—was established almost a century ago.

Bohr, Heisenberg, and Schrödinger established the wave functions and uncertainty principles in the 1920s.
Felix Bloch took those principles and mapped them into a 3D spherical geometry in the 1940s.
Phil Mittleman built the volumetric computational engine to measure that kind of physics in the 1960s.
And Richard Feynman demanded we put it all together to compute physical reality in the 1980s.

One cannot make this up. :)

To be continued.