Super Turing Computation Versus Quantum Computation

Super Turing Computation Versus Quantum Computation

The Church-Turing limit restricts all current computation, including quantum computers, to rational number computation. This is because quantum computer designs (still not scalable even with high parallelism), are still Turing machines, which are limited by Turing machine constraints.

This limits any scalable quantum computer’s ability to solve problems because their Turing machine restricted rational number computations are a tiny fraction of all real numbers, akin to our small solar system when compared to stars and planets encompassing the visible universe. The result is quantum computers only generate approximate solutions to problems that require irrational number degrees of problem solving freedom.

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This Church-Turing limit has affected everything in modern day life with no person or thing untouched. Spanning the life science fundamental challenges to cure disease, to creation of adaptive artificial intelligence systems, all are Turing constrained to narrowly defined applications.

Super Turing Machines may obsolete Turing limited quantum computation because they have infinitely more degrees of problem solving freedom. The Turing limit, defined by Dr. Alan Turing in 1936, fundamentally restricts all computers. Dr. Turing was working on a super Turing theory of computation that exceeded his original work, but he died before completing it.

If Turing had completed his work on super Turing machines the world might be a much different place today, since super Turing machines enable the solution to exponential problems, which include a form of tumor cell genomic analysis that is currently intractable today, and all so-called “NP-Hard” exponential computational problems, which only have approximate solutions using Turing machine restricted computation.

In 1992, Dr. Hava Siegelmann and Dr. Eduardo Sontag independently developed a super Turing theory of computation (access paper), however current computation was already deeply entrenched and the thesis languished as an obscure mathematical tome for decades. Now new composite semiconductor technology may enable super Turing machines, and this may transpire before practical scalable quantum computers can be built.