Algorithms for Quantum Computation: The Derivatives of Discontinuous Functions

We hope this work allows one to calculate large prime numbers directly, not by trial-and-error, but following a physical law. We report—contrary to conventional assumptions—that differentiation of discontinuous functions (DDF) exists in the set Q, which becomes central to algorithms for quantum comp...

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Bibliographic Details
Published in:Mathematics (Basel) Vol. 11; no. 1; p. 68
Main Author: Gerck, Ed
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.01.2023
Subjects:
19th century
algebraic
Algorithms
Analysis
Calculus
communication
Functions, Discontinuous
Mathematical research
Mathematics
nature
physical numbers
Physics
Prejudice
Prime numbers
Quantum computing
Quantum mechanics
Relativity
tri-state
United States
ISSN:2227-7390, 2227-7390
Online Access:Get full text
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Summary:We hope this work allows one to calculate large prime numbers directly, not by trial-and-error, but following a physical law. We report—contrary to conventional assumptions—that differentiation of discontinuous functions (DDF) exists in the set Q, which becomes central to algorithms for quantum computation. DDF have been thought to exist not in the classical sense, but using distributions. However, DDF using distributions still is defined in terms of mathematical real-numbers (MRN), and do not address the Problem of Closure, here investigated. These facts lead to contradictions using MRN, solved by this work, providing a new unbounded class of physical solutions using physical numbers in quantum mechanics (QM), that were always there (just hidden), allowing DDF without distributions, or MRN. It is worthwhile to see this only in mathematics, to avoid the prejudices found in physics, as this reforms both general relativity and QM. This confirms the opinions of Nicolas Gisin that MRN are non-computable with probability 1, and Niels Bohr that physics is not reality, it is a fitting story about reality. Mathematics can get closer to reality, surprisingly. We just have to base mathematics on nature, not on how it defines nature.
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ISSN:2227-7390
2227-7390
DOI:10.3390/math11010068