Theory of Quantum Computing and its Analog of the Halting Problem

Daegene Song

Stephen Fenner

Andrew Stewart Caldin

FINDING: The Halting Problem — proven undecidable by Turing (1936) — establishes a fundamental limit on computable knowledge; the 2020 MIP*=RE result extends this to quantum entanglement, showing the halting problem is equivalent to verifying entangled-prover protocols. | MATH: No explicit equations/constants; core logical structure: ∃H such that H(P,I) halts iff P(I) halts → contradiction via diagonalization (self-reference: D(P) = loop if H(P,P) halts, else halt). MIP*=RE: the class of problems verifiable by two entangled provers equals the class of recursively enumerable sets — i.e., the halting problem itself is in MIP*. | CONNECTION: Diagonalization mirrors the golden-ratio-like self-similarity in recursive structures — the fixed-point of the halting function is a self-referential loop, analogous to the infinite regress in φ = 1 + 1/φ. The undecidability boundary acts as a "forbidden ratio" in the space of computable functions — a cut at the 0.618 point of the computational spectr Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Myo Myo Aung

Alexander Shalyt-Margolin, A. Ya. Tregubovich, В. И. Стражев

The Halting problem for the quantum computer is considered. It is shown, that if the halting for the quantum computer takes place then the corresponding dynamics is described by an irreversible operator.

Andrew Stewart Caldin

FINDING: The halting problem establishes a fundamental limit on algorithmic knowledge — no finite procedure can decide whether an arbitrary program halts, a result foundational to computation and quantum-verification complexity (MIP\*=RE). | MATH: Undecidability via diagonalization; H(P,I) = {1 if P halts on I, 0 otherwise} is non-computable. Key corollary: MIP\*=RE implies the quantum commuting operator model (Tsirelson's problem) is undecidable — connecting operator algebras to computability. No new constants or ratios emerge; the structure is purely combinatorial/logical. | CONNECTION: The diagonalization argument mirrors the construction of irrational numbers (Cantor's slash) — a self-referential "gap" that resists closure. This is analogous to the golden ratio's non-repeating continued fraction [1;1,1,1,...] = φ, which also encodes an irreducible self-similarity. The halting problem's undecidability is a discrete analogue of incommensurability — a ratio (program vs. proof) that ca Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com