Hypercomputability of quantum adiabatic processes: Fact versus Prejudices

2005/04/14 by Tien D. Kieu, Kieu, Tien D. · 1 citation
Computer Science · Physics and Astronomy · #Computability, Logic, AI Algorithms #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #quant-ph

paper · pdf · doi:10.48550/arxiv.quant-ph/0504101

25 pages, 4 figures. Invited paper for a special issue of the Journal of Applied Mathematics and Computation

arxiv created 2005/04/14 · openalex publication_date 2005/04/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give an overview of a quantum adiabatic algorithm for Hilbert's tenth problem, including some discussions on its fundamental aspects and the emphasis on the probabilistic correctness of its findings. For the purpose of illustration, the numerical simulation results of some simple Diophantine equations are presented. We also discuss some prejudicial misunderstandings as well as some plausible difficulties faced by the algorithm in its physical implementation.

Citations

• Hypercomputation: computing more than the Turing machine
• Computable Functions, the Church-Turing Thesis and the Quantum Measurement Problem
• Finiteness of the universe and computation beyond Turing computability
• On the existence of truly autonomic computing systems and the link with quantum computing
• Quantum Complexity Theory

Cited by

• On the identification of the ground state based on occupation probabilities: An investigation of Smith's apparent counterexamples

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