Three counterexamples refuting Kieu's plan for "quantum adiabatic hypercomputation"; and some uncomputable quantum mechanical ta

-- Tien D. Kieu, in 10 papers posted to the quant-ph section of the xxx.lanl.gov preprint archive [some of which were also published in printed journals such as Proc. Royal Soc. A 460 (2004) 1535] had claimed to have a scheme showing how, in principle, physical "quantum adiabatic systems" could be used to solve the prototypical computationally undecidable problem, Turing's"halting problem," in finite time, with success probability > 2/3 (where this 2/3 is independent of the input halting problem). There were several errors in those papers, most which ultimately could be corrected. More seriously, we here exhibit counterexamples to a crucial step in Kieu's argument. The counterexamples are small quantum adiabatic systems in which "decoy" nonground states arise with high probability (> 99.999%). Kieu had wrongly claimed no decoy state could ever acquire occupation probability greater than 50%. These counterexamples destroy Kieu's entire ...

• Type: Journal
• Year: 2006
• Where: AMC
• Authors: Warren D. Smith
• Keywords: Adiabatic, AMC 2006, Finite Time, Quantum Adiabatic Systems