On the identification of the ground state based on occupation probabilities: An investigation of Smith's apparent counterexamples
arXiv:quant-ph/0602145
Abstract
We study a set of truncated matrices, given by Smith~\cite{Smith2005}, in connection to an identification criterion for the ground state in our proposed quantum adiabatic algorithm for Hilbert's tenth problem. We identify the origin of the trouble for this truncated example and show that for a suitable choice of some parameter it can always be removed. We also argue that it is only an artefact of the truncation of the underlying Hilbert spaces, through showing its sensitivity to different boundary conditions available for such a truncation. It is maintained that the criterion, in general, should be applicable provided certain conditions are satisfied. We also point out that, apart from this one, other criteria serving the same identification purpose may also be available.
This is an edited version, with updated references, of an earlier reply to Smith in July, 2005. 9 pages and 12 figures
References in corpus (4)
- Quantum adiabatic algorithm for Hilbert's tenth problem: I. The algorithm
- Hypercomputability of quantum adiabatic processes: Fact versus Prejudices
- A mathematical proof for a ground-state identification criterion
- Mathematical computability questions for some classes of linear and non-linear differential equations originated from Hilbert's tenth problem