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Spectral Representation of Some Computably Enumerable Sets With an Application to Quantum Provability | | Cristian S. Calude
; Kohtaro Tadaki
; | | Date: |
22 Mar 2013 | | Abstract: | We propose a new type of quantum computer which is used to prove a spectral
representation for a class F of computable sets. When S in F codes the theorems
of a formal system, the quantum computer produces through measurement all
theorems and proofs of the formal system. We conjecture that the spectral
representation is valid for all computably enumerable sets. The conjecture
implies that the theorems of a general formal system, like Peano Arithmetic or
ZFC, can be produced through measurement; however, it is unlikely that the
quantum computer can produce the proofs as well, as in the particular case of
F. The analysis suggests that showing the provability of a statement is
different from writing up the proof of the statement. | | Source: | arXiv, 1303.5502 | | Services: | Forum | Review | PDF | Favorites | |
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