某些可计算可积集的谱表示及其在量子可证性中的应用
Spectral Representation of Some Computably Enumerable Sets With an Application to Quantum Provability
摘要：
我们提出了一种新型的量子计算机，用于证明一类F可计算集的谱表示。当F中的S编码形式系统的定理时，量子计算机通过测量产生形式系统的所有定理和证明。我们猜想，谱表示是有效的所有可计算可列集。这个猜想意味着一般形式系统的定理，如皮亚诺算术或ZFC，可以通过测量产生;然而，量子计算机不太可能也能产生证明，就像F的特殊情况一样。分析表明，展示陈述的可证明性不同于撰写陈述的证明。
英文摘要：
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.
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