intuitionistic math can help in quantum physics?
ianon at latahona.com.uy
Mon Apr 13 22:10:01 EDT 2020
Joe Shipman (<joeshipman at aol.com>):
> This paper appears to suggest a new and interesting type of quantum speedup—certain analytic functions which are feasibly computable may have Taylor series coefficients which are not feasibly computable but which may be feasibly measurable.
> How is this different from the situation in ordinary calculus, where analytic functions can have their integrals evaluated over an interval by evaluating their derivatives at the endpoints? I’m not aware of any results delineating for which analytic functions this use of the Fundamental Theorem of Calculus does not improve on numerical integration, but that sounds like an interesting question.
As I read Kreinovitch's paper, similar ideas came to Mind.
I once gave a lecture, to a group of high level researchers in
analysis, presenting an overview of G. Takeuti's work on
computational complexity within bounded arithmetic. They were all
captivated by Takeuti's ideas, and one of the conclusions we all
reached, was the following: the problem of sieving exponential space,
is analogous to that of representing an "almost nowhere differentiable
function", by a fourier series.
Algorithms were proposed, in this context, as candidates for a quantum
speed up, similar to those of Simon and Shor.
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