> On 5 Oct 2020, at 01:04, 'Brent Meeker' via Everything List 
> <[email protected]> wrote:
> 
> 
> 
> On 10/4/2020 12:52 PM, Lawrence Crowell wrote:
>> Quantum computers, or processors, will make more inroads into things. They 
>> have a possible big role in understanding quantum black holes and quantum 
>> complexity. Any NP problem can be worked faster, at least in principle, with 
>> a quantum computer.
> 
> I don't think there's any proof of that.  Given any quantum computer 
> algorithm, it is possible that there is an equally fast classical 
> algorithm...at least that's my understanding of the state of theory.

P ≠ NP is like Riemann Hypothesis. We don’t have (yet) a proof, but very few 
people believe that it could be false.

But also, even if P = NP, it might be that in practice the polynomial will be 
so complex that a quantum computer will still run faster than any reasonable 
classical computer. Now, I sincerely doubt that P could be equal to NP, despite 
the vexing difficulty we met when trying to prove P ≠ NP.

Bruno



> 
> Brent
> 
>> In working on quantum complexity I see how this problem of a 1-dim chain 
>> filling space in a complex geometry or topology has a possible bearing on 
>> the Hodge conjecture. The use of epsilon balls and a regularization scheme 
>> in quantum complexity may play some role here.
>> 
>> LC
>> 
>> On Sunday, October 4, 2020 at 1:54:45 PM UTC-5 [email protected] 
>> <mailto:[email protected]> wrote:
>> On Sun, Oct 4, 2020 at 12:03 PM Lawrence Crowell <[email protected] 
>> <applewebdata://C927F0B5-32CC-4A5A-ABBB-AA47904D4183>> wrote:
>> 
>> > It makes sense. The phosphorylation of a protein changes its shape.
>> 
>> The linear amino acid sequence that makes up the protein changes the way it 
>> folds up even more, from a 1-D line into a complex 3-D shape. I think 
>> predicting what linear sequence of amino acids would be needed to fold into 
>> a given 3-D shape will be the first and one of the most important tasks a 
>> Quantum Computer will work on once they become large enough to become 
>> practical. 
>> 
>> John K Clark 
>>  
>>  
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