On Friday, June 21, 2019 at 6:11:03 PM UTC-5, John Clark wrote:
>
> On Thu, Jun 20, 2019 at 10:04 PM Lawrence Crowell <
> [email protected] <javascript:>> wrote:
>
> *> There is a bit of a major hurdle to leap over. That is decoherence. If
>> you write a simple program on the QE it runs in less than 10^{-6} seconds
>> and that is about all the time you have.*
>>
>
> Yes, decoherence has always been the big problem, that's why Microsoft
> wants to build a Topological Quantum Computer that uses braided
> non-Abelian Majorana sudo-particles called "anyons "; they are much less
> susceptible to decoherence than anything else for the same reason a
> random bump is unlikely to untie a knot. In the August 23 2017 issue of
> the journal Nature the Microsoft people report they have managed to braid
> anyons in a hashtag # arrangement of wires. These braids can encode a Qbit
> of quantum information and they can be manipulated.
>
> http://www.nature.com/nature/journal/v548/n7668/full/nature23468.html
>
> There is also a short video that gives a outline of the above:
>
> Nano-hashtags could provide definite proof of Majorana particles
> <https://www.youtube.com/watch?v=aakSpSXLSYY>
>
I have heard of this. I think they are using graphene sheets for this.
>
>
>
>> *> The highly entangled quantum states become mixed state entangled with
>> the environment states and the execution of the algorithm falls
>> apart.Quantum error correction has its limits, which is related to the
>> limitations of using Hamming distance.*
>>
>
> The biggest difficulty comes from the No Cloning Theorem, it says you
> can't make an identical copy of an unknown quantum state, in other words
> you can't copy a Qbit. So quantum error correction algorithms are longer
> and more complex than for conventional error correction, and thus you have
> to worry more about errors produced when running the quantum error
> algorithm itself.
>
The nocloning theorem means there is no unitary process that can duplicate
a state. If you have a state ψ = aχ_1 + bχ_2 then the duplication ψ → ψψ is
the state in the {χ_1, χ_2} basis representation.
χ_1 + bχ_2 → (aχ_1 + bχ_2)(aχ_1 + bχ_2) = a^2χ_1χ_1 + 2abχ_1χ_2 + b^2χ_1χ_2
If this is a unitary process then the duplication of the bases elements
χ_1 + bχ_2 → a^2χ_1χ_1 + b^2χ_2χ_2
would be equal, and clearly it is not.
A Hadamard gate is not a unitary operation, and so one can prepare or
duplicate states that way.
>
> Nevertheless It has been proven you could theoretically make a arbitrary
> large quantum computer even if the underlining quantum gate had a error
> rate as high as 3%, although the amount of overhead needed for error
> correction would be so large it probably wouldn't be practical. But the
> overhead drops fast with increased gate reliability, if you can get the
> error rate down to 1% then it looks like a Quantum Computer of arbitrary
> size is practical as well as possible.
>
>
This is if your QEEC to operate fast enough. I think the optimal QEEC is
based on the Jordan matrix algebra with 3 E8 groups. This is a stabilizer
of the Fischer-Griess group. All possible groups or their generating
algebras can be embedded.
> Quantum Computing with Very Noisy Devices
> <https://arxiv.org/pdf/quant-ph/0410199.pdf>
>
>
>> *> for now quantum computers are in a bit of a niche market of sorts, and
>> their practical use is largely with encryption.*
>
>
> Somebody will certainly use Shor's factoring algorithm to break RSA
> encryption once they get their hands on a Quantum Computer, but I think the
> killer application will be in efficient quantum simulation; imagine
> dreaming up a complex shape you want a protein to fold up into and the
> computer telling you what sequence of amino acids will fold up into exactly
> that shape. It would revolutionize medicine and chemistry not to mention
> give a big shot in the arm to Drexler style Nanotechnology.
>
Or quantum gravitation, which is what I am interested in simulating. I have
certain hypotheses about entanglements with quantum black holes that I want
to in a sense "test."
>
> * > I do though suspect before long ordinary computers will have some
>> qubit processor that will be executed in some algorithms.*
>>
>
> Maybe but I doubt it. Nobody knows if a conventional computer could solve
> all nondeterministic polynomial time problems in polynomial time, we don't
> even know if a Quantum Computer can do that, but there has been a recent
> development that I find suggestive. Even if, to everybody's surprise, it
> turned out that P=NP and even if we had a algorithm that could solve NP
> problems on a conventional computer in polynomial time there would STILL be
> a class of problems a conventional computer couldn’t solve efficiently but
> a quantum computer could. Yes this class of problems is very exotic and
> nobody knowns if they have any fundamental interest in themselves or if
> they're interesting only because a conventional computer can’t solve them,
> but still...
>
> Oracle Separation of BQP and PH
> <https://www.google.com/url?q=https%3A%2F%2Feccc.weizmann.ac.il%2Freport%2F2018%2F107%2F&sa=D&sntz=1&usg=AFQjCNG737Nnu31eXWHxvlxzkhsdCbVBFA>
>
> John K Clark
>
The computer of the year 2030 will have a network of processors. There will
continue to be a straight up von Neumann type processor, but what can run
in parallel with neural networks, quantum processors and other specialized
processors. The Ras-Tal theorem illustrates a reduction in the need for
oracle input.
LC
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