Re: Quantum Computers and Anyons

2020-04-13 Thread RISHABH CHAKRABARTY 
Realy interesting thoughts can we simulate/emulate the same on a Quantum 
Processing Unit?

—R

From: everything-list@googlegroups.com  on 
behalf of Bruno Marchal 
Sent: Sunday, April 12, 2020 12:45:46 AM
To: everything-list@googlegroups.com 
Subject: Re: Quantum Computers and Anyons


On 11 Apr 2020, at 19:24, John Clark 
mailto:johnkcl...@gmail.com>> wrote:

In the April 10 2020 issue of the Journal Science the best evidence yet for the 
existence of a quasiparticle called a "Anyon" is presented. Anyon's are 
important because when 2 Anyon's loop around each other their quantum state is 
altered and so that brading can be used to encode information. Such brading 
would be far less susceptible to quantum decoherence than other ways of 
encoding information, and decoherence is the only reason we don't have 
practical and scalable Quantum Computers right now.


I agree. I guess you mean braiding, like the space time description of two 
particles going around each other, or around a third one, leading to a braid 
(in 3d space).

It is why I except braiding from the projections obtained in arithmetic from 
the quantization. Braids and links, and knots are simple topological structure, 
but provides semantic for quantum logics, quantum computations, but also the 
computations as “seen from inside arithmetic” by universal 
machine/number/words/finite)-beings.

The the fractional Hall effect, the “quantum field” of the condensed matter, 
are “shortcut” to Deutsch's quantum Turing universality.

There are also extraordinary relations between Artin’s group of braids (a 
generalisation of the permutation group), Temperly-Lieb Algebra (and decoupling 
theory) and self-distributive algebra, related to the theory of high cardinal 
in Zermelo-Fraenkel set theory. A left-self-distibutive algebra is a set D with 
a a law * such that or all x, y, z:

x*(y*z) = (x*y)*(x*z)

For example, if G is a multiplicative group, the law x * y = xyx^(-1), 
conjugacy, makes (G, *) into a left-self-distributive algebra. Another typical 
exemple is a Ring, (or a Module) with a mean law: (x * y) = (x+y)/2, as you can 
easily verify, or more generally (x*y) = (1 - r)x + ry, with r in R.  Such 
structure plays a transversal role from the “logic of space” to the logic of 
some models of “powerful" Turing machine.

I recall that among the five (actually eight) mains variant of provability 
imposed by incompleteness,

P
[]p
[]p & p
[]p & <>t
[]p & <>t & p


on p partially computable (provable when true, sigma_1, obeying p -> []p), the 
observable is given by the three last one, which are five, as the two last one 
splits along G and G* (which I hope you all have an idea go the importance in 
self-reference, but ask if you have missed this).

Now, they are all graded, by the fact that you have variant brought by 
replacing []p by [][]p,or []…[]p, with n boxes, written []^n p?
<>^m t can replace <>t, and from those numbers comes the braiding, and normally 
the “illusion” of space, in self-introspecting universal machine. But here, 
that is not yet proven, and relies on conjecture in mathematical logic, set 
theory, etc. Anyon are cool, anyway! (Not easy mathematics though)

Bruno







Fractional statistics in anyon 
collisions<https://science.sciencemag.org/content/368/6487/173.full>

John K Clark

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Re: Quantum Computers and Anyons

2020-04-12 Thread Philip Thrift 


On Sunday, April 12, 2020 at 2:06:00 PM UTC-5, Lawrence Crowell wrote:
>
>
>> Nonabelian anyons have a braid group structure.
>
> LC
>  
>
>> Anyons in topological QM:

Topological Quantum: Lecture Notes
http://www-thphys.physics.ox.ac.uk/people/SteveSimon/topological2016/TopoBook.pdf
 

@philipthrift

> -
>>
>>

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Re: Quantum Computers and Anyons

2020-04-12 Thread Lawrence Crowell 
On Saturday, April 11, 2020 at 2:15:48 PM UTC-5, Bruno Marchal wrote:
>
>
> On 11 Apr 2020, at 19:24, John Clark > 
> wrote:
>
> In the April 10 2020 issue of the Journal Science the best evidence yet 
> for the existence of a quasiparticle called a "Anyon" is presented. Anyon's 
> are important because when 2 Anyon's loop around each other their quantum 
> state is altered and so that brading can be used to encode information. 
> Such brading would be far less susceptible to quantum decoherence than 
> other ways of encoding information, and decoherence is the only reason we 
> don't have practical and scalable Quantum Computers right now.
>
>
>
> I agree. I guess you mean braiding, like the space time description of two 
> particles going around each other, or around a third one, leading to a 
> braid (in 3d space). 
>
>
Nonabelian anyons have a braid group structure.

LC
 

> It is why I except braiding from the projections obtained in arithmetic 
> from the quantization. Braids and links, and knots are simple topological 
> structure, but provides semantic for quantum logics, quantum computations, 
> but also the computations as “seen from inside arithmetic” by universal 
> machine/number/words/finite)-beings.
>
> The the fractional Hall effect, the “quantum field” of the condensed 
> matter, are “shortcut” to Deutsch's quantum Turing universality. 
>
> There are also extraordinary relations between Artin’s group of braids (a 
> generalisation of the permutation group), Temperly-Lieb Algebra (and 
> decoupling theory) and self-distributive algebra, related to the theory of 
> high cardinal in Zermelo-Fraenkel set theory. A left-self-distibutive 
> algebra is a set D with a a law * such that or all x, y, z:
>
> x*(y*z) = (x*y)*(x*z)
>
> For example, if G is a multiplicative group, the law x * y = xyx^(-1), 
> conjugacy, makes (G, *) into a left-self-distributive algebra. Another 
> typical exemple is a Ring, (or a Module) with a mean law: (x * y) = 
> (x+y)/2, as you can easily verify, or more generally (x*y) = (1 - r)x + ry, 
> with r in R.  Such structure plays a transversal role from the “logic of 
> space” to the logic of some models of “powerful" Turing machine.
>
> I recall that among the five (actually eight) mains variant of provability 
> imposed by incompleteness, 
>
> P
> []p
> []p & p
> []p & <>t
> []p & <>t & p
>
>
> on p partially computable (provable when true, sigma_1, obeying p -> []p), 
> the observable is given by the three last one, which are five, as the two 
> last one splits along G and G* (which I hope you all have an idea go the 
> importance in self-reference, but ask if you have missed this).
>
> Now, they are all graded, by the fact that you have variant brought by 
> replacing []p by [][]p,or []…[]p, with n boxes, written []^n p? 
> <>^m t can replace <>t, and from those numbers comes the braiding, and 
> normally the “illusion” of space, in self-introspecting universal machine. 
> But here, that is not yet proven, and relies on conjecture in mathematical 
> logic, set theory, etc. Anyon are cool, anyway! (Not easy mathematics 
> though)
>
> Bruno
>
>
>
>
>
>
>
> Fractional statistics in anyon collisions 
> 
>
> John K Clark
>
> -- 
> You received this message because you are subscribed to the Google Groups 
> "Everything List" group.
> To unsubscribe from this group and stop receiving emails from it, send an 
> email to everyth...@googlegroups.com .
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>  
> 
> .
>
>
>

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Re: Quantum Computers and Anyons

2020-04-11 Thread Bruno Marchal 

> On 11 Apr 2020, at 19:24, John Clark  wrote:
> 
> In the April 10 2020 issue of the Journal Science the best evidence yet for 
> the existence of a quasiparticle called a "Anyon" is presented. Anyon's are 
> important because when 2 Anyon's loop around each other their quantum state 
> is altered and so that brading can be used to encode information. Such 
> brading would be far less susceptible to quantum decoherence than other ways 
> of encoding information, and decoherence is the only reason we don't have 
> practical and scalable Quantum Computers right now.


I agree. I guess you mean braiding, like the space time description of two 
particles going around each other, or around a third one, leading to a braid 
(in 3d space). 

It is why I except braiding from the projections obtained in arithmetic from 
the quantization. Braids and links, and knots are simple topological structure, 
but provides semantic for quantum logics, quantum computations, but also the 
computations as “seen from inside arithmetic” by universal 
machine/number/words/finite)-beings.

The the fractional Hall effect, the “quantum field” of the condensed matter, 
are “shortcut” to Deutsch's quantum Turing universality. 

There are also extraordinary relations between Artin’s group of braids (a 
generalisation of the permutation group), Temperly-Lieb Algebra (and decoupling 
theory) and self-distributive algebra, related to the theory of high cardinal 
in Zermelo-Fraenkel set theory. A left-self-distibutive algebra is a set D with 
a a law * such that or all x, y, z:

x*(y*z) = (x*y)*(x*z)

For example, if G is a multiplicative group, the law x * y = xyx^(-1), 
conjugacy, makes (G, *) into a left-self-distributive algebra. Another typical 
exemple is a Ring, (or a Module) with a mean law: (x * y) = (x+y)/2, as you can 
easily verify, or more generally (x*y) = (1 - r)x + ry, with r in R.  Such 
structure plays a transversal role from the “logic of space” to the logic of 
some models of “powerful" Turing machine.

I recall that among the five (actually eight) mains variant of provability 
imposed by incompleteness, 

P
[]p
[]p & p
[]p & <>t
[]p & <>t & p


on p partially computable (provable when true, sigma_1, obeying p -> []p), the 
observable is given by the three last one, which are five, as the two last one 
splits along G and G* (which I hope you all have an idea go the importance in 
self-reference, but ask if you have missed this).

Now, they are all graded, by the fact that you have variant brought by 
replacing []p by [][]p,or []…[]p, with n boxes, written []^n p? 
<>^m t can replace <>t, and from those numbers comes the braiding, and normally 
the “illusion” of space, in self-introspecting universal machine. But here, 
that is not yet proven, and relies on conjecture in mathematical logic, set 
theory, etc. Anyon are cool, anyway! (Not easy mathematics though)

Bruno






> 
> Fractional statistics in anyon collisions 
> 
> 
> John K Clark
> 
> -- 
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>  
> .

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Quantum Computers and Anyons

2020-04-11 Thread John Clark 
In the April 10 2020 issue of the Journal Science the best evidence yet for
the existence of a quasiparticle called a "Anyon" is presented. Anyon's are
important because when 2 Anyon's loop around each other their quantum state
is altered and so that brading can be used to encode information. Such
brading would be far less susceptible to quantum decoherence than
other ways of encoding information, and decoherence is the only reason we
don't have practical and scalable Quantum Computers right now.

Fractional statistics in anyon collisions


John K Clark

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