this is a big deal

S

scruffy

Diamond Member
Mar 9, 2022
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States of matter with "non-Abelian topological order".

Abelian means commutative - so non- Abelian means "order matters".

www.nature.com

Non-Abelian topological order and anyons on a trapped-ion processor - Nature

A trapped-ion quantum processor is used to create ground-states and excitations of non-Abelian topological order on a kagome lattice of 27 qubits with high fidelity.
www.nature.com www.nature.com

To help decipher the vocabulary:

Anyon: Anyon - Wikipedia

Kagome lattice: Trihexagonal tiling - Wikipedia

Borromean ring: Borromean rings - Wikipedia

Quantum braiding: Quantum braiding: It’s all in (and on) your head.

knotphysics.net

Knot Physics - Braids and Quantum Information on a Branched Spacetime Manifold

We use a branched spacetime manifold to describe quantum mechanics. The branches are braided, and the braids can help us understand quantum entanglement.
knotphysics.net knotphysics.net

phys.org

Braiding may be key to using time crystals in quantum computing

Over the past few years, physicists have predicted that a new form of matter called time crystals may have potential applications in quantum computing. Now in a new study, physicists Raditya Weda Bomantara and Jiangbin Gong at the National University of Singapore have taken some of the first...
phys.org phys.org
 
scruffy said:
States of matter with "non-Abelian topological order".

Abelian means commutative - so non- Abelian means "order matters".

www.nature.com

Non-Abelian topological order and anyons on a trapped-ion processor - Nature

A trapped-ion quantum processor is used to create ground-states and excitations of non-Abelian topological order on a kagome lattice of 27 qubits with high fidelity.
www.nature.com www.nature.com

To help decipher the vocabulary:

Anyon: Anyon - Wikipedia

Kagome lattice: Trihexagonal tiling - Wikipedia

Borromean ring: Borromean rings - Wikipedia

Quantum braiding: Quantum braiding: It’s all in (and on) your head.

knotphysics.net

Knot Physics - Braids and Quantum Information on a Branched Spacetime Manifold

We use a branched spacetime manifold to describe quantum mechanics. The branches are braided, and the braids can help us understand quantum entanglement.
knotphysics.net knotphysics.net

phys.org

Braiding may be key to using time crystals in quantum computing

Over the past few years, physicists have predicted that a new form of matter called time crystals may have potential applications in quantum computing. Now in a new study, physicists Raditya Weda Bomantara and Jiangbin Gong at the National University of Singapore have taken some of the first...
phys.org phys.org
Click to expand...
This is nice. So, what will this lead to? Time travel? Bigger nuclear bombs? Why is this huge?
 
I read the Wikipedia article on Borromean Rings ... most of it describes the artistic symbolism of such a shape ... some of it from cave drawings during prehistorical times ... Cro-magnon technologies ... woot ...

Please tell us in your own words why this isn't some Wiccan bullshit ... or are you just throwing long four syllable phrases out there hoping no one bothers to read your citations ... for example, how are you calculating non-local work performed along this surface? ... these are manifolds so we all know how to calculate local work ...
 
Cougarbear said:
This is nice. So, what will this lead to? Time travel? Bigger nuclear bombs? Why is this huge?
Click to expand...
This provides us with a tool to investigate dimensionality.

If you read the article, something should leap out at you:

These anyons are TWO dimensional.

TWO

Think about it.

Braiding requires topological embedding, just like compactification does.
 
ReinyDays said:
I read the Wikipedia article on Borromean Rings ... most of it describes the artistic symbolism of such a shape ... some of it from cave drawings during prehistorical times ... Cro-magnon technologies ... woot ...

Please tell us in your own words why this isn't some Wiccan bullshit ... or are you just throwing long four syllable phrases out there hoping no one bothers to read your citations ... for example, how are you calculating non-local work performed along this surface? ... these are manifolds so we all know how to calculate local work ...
Click to expand...
Two dimensional.

What else do you know that's two dimensional, yet we can see it and measure it?

Sounds like Flatland, doesn't it?
 
See so, this is directly applicable to probability theory.

In probability theory, there is a "generator", which has a shape. The distribution can either remain stable, or change over time. In either case the "process" is much like a quantum state. It's not just 0 or 1, it's a combination of all possible states of 0 and 1 - which you can look at in the phase plane and thereby see if your generator has any limit cycles n stuff like that.

The side effect of an "outcome" is irreversibility, which is a rudimentary form of memory. The minute you define an "outcome", you have both. The shape of the outcome matches the shape of the generator. An outcome defines a moment in time, it's like a prototypical "next" operator, it's the "d" in dt. You can think of it like a measurement.

Well, it turns out, you can generate just about any desired shape, just by "spraying" the required dimensions with outcomes. The difference between the point cloud and the continuous surface though, is the point cloud can be embedded in ways the continuous surface can't. For example you actually CAN embed a Klein bottle in 3 dimensions with a point cloud. And using algebraic topology, you can figure out "how much" space is required between the points, so to speak - and therefore what kinds of dusts will work, in terms of both shape and density.

When it comes to combinatorics, the non-Abelian sequences outnumber the commutative by a power of the dimension. So, as distinct from a Markov process, its non-Abelian cousin remembers how it got there - which makes it nonlinear, and if you parametrize the nonlinearity you can still control the shapes of the outcomes. It's easy in a linear system, not so easy trying to predict chaotic dynamics.

An electron in an orbital around a nucleus, is "chaotic dynamics". And yet the shape of the set of outcomes is well defined. The whole idea behind 'outcomes' is you can only measure them one at a time, they are by nature sequential. The set of outcomes is ORDERED, in the order of observation. The act of ordering is ALMOST like another dimension, because you're defining a path - which then lets you define velocity - which then lets you curve the velocity surface. Doing so will result in a second order metric.

The importance of this in part, is it represents a working and experimentally açcessible "membrane" in the sense of string theory. The knotting can be considered "points in time", whenever they define paths (that is, whenever they are "oriented" which means the paths have a "direction" - otherwise they're just shapes).
 
And here we are folks... this paper shows exactly what I said. Fig 1 in the PDF shows how to get a 3+1 topology by stacking and compactifying 2-d "branes".

Non-Abelian string and particle braiding in topological order: Modular $\mathrm{SL}(3,\mathbb{Z})$ representation and $(3+1)$-dimensional twisted gauge theory

String and particle braiding statistics are examined in a class of topological orders described by discrete gauge theories with a gauge group $G$ and a 4-cocycle twist ${\ensuremath{\omega}}_{4}$ of $G$'s cohomology group ${\mathcal{H}}^{4}(G,\mathbb{R}/\mathbb{Z})$ in three-dimensional space...
link.aps.org link.aps.org

This is how it's done. Basically in a commutative world exchanging two elements twice results in the original state, whereas in a non-Abelian world it doesn't. This idea has direct and profound implications for everything from physics to neuroscience.
 
scruffy said:
And here we are folks... this paper shows exactly what I said. Fig 1 in the PDF shows how to get a 3+1 topology by stacking and compactifying 2-d "branes".

Non-Abelian string and particle braiding in topological order: Modular $\mathrm{SL}(3,\mathbb{Z})$ representation and $(3+1)$-dimensional twisted gauge theory

String and particle braiding statistics are examined in a class of topological orders described by discrete gauge theories with a gauge group $G$ and a 4-cocycle twist ${\ensuremath{\omega}}_{4}$ of $G$'s cohomology group ${\mathcal{H}}^{4}(G,\mathbb{R}/\mathbb{Z})$ in three-dimensional space...
link.aps.org link.aps.org

This is how it's done. Basically in a commutative world exchanging two elements twice results in the original state, whereas in a non-Abelian world it doesn't. This idea has direct and profound implications for everything from physics to neuroscience.
Click to expand...
How? How will this be used in physics and neuroscience?
 
This paper also explains the theory pretty well.


What we see is a "fractional dimensionality", but what's really going on is a mixture of the number of braiding events between one tick and the next.

Here's what I propose - don't try to force an artificial clock on this system. Let IT define what dt is, based on the braiding interval. What you'll get is a lot of little intervals that "cover" the configuration space, like a stack of pancakes.

When seen from afar (1-sec window), the whole space looks regular. But close-up it's a dust, and the non-Abelian braiding makes it irregular. There is never any loss of information, in fact exactly the opposite occurs, there is a GAIN of information because of the braiding events.

Eventually I suspect this could explain entropy. "Braiding happens". The diagrams in the link show how it happens. Our "time" that we see, results from a collection of braiding events that happen at the Planck scale, the actual duration of next is somewhere around 10^-44 seconds.
 
Cougarbear said:
How? How will this be used in physics and neuroscience?
Click to expand...
Well, it's easier for me to explain the neuroscience part.

Start with a mapping of time to space in the brain, based on electrical signals. You have evoked potentials, and premotor potentials, and together they define a timeline. The brain is a window moving through time, centered on "now".

We can the "compactify" this timeline by joining the two points at infinity, and when we do this we get a circle. A circle is a topological entity defined by an algebraic group that only embeds certain ways - however, there are "non-physical" ways that can be achieved by making the timeline into a "dust" instead of a continuous line (1-d surface).

So for example, you can think of a local phase transition in a crystal as a braiding event, and if something's driving it, it can even be a generator. Pay attention to the use of the word "generator" in the link, they're using it in the context of group theory but it also applies to "outcomes" resulting from a distribution. They're showing you how braiding events arise spontaneously from the vacuum, which can then be looked at as a time series of random events, "and" as a topological group.

The history on this goes back to 1977, but this is the first time it's been realized. It has a lot to do with the elusive "Majorana states" in topological quantum computing. Note especially the 2nd and 3rd sections here:

Topological quantum computer - Wikipedia

en.wikipedia.org en.wikipedia.org
 
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Here - in backwards neuroscientific order, from the industry standard Ising (Hopfield) model.

Potts model - Wikipedia

en.wikipedia.org en.wikipedia.org

Jones polynomial - Wikipedia

en.wikipedia.org en.wikipedia.org

The first link shows how you get from the topology to the probability distribution.

"any (desired) level of precision for the answer can be obtained by adding more braid twists"
 
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Today: quantum computing at the speed of light.

At room temperature.

Using the same principles, only photonic instead of wired.

phys.org

New chip opens door to AI computing at light speed

University of Pennsylvania engineers have developed a new chip that uses light waves, rather than electricity, to perform the complex math essential to training AI. The chip has the potential to radically accelerate the processing speed of computers while also reducing their energy consumption.
phys.org phys.org

As this earlier paper describes, such a system is easily tunable.


You can do the math on this, for a 10 cm brain. It takes light a fraction of a nanosecond to get from one end of the brain to the other. In that time, our brains are 5 orders of magnitude more resolute, in terms of time discrimination, when every neuron is used.

This is why the topological term "unfolding" applies. You're taking a point ("now"), and basically "completing" it, in the same sense as AI computer graphics can complete an image. Because "now" is a singularity, it has to be modeled by completion.

The big benefit of this architecture is super-fast completion. So fast, it can affect the shape of light speed distributions.
 
scruffy said:
Today: quantum computing at the speed of light.

At room temperature.

Using the same principles, only photonic instead of wired.

phys.org

New chip opens door to AI computing at light speed

University of Pennsylvania engineers have developed a new chip that uses light waves, rather than electricity, to perform the complex math essential to training AI. The chip has the potential to radically accelerate the processing speed of computers while also reducing their energy consumption.
phys.org phys.org

As this earlier paper describes, such a system is easily tunable.


You can do the math on this, for a 10 cm brain. It takes light a fraction of a nanosecond to get from one end of the brain to the other. In that time, our brains are 5 orders of magnitude more resolute, in terms of time discrimination, when every neuron is used.

This is why the topological term "unfolding" applies. You're taking a point ("now"), and basically "completing" it, in the same sense as AI computer graphics can complete an image. Because "now" is a singularity, it has to be modeled by completion.

The big benefit of this architecture is super-fast completion. So fast, it can affect the shape of light speed distributions.
Click to expand...
So, in everyday life, how will this benefit humanity?
 
scruffy said:
Two dimensional.

What else do you know that's two dimensional, yet we can see it and measure it?

Sounds like Flatland, doesn't it?
Click to expand...

Yes, you said it was a manifold ... duh ... I understand what the Wiccan Priestesses say ... a manifold is a non-Euclidian space such that the space is Euclidian locally ... it's safe to map a small town on a flat 2D map, even though we know the Earth is curved ...

You didn't explain how you're calculating work performed within the Borromean Ring System ... your citation only covers the religious uses ... I'm asking because I think this is a bullshit link and I won't bother if all your citations are bullshit ...

I'm an uneducated construction laborer and the first thing I did to these Borromean Rings is slap a set of Cartesian Coordinates over them, x-, y-, and z-axes all orthogonal ... and see what their derivatives are doing ... that's three spacial dimensions sir, your claim these are two dimensional is wrong ... in fact, I see nothing in the definition of the Borromean Rings limiting the dimensions, these things can be 5D, 37D, even 1,000,000D; just the algebra gets too complicated [grin] ... it's not useful ...

Is this just useful with statistical trickery? ... you know the public is a lot easier to deceive than this garbage ...c.f. climate change rhetoric ...

Today: quantum computing at the speed of light ...

Wait ... What? ... my electronic computer here in front of me operates as close to the speed of light as to make no difference ... it's the transitors that take time to switch ... you know ... work performed ...

All matter and all energy cannot travel faster than the speed of light ... period ... however, it appears information can travel instantaneously, without the passage of time ... anywhere in the universe ... Star Trek's transporter-to-transporter travel ... quanum computing is the first step in making such travel possible ... instead of taking the time to perform the work re-biasing a transitor structure, we just flip the spin of an electron ... less work means less time ... computers will be faster ... faster than the speed of light ...
 
ReinyDays said:
Yes, you said it was a manifold ... duh ... I understand what the Wiccan Priestesses say ... a manifold is a non-Euclidian space such that the space is Euclidian locally ... it's safe to map a small town on a flat 2D map, even though we know the Earth is curved ...

You didn't explain how you're calculating work performed within the Borromean Ring System ... your citation only covers the religious uses ... I'm asking because I think this is a bullshit link and I won't bother if all your citations are bullshit ...

I'm an uneducated construction laborer and the first thing I did to these Borromean Rings is slap a set of Cartesian Coordinates over them, x-, y-, and z-axes all orthogonal ... and see what their derivatives are doing ... that's three spacial dimensions sir, your claim these are two dimensional is wrong ... in fact, I see nothing in the definition of the Borromean Rings limiting the dimensions, these things can be 5D, 37D, even 1,000,000D; just the algebra gets too complicated [grin] ... it's not useful ...

Is this just useful with statistical trickery? ... you know the public is a lot easier to deceive than this garbage ...c.f. climate change rhetoric ...

Today: quantum computing at the speed of light ...

Wait ... What? ... my electronic computer here in front of me operates as close to the speed of light as to make no difference ... it's the transitors that take time to switch ... you know ... work performed ...

All matter and all energy cannot travel faster than the speed of light ... period ... however, it appears information can travel instantaneously, without the passage of time ... anywhere in the universe ... Star Trek's transporter-to-transporter travel ... quanum computing is the first step in making such travel possible ... instead of taking the time to perform the work re-biasing a transitor structure, we just flip the spin of an electron ... less work means less time ... computers will be faster ... faster than the speed of light ...
Click to expand...
Huh what?

Information cant propagate faster than the speed of light either. The best we can achieve is massive parallelism (like that found in the brain).

The beauty of an unfolding is it's a virtual entity, just like the distributions that are hidden from us. We can't "see" it/them, we can only infer. We're living in Flatland.

Braiding is an 'exchange', it's yet to be determined whether there is any actual information transfer (that's measurable).
 
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