Computer program dreams up new quantum experiments and the result of one of it's solution

Quantum mechanics is a tough thing to understand. At the very small distances quantum interactions between particles happen (called, "effects"). The mag-lev train is an example of a quantum effect when a superconducting magnet is cooled below a critical temperature point (called, "phase transition"), the magnet loses resistance and current flow around. Like magnets repulse and the train is charged opposite and the train levitates.

The math gets more problematic as larger amount of atoms are added (in math, the "number of dimensions" increases. In math, a dimension can be thought of as a variable. The more variables you have the more complex and the more work has to be done). Faced with tis problem of both physics and math, two researchers decided to team up. They realized they had built in preconceived notions on what should and shouldn't work. They left those notion out of their program on purpose.

The idea was developed by graduate student Mario Krenn and colleagues in the group of quantum-physicist Anton Zeilinger. The algorithm is dubbed "Melvin", and the team believes that it might be able to explore hitherto unknown properties and behaviours of quantum systems. In doing so, Melvin would take the complexity of quantum experiments to a level beyond the imaginations of human designers.

These experiments include those with the particular goal of achieving quantum entanglement between many particles. Experimental methods for achieving entanglement of two or a very few particles are well-known. But entanglement is so counter-intuitive that it can be very difficult to see how to combine the known experimental "building blocks" to attain a more complicated state, such as "high-dimensional" entanglement between many of the particles' degrees of freedom.

Melvin works that out unencumbered by human preconceptions. The algorithm is supplied with a set of standard experimental components that it can combine and reshuffle to achieve the desired goal. These elements consist of devices for manipulating the trajectories and quantum properties of photons. These include beam splitters, which can send a photon in two possible directions, thereby putting it into a superposition of two quantum states.

physicsworld.com, Feb. 2016 - Computer program dreams up new quantum experiments.
-and-
arXiv.org - Automated Search for new Quantum Experiments.

Well, that was last year with the announcement of Melvin. It now looks like they got a rather unexpected answer from Melvin!

An answer to a quantum-physical question provided by the algorithm Melvin has uncovered a hidden link between quantum experiments and the mathematical field of Graph Theory. Researchers from the Austrian Academy of Sciences and the University of Vienna found the deep connection between experimental quantum physics and this mathematical theory in the study of Melvin's unusual solutions, which lies beyond human intuition. They now report in the journal Physical Review Letters.

...
In the analysis of this solution calculated by Melvin, the researchers initially groped in the dark. Until they came up with a remarkable sequence of numbers known only in the so-called graph theory—a sophisticated area of mathematics that has been used to describe networks such as the Internet or neural networks.

The unusual approach, which would have remained hidden to quantum physicists, prompted the scientists to further investigate this connection. As they now report in the journal Physical Review Letters, there are great similarities between experimental quantum physics and mathematical graph theory: If methods and knowledge from graph theory are used to calculate and plan a quantum experiment, it is possible to make very precise and novel statements about the results. "Properties of quantum experiments can be calculated using graph theory, and questions in graph theory can be answered in quantum experiments," explains Krenn. In this way, it is also possible to grasp quantum technology as a graph or a network in order to explore new experimental possibilities.

phys.org, Dec. 19, 2017 - Hidden bridge between quantum experiments and graph theory uncovered.

Graph theory asks questions like, "How many paths can you take from one vertex to another? Add another? And another? A hundred? And what can be generalized about all this." They then add rules and ask again.

The "neural network and internet" is very interesting! Remember a year or so back when the superstring guy (Gates?? IIRC) freaked out after finding "error correcting codes" in his study of quarks, electrons, and super symmetry? There is a thread here on ATS about it. Now there is perfectly logical explanation: the math came part and parcel from graph theory!

My thoughts... getting over the weirdness of quantum mechanics is a hurdle. Scientists like finding solutions but brute force is not always the best method. The physics world article says Melvin is "creative" but going through an exhaustive list is not "creative" in my view. The "creative" part came when looking at the data a series of numbers was recognized which lead to the graph theory-quantum experiment bridge. Had Melvin purposed it himself then I would be in a different frame of mind. Cool find! Glad both math and physics can help each other now! Melvin is pretty cool (I could be totally missing something about how it works. My bad if so!)

Maybe Gates and Melvin can become study buddies!

Or is this an example of AI taking a human's job? Elaborate confirmation bias? Another boring QM thread from TEOT? Hey, that's cool! The AIs are coming!!

James Gates

And that sounds an awful lot like laws of physics, as James Gates, a theoretical physicist at the University of Maryland, pointed out:

"In my research I found this very strange thing. I was driven to error-correcting codes - they're what make browsers work. So why were they in the equations I was studying about quarks and electrons and supersymmetry? This brought me to the stark realisation that I could no longer say people like Max are crazy."

-James Gates

Source: Science Alert

They discover the "Amplitudehedron" and don't realize that it defines graph theory?

en.wikipedia.org...

It seems that everyone wants to define their own mathematical objects and not resort to using those of other people:

Quantum cohomology - isn't that just group theory?
en.wikipedia.org...
en.wikipedia.org...

There are other representations like Octonions, Quaternions - those were originally used in Maxwell's Equations until another scientist figured some were unnecessary.

I read this a while ago. I am still trying to understand where the cross-over happens but it looks like math and physics are interwoven.

scienceblog.com (neeti) - Prime Numbers Paralleling Reality: Possible?

The Riemann zeta function is an inverted series summation. It is extended into the real numbers. Euler provided a clever method of sieving out non-prime numbers. The result is a product function of primes, known as the primorial. Then Riemann extended around the undefined point and had to add the gamma function.

He presented his findings as a paper. In his original he noted, handwritten, "All non-trivial zeroes have a real part 1/2" (or something close) but he did not have the time to provide a rigorous proof (his original paper did not involve this notion so he only worked on what he wanted to present). The trivial zeroes are negative even numbers. The non-trivial zeroes are the prime numbers.

He shortly died thereafter.

Now known as the Riemann Hypothesis, all attempt at attacking it have failed for over 160 years.

Last year, the connection between Riemann zeta zeroes and physics was noted. The above blog is the deep math, eliding over several steps, and asking it's question.

Does group theory and graph theory produce real world physics we know as chaotic quantum mechanics which also gives rise to matter like stars and galaxies and us?

Huh. My head hurts!

a reply to: stormcell

Yeah, I know the names are all over the place!

I started looking at cohomology and wound up asking myself, "What is the big deal? Ain't this the same as this other one?" There are variances but can't we agree on a consistent naming convention?

The truth of the matter is that physicists don't know what the mathematicians are doing (and vice versa). When they do meet up some good stuff happens but they go off back to their own field again. If you have read Quanta magazine you can read about this when they profile scientists/mathematicians .

The math guys (and gals) are just now starting to collect these ideas and order them. Even they are amazed when one school of thought that has nothing to do with another can be used to solve both their problems.

It is confusing and frustrating sitting here trying to understand what/why terms have come in or gone out of favor. Like, quaternions, I never really understood it until I read Pynchon's Against the Day.

After saying all that, maybe that is why I feel good about, Melvin! Straight and simple.

ETA: It is a physicist writing about graph theory. I would not expect a deep level of the history of graph theory. And two other contributors is too few eyes. Maybe they will be helped in coalescing their idea with a wider audience.

Thanks, this is a cool thread! I don't think this is an example of a computer taking a human's job because this particular computer was programmed to do something that no human would be able to do anyway.

After a few hours of calculation, their algorithm - which they call Melvin - found the recipe to the question they were unable to solve, and its structure surprised them. Zeilinger says: "Suppose I want build an experiment realizing a specific quantum state I am interested in. Then humans intuitively consider setups reflecting the symmetries of the state. Yet Melvin found out that the most simple realization can be asymmetric and therefore counterintuitive. A human would probably never come up with that solution."

The physicists applied the idea to several other questions and got dozens of new and surprising answers. "The solutions are difficult to understand, but we were able to extract some new experimental tricks we have not thought of before. Some of these computer-designed experiments are being built at the moment in our laboratories", says Krenn.

Melvin not only tries random arrangements of experimental components, but also learns from previous successful attempts, which significantly speeds up the discovery rate for more complex solutions.

phys.org, Feb. 2016 - Quantum experiments designed by machines.

A bit more insight on how Melvin works.

The set up for experiments seemed like guesses and they realized a program can do it faster. Then they built upon it successes. Melvin came up "asymmetrical" solutions (like parking your car where nobody else is and walking instead of waiting for a closer space). Its successful ones were rewarded so Melvin found other solutions faster.

It is a learning algorithm and not just randomly and exhaustively going through a list.

On Graph Theory

The topic of "graph theory", as StormCell pointed out, has many branches. At the arXiv, they do not even have a topic called 'graph theory'. The following paper is a great example of what "graph theory" can cover:

arxive.org (PDF) - Graph and Network Theory in Physics. A Short Introduction.

The paper is 52 pages long!

From the looks of things, almost any topic can be mapped to "graph theory". So that was not much of a help.

Graph Theory has proven to be a useful tool to describe a discrete time-evolution of a given state in a system. In our investigation, we consider particles moving along the real line in a wave form, and develop a discrete version by entirely reconstructing the setup into particles moving through a graph instead. By doing so, we hope to build upon our current understanding of quantum states and how a discrete analogue of quantum evolution exists.

medium.com - Applications of Graph Theory to Concepts in Quantum Mechanics: A Python Perspective.

Not exactly what I was looking for but a good generalization. Graph theory has already been applied quantum states and how they change over time. "Particles moving along the real line in a wave form" is an apt description. I tend to view the general topic of "graph theory" as a discrete (i.e., countable) item. That may be my hang up, discrete vs. the real.

Problems with OP Article

I re-read everything in the "Bridge" article again. Here is what I noticed.

(1) There is only one source. Typically that is not a huge problem but in this instance it is a problem. You can read the abstract of the paper but need to pay to read it. Not very scientific.
(2) That source wrote the press release (PR). The story has been picked up by other sites that take PR and publish them, usually with no modification. This is a problem because I cannot see the "number series" for myself and pin down which "graph theory" they are referring to.
(3) Time to check out the researchers. One is the president of blah-blah-blah and has been involved in multiple, "Quantum First!" stories. The other has multiple stories of quantum mechanics claims over the years too. Which mean both could be making some announcement to keep their names in the headlines (i.e., funding).

3 may or may not be true but having access to 1 would put me at ease with 2. A implies B, B implies C, therefore A implies C.

This may not actually be "real news" as the science cannot be verified. I honestly am not going to pay-to-read. Let us hope that real science is done by peer reviewing their paper!

I've quipped that I swear Phys.org is punking me. They may have actually pulled their best one yet!

Happy Winter Solstice!

a reply to: stormcell

I've been turning this over and over, "What the h3ll do they mean by 'topology' and quantum mechanics"? While the OP was about specifically their experiments we both noticed that "topology", at least in math terms, covers vast amounts of different ideas and concepts.

Leave it to Quanta Magazine to throw a rope to a drowning man!

In the last three decades, condensed matter physicists have discovered a wonderland of exotic new phases of matter: emergent, collective states of interacting particles that are nothing like the solids, liquids and gases of common experience.

The phases, some realized in the lab and others identified as theoretical possibilities, arise when matter is chilled almost to absolute-zero temperature, hundreds of degrees below the point at which water freezes into ice. In these frigid conditions, particles can interact in ways that cause them to shed all traces of their original identities. Experiments in the 1980s revealed that in some situations electrons split en masse into fractions of particles that make braidable trails through space-time; in other cases, they collectively whip up massless versions of themselves. A lattice of spinning atoms becomes a fluid of swirling loops or branching strings; crystals that began as insulators start conducting electricity over their surfaces. One phase that shocked experts when recognized as a mathematical possibility in 2011 features strange, particle-like “fractons” that lock together in fractal patterns.

...

Led by dozens of top theorists, with input from mathematicians, researchers have already classified a huge swath of phases that can arise in one or two spatial dimensions by relating them to topology: the math that describes invariant properties of shapes like the sphere and the torus. They’ve also begun to explore the wilderness of phases that can arise near absolute zero in 3-D matter.

Enumerating phases of matter could have been “like stamp collecting,” Vishwanath said, “each a little different, and with no connection between the different stamps.” Instead, the classification of phases is “more like a periodic table. There are many elements, but they fall into categories and we can understand the categories.”

quantamagazine.org - Physicists Aim to Classify All Possible Phases of Matter.

This is happening both theoretically and in experiments. They use the topic of topology as a guide for what is already known (on the math side) to predict/explain what is happening on the QM side. They create states near absolute zero and begin to look at 1-D and 2-D interactions. Topology helps classify groups of what would normally just be thought of "strange" or "odd" but not meaningful instances or examples; from topology, they know certain states should belong together because they can be described using the same math.

I like the "periodic table" comment because that describes how they are conceiving these phase states; similar groups classified together under broader families.

A long read. A very good one. Lots of crazy QM concepts but very well explained. And way better than my floundering around!

Ya'll remember Melvin? The computer that designs quantum experiments?

Qutrits, ququarts, or any other d-dimensional qudits are possible. Now Manuel Erhard and his colleagues at the Institute for Quantum Optics and Quantum Information (IQOQI) in Vienna have created a trio of entangled qutrits, the first demonstration in which more than two particles were entangled in more than two quantum states.

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The researchers designed and built a femtosecond light source that produced two pairs of photons, with each pair entangled in the ℓ = 0, 1, and –1 OAM levels. The path to creating the complex entanglement between three of the photons wasn’t obvious—in fact, it required a computer’s help. Using an algorithm named Melvin that essentially plays with various configurations of quantum optics instruments, Erhard and coworkers developed a novel device that consisted of a beamsplitter, nested interferometers, and more. As shown in the diagram, the multiport processed three photons at a time—previous multiphoton-entanglement experiments manipulated only two—and transformed some of the correlations between OAM levels. Simultaneous clicks in four final photon detectors signaled that two of the photons exiting the multiport, B and C, plus photon D, were entangled in three dimensions.

The new technique opens the possibility of conducting more complex tests to rule out local realism alternatives to quantum mechanics. Researchers could also exploit high-dimensional-encoded photons to design quantum systems that carry more information and are less susceptible to eavesdropping. (M. Erhard et al., Nat. Photonics, 2018,

An alternative route is to increase the number of entangled quantum levels. Here, we overcome present experimental and technological challenges to create a three-particle GHZ state entangled in three levels for every particle. The resulting qutrit-entangled states are able to carry more information than entangled states of qubits. Our method, inspired by the computer algorithm Melvin, relies on a new multi-port that coherently manipulates several photons simultaneously in higher dimensions.

doi:10.1038/s41566-018-0257-6.)

physicstoday.scitation.com, Nov. 1, 2018 - Multiparticle, multidimensional entanglement.

Glossary (in main physic today article):

GHZ - Greenberger-Horne-Zeilinger entanglement
OAM - Orbital Angular Momentum

How crazy! They created 3D quantum entanglement in 3 photons! And it was because Melvin was screwing around and figured out a method of beam splitting a femtosecond laser. It is rather genius!

Source A and B pairs, enters a multibeam splitter. Pairs C and D are treated a bit differently as only photon source C enters the splitter. It hits photon A which acts as the trigger to allow the split beam to hit photon B and photon C. Photon D is in close proximity. Photon D gets a direct hit from the source pair. They set the photons spinning and entangle the angular momentum which could be any way you want to spin a sphere!! All three qudits (quantum bits than can assume a range of values instead of the qubits: 0, 1, 0+1, 1+0, states. In this case angular moment in any direction). The three together are called "qutrits" for some horrible reason.

Anyway, Melvin helped create the setup! The researchers built it. Tested it and found that, indeed, the three photons' OAM were entangled in 3D by watching photon detectors count off the "hits" each was taking when triggered (hehe).

That is a crazy set up! Way to go, you Melvin!!

There have been lots of changes that we already do not know about that and it is also necessary for the user who is in a similar field and the main thing is that the new quantum experiment can b the solution and that is why the update of everything is required.



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a reply to: TEOTWAWKIAIFF

You like your maths.

Do you think it will be something like this?

If matter and antimatter were represented by odds and even numbers. To describe an odd number as having symmetry. How? You can always find your position with odd numbers by choosing the central number. Each side of you to the left and right are now symmetrical. Now. If you remove the middle number. which was an odd number. You have an even number to your left in descending order. And. an even number to the right in ascending order. Those 2 even numbers are antimatter. The next 2 numbers to the side of them are odd numbers. Matter one descending and one ascending. And, so on. Maybe other matter is represented by ascending and descending numbers. With even numbers. You have no true position except by a half integer. If you position yourself in front of an even number. There is no symmetry. Your always left with more numbers to either the left or right.

a reply to: TEOTWAWKIAIFF

This is a little more about my above reply.

Time is on the curve of the wave. Number a curve with an odd number. Start at the central number. Work with odd numbers. Remove an amount of odd numbers from centre. You will be left with a gap. And, the two numbers each side of gap will be matter particles. The size of particle is determined by how many amount points it has. On the numbered curve. You can see all the matter particle pairs and the antimatter pairs. Because it's on a curve. It has time included in it too.

If you're interested in it.

Go to ask any question about physics. Go back a page or two, to where earthquakes stop being discussed.

a reply to: blackcrowe




(It was easier to write it up in word and take a picture!)

Then there is this (scienceblog.com): Prime Numbers Paralleling Reality: Possible?

That is also kind of hinting at the same idea but from a physics perspective. It is a bit dense math but the message is the same: prime numbers, via Riemann zeta function, cross the border from abstract math to physical reality. They also go from a continuous curve to individual, discrete, numbers (i.e., primes), which is kind of mind blowing!

Sorry, been on vacation for a bit. All while having access issues. Now, swamped at work with end of year stuff. I will have give this more of a review but I got kind of excited about how all this seems to crossover with so many different topics!



ETA: The paper should have read, "2n+1 are known as the odd numbers"

a reply to: TEOTWAWKIAIFF

Thanks TEOT.

The 2n/2n+1 does make some sense to me. Although the prime numbers are something i tried to think about with my proposal. But, i don't think i understand how to represent them in it. If they did fit in. It would be a bonus.

I'm no math man. I am learning. But, struggling through algebra 1.

My idea actually originated from Feynman's double slit experiment.

I think it can be done a little differently. And, maybe was left representing antimatter (even number). When, if an odd number of slits were used. You could find position by releasing a wave from in front of the central position number.

It's really simple i think.

It can also be plotted in 3d by using a graph chart.

I did read your Riemann hypothesis thread. Sorry, it was beyond me.

The link is still confusing for me. Although the quadrant chart with the circle and zero in the centre makes sense in that, zero would be the point of position in my idea.

If even numbers are used. There is no real position. It's unstable. And the only centre can be a half integer number. (Which sounds similar to non trivial zero's).

Maths is complicated. But in an interesting way.