How Space and Time Could Be a Quantum Error-Correcting Code

https://www.quantamagazine.org/how-space-and-time-could-be-a-quantum-error-correcting-code-20190103/

by _Microft • 8 years ago

509 132 8 years ago

jchrisa• 8 years ago

Just came to say it makes me happy to see the term "discovered" used in a what is essentially an engineering/software context, instead of the term "invented." The more that people in our industry speak clearly about that fact that many of the constraints in our problem space are universal, and thus much of our solution space is discovered, not invented, the more we shift the culture to understand e.g. the absurdity of software patents, etc.

izzydata• 8 years ago

Do they use a similar terminology in mathematics when talking about proofs? Software solutions don't seem that much different in regards to solving specific problems.

gregknicholson• 8 years ago

This question — is maths discovered or invented? — was discussed at length in a recent BBC series: https://www.bbc.co.uk/programmes/b0bn9dth

inopinatus• 8 years ago

All matter is information, and all information is functional. Therefore perception is the lazy evaluation of the universe, and discovery is the fountain of invention.

mttyng• 8 years ago

That depends heavily on your philosophical interpretation of mathematics: Platonism vs. Formalism

Someone linked the BBC video, which is great, but there’s also a wonderful book that discusses this and many other facets of mathematical philosophy:

https://www.amazon.com/Thinking-about-Mathematics-Philosophy...

(Sorry for the link spew) I highly recommend that book to anyone remotely interested in the field.

jessriedel• 8 years ago

Not sure if it was rhetorical, but to answer your actual question: Mathematicians often say they "discovered" or "found" a proof. I've never heard one say they "invented" a proof, although they might talk about "building" a formalism or framework.

ashleyn• 8 years ago

"Discovered" in place of "invented" is actually cited as a common error in many English style guides.

malloryerik3• 8 years ago

Unconvinced, with respect. Patents and systems of intellectual property are also codes that create space and time, in this case financial. Without them, scientific and engineering discovery/invention has often (usually?) tended to collapse in on itself.

stronglikedan• 8 years ago

I inferred that OP was referring to the absurdity of the current software patent system and not the idea of patenting IP directly, and I agree that the current system is in dire need of an overhaul.

jonbesga• 8 years ago

Do you have a source to read about this? Seems an interesting topic.

zzbzq• 8 years ago

The etymological roots of "discover" and "invent" converge.

dclowd9901• 8 years ago

I'm not sure I really understand the article, as it is, but space-time seemed preternaturally a macrocosm of the quantum universe, a way to smooth out the infinitely possible subspace into a predictable and understandable macro space, the collapsing of all possible realities at the atomic level into a definite reality. In other words, this seems too obvious to be this obvious, so what am I missing here?

vtomole2• 8 years ago

What am I missing here?

It's not obvious how to reconcile the laws quantum mechanics with gravity and vice-versa as they seem to make incompatible descriptions of reality.

notduncansmith• 8 years ago

Mandelbrot cosmology offers some interesting potential resolutions, but more research definitely needs to be done.

airstrike• 8 years ago

The bendy fabric of space-time in the interior of the universe is a projection that emerges from entangled quantum particles living on its outer boundary.

Guess we are living in a simulation, after all. A quantum one, to be precise.

kamac2• 8 years ago

Wow that was a tough read for a layman like me.

[...] after the renowned physicist Juan Maldacena discovered that the bendy space-time fabric in its interior is “holographically dual” to a quantum theory of particles living on the lower-dimensional, gravity-free boundary.

What does "holographically dual" mean?

What boundary are we talking about here?

The bendy fabric of space-time in the interior of the universe is a projection that emerges from entangled quantum particles living on its outer boundary

What is the "interior" of the universe? What is the "outer boundary"?

toufiqbarhamov2• 8 years ago

There isn’t an exterior in this model, just a boundary you can’t get “outside of” because everything including space and time are part of the universe. What this is all based on is the observation that the information required to describe the volume of (for example) a black hole, can be encoded on its event horizon. The theory says that the universe and it’s horizon(s) can be similarly modeled. In essence that we live not in the volume of a soap bubble but in the fluctuations of the skin of the bubble. It’s only to us, at our energy level and scale that a higher dimensional volume appears to emerge.

It’s important to say that this is all entirely speculative, based on the physical possibility which allows for the resolution of some outstanding problems in physics. That doesn’t mean it is in any way real, it is just another possible model, and one without observation to support it as the way our universe actually works.

wallace_f4• 8 years ago

Perhaps a stupid question:

If a 3d universe can be encoded in a 2d space, then I suppose a 2d universe can be in a 1d space? And could 1 dimeneion be encoded in 0? Just some bits or fluctuations?

galaxyLogic• 8 years ago

I don't know much about it but from what I've read imagine that we are inside a black hole. Every black hole is a universe of its own. The boundary of the black hole is the outer boundary if we are inside it. From the outside it would be just the surface of the black hole. Something like that perhaps

rightbyte• 8 years ago

Should be verifiable on the inside with stuff popping up at the boundary, right?

When I read these quantum articles I think it's might as well be mambo jambo. Are the fundamentals of quantum physics even falsifiable?

vnnkov• 8 years ago

I really liked cosmological natural selection of Lee Smolin in that regard. For me it's just looks so simple and obviously. https://en.wikipedia.org/wiki/Lee_Smolin#Fecund_universes

roywiggins9• 8 years ago

anti-de Sitter universes are bounded by a horizon. The example given in the article is an Escher print with an infinite number of tiles bounded by a circle. They get smaller as they get closer to the edge, but there's an infinitude of them, so you have a universe that is infinite from "inside", but "from the outside", there's an outer boundary. As far as occupants of a hyperbolic universe go, they can't see the horizon directly because there's an infinite number of tiles between them and the edge.

That boundary has lower dimensionality than the universe itself (the Escher universe boundary is 1D and the interior is 2D).

Holographic duality is where you can describe the entire interior of the universe by characterizing "stuff happening" on the boundary- that the stuff happening inside the universe looks 2D, but is fundamentally one dimensional. Real-world holograms work like this- they encode a 3D scene onto a 2D substrate.

Our universe is not anti-de Sitter- it appears to be flat and does not pack away nicely into a bounded area like the Escher universe does, so it's as yet unclear how to apply the stuff they've found in their model universe to our own.

floatrock• 8 years ago

They get smaller as they get closer to the edge, but there's an infinitude of them, so you have a universe that is infinite from "inside",
Our universe is not anti-de Sitter- it appears to be flat and does not pack away nicely into a bounded area like the Escher universe

How do you tell from the "infinite inside" whether it packs away nicely into a bounded area? Or is figuring that out the trick?

spenczar5• 8 years ago

Thank you for a terrifically clear description of difficult concepts. This helped me a lot!

badloginagain• 8 years ago

They talk about black holes being possible in AdS universe- in the Escher universe does that look like a group of the fish "missing"?

Also, near the end they get into black hole information preservation. What information are they referring to? My assumption has always been that black holes essentially zero out all information, like making all bits zero on a hard-drive.

nabla9• 8 years ago

How do black holes fit into this picture? Are they anti-de Sitter locally?

I mean if our universe maps to 2d boundary, you could find it out if you try to pack 3d volume of space full of information/matter. The volume must become full earlier than if the the information is limited by the surrounding area and not by the volume.

0db532a02• 8 years ago

What do you mean by saying that our universe is flat. Are you saying that it’s a 2-manifold?

jahnu• 8 years ago

Not sure if it's related but this lecture gave me some basic grasp on the notion of holographic representations

https://www.youtube.com/watch?v=2DIl3Hfh9tY

rubyn00bie• 8 years ago

Sounds like if you imagine the universe as a sphere, like we (me?) "normally" do (3 dimensions), you use volume to describe its contents. Well... I think what they're saying is that the outside of the sphere, in this case the universe, just its surface, describes everything (all the information) inside of it... because in fact the volumetric area we know as the universe is a projection of a "flat" surface.

And... like I'm not very smart, but this is probably a bit like the non-euclidean space demo from yesterday's front page, where the geometry is doing really weird things... perhaps someone smart will come along and give a proper explanation.

empath75• 8 years ago

So, let's imagine you have a function that takes a phase space (ie, the positions, momentum, etc of a bunch of particles in normal 3+1 space time) as an argument and produces an evolution of that phase space in time. It's got a bunch of rules in the function regarding gravity.

Now imagine you've new function, which also takes a phase space as an argument, but instead of operating in 3 spacial dimensions, it has five. And that it doesn't have any rules regarding gravity.

Now imagine, you have a one to one mapping between states in those functions. So you can take a state in 3d space, translate it to 4d space -- run both functions for the same amount of time, and they both should produce states which you can still map to each other.

avmich2• 8 years ago

I think a good illustration could be provided by the Gauss law. https://en.wikipedia.org/wiki/Gauss%27s_law

It states that if you have a volume of space - say, a cube 1 meter side - containing some electric charges, and you calculate the total flux of the electric field across the boundary of that volume - that is, across the surface of that cube - then you'll find that total charge Q and total flux FF are proportional, FF = Q / epsilon_0 , where epsilon_0 is a fundamental constant. And that ratio doesn't in fact depend on shape or size of that volume of space.

That means Gauss law allows you to go along the boundary surface, calculate total electric flux and calculate the total charge inside the volume within that surface.

Similarly here, "holographically dual" means that you can derive important properties of matter inside some volume from properties which are observable on the boundary surface of that volume. What are those properties is another matter - but this duality principle says that there is a certain relation between them.

aaaaaaaaaab2• 8 years ago

That’s a bad analogy. You can’t deduce the charge distribution within a volume from the flux through its boundary. You can only deduce its magnitude.

irrep• 8 years ago

What does "holographically dual" mean?
What boundary are we talking about here?

"Boundary" refers to the boundary of Anti-de Sitter (AdS) space. The model that is typically studied is that of five-dimensional AdS space for which the boundary is four-dimensional. One can now formulate a quantum field theory on this boundary that is "dual" to the theory in the interior in the sense that there is precise dictionary between quantities living on the boundary and quantities in the interior ("the bulk"). "Holographically" refers to the difference in dimensions of the theory living on the boundary and the one living in the bulk.

psychometry• 8 years ago

Quanta is great, but there's definitely a limit to what can be portrayed to a popular audience and this is well past it.

kamac2• 8 years ago

I think anything can be portrayed to the popular audience. Other comments here explaining the terms used in the article suggest that this is possible. The only problem is that some fine information would most likely be lost with a simplified explanation.

labster• 8 years ago

On the contrary, this is the perfect article to explain to audiophiles why to buy my cable with quantum error correction. By increasing the qubit parity, we bring your sound system to a whole new level of clarity.

scottlocklin• 8 years ago

Its cod profundity which the author shouldn't have attempted to popularize. People haven't even demonstrated quantum error correction in a single qubit in an actual quantum computer, and suddenly it's the source of space and time. Chyeah, dude; whaddevah.

The model universes they're talking about, FWIIW, are all just models, with very little relationship to the world of matter we all live in.

ojosilva• 8 years ago

To my computer scientist mind this can easily be a parallel to checksum and hashing. Quantum error correction is analogous to using checksum to validate file integrity. Memory chips use similar schemes (ie parity bits) to correct errors. The same is being applied to quantum computing, ie. a sort of quantum hashing scheme based on (spacial) logic gates.

Now new research is being conducted where this quantum hashing scheme could be used to solve some of physics hardest problems. One of them could be Hawkins paradox, where "data" gets corrupted while being "processed" by a black hole. Maybe, scientists argue, error correcting data is stored at the black hole entrance so that it can be somehow applied as correcting code at the exit, ie when Hawkins radiation is released.

Or maybe the entire universe has gone through a hashing function and now there's error correcting code keeping information error-free using the "hash value". That's what the boundary stores that describes the bulk in certain theoretical universes.

Hashes have always fascinated me. The fact that a relatively short binary sequence can uniquely describe all of Shakespeare's works. What if we could completely reverse hashes, creating the most powerful compression ever? Well quantum physicists just might do that at cosmic scales!

stubish• 8 years ago

Hashes do not uniquely describe things. There are an infinite number of alternative texts that also match your hash that describes all of Shakespeare's works. A hash function is pretty much just a very lossy compression algorithm.

logfromblammo• 8 years ago

In our universe, construct an object that is perfectly spherical, and perfectly reflective. Now glue it to a table somewhere. Put another 3D object on the table. It has mass and volume, and felt real when you held it. Now look at the sphere. The 3D object is mapped onto the 2D surface of the sphere.

Now turn reality inside out. Because of various symmetries, it looks pretty much the same as it did before. Mathematically, it isn't all that important whether the signs of various things are positive or negative.

Instead of placing a 3D object on the table, draw a 2D shape on the surface of the sphere. Because you everted reality, this causes a 3D object to be reflected onto the table. The math can't really tell whether the object causes the reflection on the sphere, or the pattern on the sphere causes the object to exist.

Now turn the sphere inside out. Put the entire universe on the inside, and all of the stuff inside it (that you knew nothing about anyway, because it's perfectly reflective) on the outside. Now that your sphere encloses the entire universe, you can draw a 2D shapes on the outer boundary and reflect them as 3D shapes somewhere in the interior.

jfhufl• 8 years ago

The only reason I have any vague understanding of this article is all thanks to PBS Space Time on Youtube.

It's an amazing series. Must watch if you want to know how much we humans understand about our universe.

wallace_f4• 8 years ago

Or equally fairly, how much we dont understand.

One of the reasons I like that series is they seem intent to do some justice to competing theories and the fact that we still don't really have a working model of the universe, or know answers as to why theories work the way they do.

Anyways this article was a really hard read for me. It's like the relatively-readable paragraphs are laughing at me--written like I should be understanding them, but I don't, ie:

The best error-correcting codes can typically recover all of the encoded information from slightly more than half of your physical qubits, even if the rest are corrupted. This fact is what hinted to Almheiri, Dong and Harlow in 2014 that quantum error correction might be related to the way anti-de Sitter space-time arises from quantum entanglement.

earthicus• 8 years ago

I'd also like to recommend the semi-technical talks by Nima Arkani-Hamed and Leonard Susskind. They are the only reason I have the faintest hint of what is going on in theoretical physics and cosmology.

jgrowl• 8 years ago

I caught a physics bug several weeks ago and finding PBS Space Time was exhilarating. I would also highly recommend it.

joemag• 8 years ago

Space Time is fantastic. Upon watching the entire series (catching up to present time, to be more exact, since new episodes are still being released weekly), I went on a graph traversal spree of related YouTube videos. Another great series I loved was from Fermilabs, with Dr. Don Lincoln.

jcoffland• 8 years ago

But a fundamental problem stood in the way of actually building quantum computers: the innate frailty of their physical components.

It's entirely possible that there is some sort of physically limiting factor that makes it nearly impossible to entangle more than X qbits. Something akin to Amdahl's law for quantum computing. It wouldn't be a very sexy result.

perl4ever2• 8 years ago

I'm thinking of the infeasibility of building a rocket to get off a large planet (compared to earth).

The intuition of a layperson is a bad guide, but I've always had the gut feeling that quantum error correction would prove to be exponentially difficult to scale. If smart people think otherwise, I can hope they're right, but I wouldn't bet money on it until I find an explanation I can grasp. It just sounds like a free lunch, or cold fusion.

kerenua2• 8 years ago

I feel I don't have enough background information to understand this article.

...space-time in the interior of the [anti-de Sitter] universe is a projection that emerges from entangled quantum particles living on its outer boundary

A projection? How would this differ if the quantum particles on the outside were not entangled?

holographic “emergence” of space-time works like a quantum error-correcting code.

holographic in what way? and how is this similar to error correcting code?

quantum error correction explains how space-time achieves its “intrinsic robustness,”

what is an example of this robustness in space-time?

...error-correcting codes can recover the information from slightly more than half of your physical qubits, even if the rest are corrupted. This fact that hinted quantum error correction might be related to the way anti-de Sitter space-time arises from quantum entanglement.

how does the effectiveness of error correcting codes, being able to recover information despite 50% corruption, explain space-time?

if anyone could point me in the right direction, I'd really appreciate it. I find this interesting and important but am not smart enough to comprehend it.

tbabb3• 8 years ago

In quantum physics and cosmology, "holographic" (and "projection", in this context) are related to the holographic principle, which is kind of like a Stokes' theorem for information-- it says that specifying the state of the universe on the boundary of a manifold is sufficient to completely specify the state inside.

If someone's read the full paper, maybe they can explain the other things-- this article is a bit too vague.

kerenua2• 8 years ago

roywiggins said

you have a universe that is infinite from "inside", but "from the outside", there's an outer boundary.

and you say

specifying the state of the universe on the boundary of a manifold is sufficient to completely specify the state inside

this would be similar to me viewing a Mandelbrot set and being able to tell its infinitely deep?

jazzyjackson2• 8 years ago

" the universe on the boundary of a manifold is sufficient to completely specify the state inside " made it click for me if I understood you right. Makes me think of cellular automata: the state of the whole grid can be specified by the information contained in the first row + the laws of physics on the grid (game of life, etc) - is that kind of like the "boundary" we're talking about here?

joycian2• 8 years ago

Perhaps this lecture by Leonard Susskind can help you with the hologram universe concept:

https://youtu.be/2DIl3Hfh9tY

chrispeel2• 8 years ago

Here's a talk given by Patrick Hayden, one of the guys quoted in the article, about related topics. It was to an IEEE Information Theory chapter, so may use a bit more information theoretic terminology than you're used to. Even so, I think it is very accessible.

https://www.youtube.com/watch?reload=9&v=v5UbN0xx4X0

kieckerjan• 8 years ago

Cool talk, thanks!

vtomole2• 8 years ago

The study of Black Holes with the lens of Quantum information has been an exciting sub-field of Physics for the past couple of years. If you are curious about it, I recommend Patrick Hayden's "The Quantum Computational Universe" lectures [0][1]. The first one is an introduction to Quantum computation and the second one is more in line with what this Quantamagazine article is about.

[0] https://www.youtube.com/watch?v=AqWuyeh0SxQ

[1] https://www.youtube.com/watch?v=F6vGAiMz5kQ

yetihehe• 8 years ago

It reminds me of old quote "Time is what keeps everything from happening at once" [1] and similar "Space is what keeps everything from happening in the same place".

[1] https://skeptics.stackexchange.com/a/30402

Bombthecat• 8 years ago

Nice, feels like we are getting closer.

baron816• 8 years ago

I have a feeling I would get a brain aneurysm if I tried to read this.

joycian2• 8 years ago

Could someone explain to me why we should look into this, because we do not live in an anti-deSitter universe. So what is the relevance (beyond the obvious mathematical curiosity and elegance)?.

chrispeel2• 8 years ago

My understanding (from Patrick Hayden) is that in the center of AdS space, things look very much like normal space. Physicists are working in AdS space because they can actually do some analysis there, even though they would very much like to work in de Sitter space.

roywiggins9• 8 years ago

It's a toy model, but the hope is that the insights gained by playing with it will apply to ours: "On the physics side, it remains to be seen whether de Sitter universes like ours can be described holographically, in terms of qubits and codes. “The whole connection is known for a world that is manifestly not our world,” Aaronson said. In a paper last summer, Dong, who is now at the University of California, Santa Barbara, and his co-authors Eva Silverstein and Gonzalo Torroba took a step in the de Sitter direction, with an attempt at a primitive holographic description. Researchers are still studying that particular proposal, but Preskill thinks the language of quantum error correction will ultimately carry over to actual space-time."

Also, black holes at least superficially have a spatial boundary (the event horizon) so perhaps you can model what happens inside using the holographic principle.

planck01• 8 years ago

For the same reason as why biologist spend a lot of time studying E. Coli, fruit flies and mice (besides being interested in them in themselves). It's because those organisms are similar enough to humans, but still a lot simpler to study. In this way we get important clues and ideas of how stuff might work for human cells, which is still very hard to work out and prove, but is a lot easier than just starting in the dark with human cells.

jcranmer• 8 years ago

Because string theory gave us AdS/CFT correspondence, and maybe if we try harder than we tried for the past 20 years, something similar will pop out that works for our universe.

My personal belief is that it's very much a case of looking for the keys where the light is.

darkerside4• 8 years ago

That year — 2014 — three young quantum gravity researchers came to an astonishing realization. They were working in physicists’ theoretical playground of choice: a toy universe called “anti-de Sitter space” that works like a hologram.

Wow, so we truly are in a simulation

Edit: Sorry, I thought this was a funny play on ambiguous words, but apparently HN disagrees!

danbruc2• 8 years ago

No, not that we know.

perl4ever2• 8 years ago

You will often get downvoted for humor on HN. On the other hand, I have at times gotten double digits worth of karma for a humorous post. I guess you have to appeal to a certain type of person.

darkerside4• 8 years ago

Yeah, I've definitely noticed. Guess I can't help taking a gamble on occasion.

On this particular occasion, I truly couldn't tell if my joke was a whoosh, or just not funny! I made myself laugh, but that's not difficult.

mkaziz• 8 years ago

Ahmed Almheiri, Xi Dong and Daniel Harlow did calculations ...

It's pretty cool to see a Westerner, Middle Easterner and an East Asian dude (at least based on names ...) collaborate to push the frontiers of science like this!

ralusek• 8 years ago

This happens literally all the time. This is probably more common than uncommon.

vorg• 8 years ago

Westerner, Middle Easterner and an East Asian [...] based on names

This international variety of names is common outside the English-speaking world, e.g. the 3 biggest internet companies in China (Alibaba, Tencent, Baidu).

xchip• 8 years ago

I'm wondering how many physicists roll their eyes each time they see similar extraordinary headlines like this one

edit: I am a physicist.

joe_the_user• 8 years ago

Well, I think a lot of folks here find the description strange and opaque - I studied a bit differential geometry for my math degree and this seems way up there.

I'd love to hear why a physicist would roll their eyes at this.

dsnuh• 8 years ago

So, how do quantum error-correcting codes work? The trick to protecting information in jittery qubits is to store it not in individual qubits, but in patterns of entanglement among many.

So are quantum encoding patterns the Proof Of Work of multidimensional holgraphic blockchains?

Edit: accidentally pasted entire article

maggots• 8 years ago

Gee, sounds like a theory seeking facts. Isn't it supposed to work the other way around?

You know, math is really great and all, and you can transform a sphere into a torus, but meat doesn't transform into flies.

osrec• 8 years ago

How I understand it: The world around us is some sort of "projection" of stuff at the very edges of our universe, and that stuff is inherently fragile and unstable. Yet our world/reality/spacetime is not fragile and unstable - quite the opposite, despite being dependent on that fragile stuff in the first place.

Thus it must somehow be "correcting" for the intrinsic instability of the stuff on the outer edges that gives rise to our reality. Therefore it is in some sense an error correcting code.

Happy to be corrected by those with a deeper understanding!

neom• 8 years ago

The world science festival has a good video about this: https://www.youtube.com/watch?v=HnETCBOlzJs - The "correction" could very well be reconciliation, the output of what plays out in the program + the program is procedurally generated based on the outputs. Another good talk is this one by John Preskill from 2015: https://www.youtube.com/watch?v=SW2rlQVfnK0

jhuni• 8 years ago

This makes error-correcting the foundation of the universe, but I would prefer to have causality be fundamental, such as with the causal sets program. This is interesting though, especially for quantum computing.

ziont• 8 years ago

does this mean that out of all the possibilities space and time brings about order and chaos?

luc4sdreyer• 8 years ago

Awesome idea, but is there any way to test the hypothesis? Or will it be forever locked in the box of "extremely elegant but untestable" along with string theory?

dmurthy• 8 years ago

Curious what are the logic gates made of? What kind of engineering does it take to build the gates?

How Space and Time Could Be a Quantum Error-Correcting Code

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