
How Space and Time Could Be a Quantum Error-Correcting Code - _Microft
https://www.quantamagazine.org/how-space-and-time-could-be-a-quantum-error-correcting-code-20190103/
======
kamac
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"?

~~~
roywiggins
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
> 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?

~~~
antidesitter
> How do you tell from the "infinite inside" whether it packs away nicely into
> a bounded area?

Roughly speaking, you measure how fast the volume of a ball grows with its
radius [1]. If it grows faster than you’d expect in Euclidean space, you know
you’re in a hyperbolic space.

You can also draw a big triangle and see whether the interior angles add up to
less than 180 degrees [2].

[1]
[https://en.wikipedia.org/wiki/Scalar_curvature#Direct_geomet...](https://en.wikipedia.org/wiki/Scalar_curvature#Direct_geometric_interpretation)

[2]
[https://en.wikipedia.org/wiki/Hyperbolic_triangle#Properties](https://en.wikipedia.org/wiki/Hyperbolic_triangle#Properties)

~~~
roywiggins
And we've done exactly that using our cosmological models of the Big Bang:

[https://map.gsfc.nasa.gov/mission/sgoals_parameters_geom.htm...](https://map.gsfc.nasa.gov/mission/sgoals_parameters_geom.html)

One side of the triangle is the width of Cosmic Microwave Background
variations (calculated from models of the early universe); the other two sides
are known from how far away the CMB appears to be, which is known from
independent measures of the expansion of the universe. Some trigonometry will
tell you what the interior angle that should make with the Earth, which you'll
see as the angular width of the variations in the sky. You can compare those
two numbers (the one by trigonometry and the one observed), and determine
whether they are different enough to exclude a flat universe.

In other words, if someone holds an 1 foot ruler at a distance, you can use
trigonometry to work out how far away it is by using the apparent size. But if
you know how far away it is, and the apparent size disagrees with the
trigonometry, then the shape of the universe must not be flat. The longer the
ruler and the further away it is, the greater the deviation will appear (if
there is one). The CMB is very far away indeed so it makes for a good ruler.

~~~
hammock
> And we've done exactly that using our cosmological models of the Big Bang

What's the result- flat or not?

~~~
roywiggins
Flat, as far as WMAP can tell!

[https://wmap.gsfc.nasa.gov/universe/uni_shape.html](https://wmap.gsfc.nasa.gov/universe/uni_shape.html)

Of course the curvature could maybe be arbitrarily small, but... it's
definitely very close to flat.

~~~
jazzyjackson
Hold up, so the flat-earthers just need to think a little bigger?

(Legit tho I've been trying to understand the 'shape' of the universe for a
while now -- in the sense of, when I look at stars and galaxies in the sky
above me, what direction am I looking as it relates to where things are in the
universe relative to each other? As a kid I took Bill Nyes word for it:
everything is on the surface of a balloon, expanding from the center. But do I
ever see the far side of the balloon? Or is everywhere I look somehow
constrained to the surface in every direction away from me, such that the
'other side of the balloon' is infinitely far away... but if I could see far
enough, my own spot on the surface of this sphere would be visible to me,
minus a few billion years... I want to understand this but I am very confused!
This looks like an informative website so I'll keep reading ... thank you)

~~~
roywiggins
The balloon-surface model works if the universe is actually positively curved.
It bends around in on itself and comes back. So you would be able to see
yourself (eventually) after light made its way around the surface and back to
you.

As far as anyone can tell, though, the universe is flat. So photons traveling
outwards from you will never come back around- they'll just keep going.

I'm partial to the raisin bread model of the universe:

[https://www.loc.gov/rr/scitech/mysteries/universe.html](https://www.loc.gov/rr/scitech/mysteries/universe.html)

It's a tad misleading: the raisin bread is, probably, infinite in extent. As a
practical matter, we can only see a finite portion of the raisin bread. As we
gaze more deeply into the sky, we're looking further into the raisin bread.
Because light only travels at a finite speed, the further something is away,
the older the image we see of it is. At a certain point, all we can see is the
goopy bread batter that the raisin bread used to be: that's (sort of, kinda)
the Cosmic Microwave Background: it's the oldest light in the universe, and we
can't see anything older than it.

So the universe looks like a bunch of galaxies, with us at the center, and a
sphere of microwave radiation at the edge. But every single observer sees a
similar sphere around their exact location, so it's a kind of illusion.

~~~
eridius
Does the expansion of the universe mean that galaxies that are too far away
from us are seemingly moving faster than the speed of light, and this is why
we can't see any galaxies past a given point (because that's where they
"accelerate" faster than light)?

~~~
roywiggins
A lot of the visible universe actually appears to be receding faster than the
speed of light:

[https://phys.org/news/2015-10-galaxies-
faster.html](https://phys.org/news/2015-10-galaxies-faster.html)

It's because the space inbetween is getting bigger. But light keeps moving
towards us from those galaxies, so we see those photons eventually anyway. You
can still hear things that are going above the speed of sound, as long as
they're headed away from you- if they're headed toward you, you'll not hear
them (probably?). But the waves they throw off will expand behind them just
fine.

~~~
acqq
> if they're headed toward you, you'll not hear them (probably?)

Actually, you would not have much time to hear, but what you would hear (among
the other effects) would be the sound “in reverse”(!)

[https://physics.stackexchange.com/questions/14880/hearing-a-...](https://physics.stackexchange.com/questions/14880/hearing-
a-sound-backwards-because-of-doppler-effect)

~~~
rcxdude
For a practical (if dangerous!) example, see supersonic rounds: if one is shot
towards you, you hear the bullet whizzing by before you hear the gunshot.

~~~
LgWoodenBadger
Well, a supersonic round wouldn't whizz until it drops down to subsonic
speeds.

You'd hear the crack of the round then the crack from the original shot.

------
kerenua
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.

~~~
tbabb
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.

~~~
jazzyjackson
" 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?

~~~
tbabb
Yes, that's a good analogy.

------
jfhufl
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_f
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.

------
osrec
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
The world science festival has a good video about this:
[https://www.youtube.com/watch?v=HnETCBOlzJs](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](https://www.youtube.com/watch?v=SW2rlQVfnK0)

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

~~~
darkerside
I wonder if there are languages where there is no real dichotomy between these
two terms

~~~
wlib
"Invent" comes from Latin and simply means "find". If you think about it, no
matter what language, there is no fine line. An invention is just a discovery,
but we typically use the word to describe a very _specific_ discovery.

~~~
darkerside
The English language often has multiple synonyms with a difference in
connotation. Discover and invent may be synonyms (although many would
disagree), but everybody would agree at least the connotation is different.

My hypothesis above was that there may be languages where that connotation
does not exist.

------
vtomole
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](https://www.youtube.com/watch?v=AqWuyeh0SxQ)

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

------
yetihehe
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](https://skeptics.stackexchange.com/a/30402)

------
joycian
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)?.

~~~
roywiggins
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.

------
luc4sdreyer
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?

------
xchip
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
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
>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

------
jcoffland
> 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.

~~~
perl4ever
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.

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

------
jhuni
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.

------
maggots
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.

------
baron816
I have a feeling I would get a brain aneurysm if I tried to read this.

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

------
airstrike
> 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.

------
Bombthecat
Nice, feels like we are getting closer.

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

------
darkerside
> 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!

~~~
perl4ever
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.

~~~
darkerside
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.

------
dclowd9901
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?

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

