Quantum computing, Bose-Einstein condensates, and other cool stuff I just learned…
My friend and muse, Naomi, sent me this article:
Is the black hole at our galaxy’s centre a quantum computer?
https://aeon.co/essays/is-the-black-hole-at-our-galaxy-s-centre-a-quantum-computer
Well, that’s the clickbait title, that actual title of the article was: “Black-hole computing – Might nature’s bottomless pits actually be ultra-efficient quantum computers? That could explain why data never dies.” Which is much closer to what it actually was about. The point is that there’s a new theory that could resolve the black hole information loss paradox that is one of the annoyingly persistent ways in which the two most successful theories in the history of science stubbornly refuse to get along with each other.
General Relativity says nothing escapes a black hole, even information. Further, it seems that black holes radiate away into nothing via Hawking radiation, and the math says that the only information left in that radiation concerns only the total mass, electric charge and angular momentum of the thing. All other information would be lost.
Quantum mechanics says information is never lost… Ever…
So what gives?
Trouble is, we can’t actually study event horizons very well, let alone the interior of black holes. In fact, we could barely study them at all until just recently, when for the first time we measured gravitational waves from two black holes crashing into each other and we were able to get telescopes pointed at them at the same time. We’ll definitely learn some fun new things from crunching that data, but what we can learn is still pretty limited.
The clickbait title comes from the idea that a black hole is described these days as the most efficient possible way to store information, and would therefore make an awesome quantum computer, if you could feed it input and get output. Trouble is, experiments testing theories about black holes are, unlike those demonstrating the relentlessly accurate predictions of quantum mechanics, are pretty much impossible to conduct. Even if you could make a black hole, the Hawking radiation you get out has very little to do with the information you put in. Like if you were to burn my body to ash and put me in a mass-spectrometer, you could learn some pretty interesting things, like how much corn was in my diet (corn, and only corn out of all that we eat, fixes carbon 12 and 14 isotopes at a different rate than everything else, so the ratio in the ash tells you how much corn you ate,) but you wouldn’t know what color my eyes were, let alone my favorite Beatles song. A computer program that takes in all the written documents in existence and can only output how many there were of each letter, in which alphabets, wouldn’t really be very useful.
Scientists had figured out some things that would have to be true to get information back out of black holes and solve the information paradox, like the rate it would have to be radiated at to make sure it all got out in time, etc. Trouble is, there’s no way to actually probe the structure of black holes in the lab, so it’s a dead end.
Or so everyone thought.
In this article, the author shows that Bose-Einstein Condensates (BECs) store and release information the way quantum mechanics say they should, but that they do it in a way that looks an awful lot like how black holes would have to do it, if they do it at all. This yields the startling conclusion that you could use BECs as a surrogate to study black holes. This is a wildly exciting prospect, because it gives a huge leg up to the ultimate holy grail of physics, a testable Grand Unification Theory (GUT) of everything that could finally combing Relativity and quantum mechanics. String Theory is a GUT, but it makes no testable predictions, so until it can, it’s just a cool thought, not a proper theory.
It was a fascinating article. I had to research a lot of things they had learned since last I checked to even process it. For example, apparently, they can manipulating individual states in a Bose-Einstein Condensate now. This took me by surprise, and meant I didn’t really understand what they were. I’ll share with you some of the things I learned trying to wrap my head around that bit.
The Standard Model (SM) of physics describes all the particles that exist, and predicted the Higgs Boson. When two separate collider teams found that a few years ago, people were pretty jazzed. Spin is one of the inherent properties of particles. It’s not actually just that particles are spinning, they’d have to be spinning a million times the speed of light, but whatever it is makes them act like tiny gyroscopes when you push on them, so it’s a pretty good description. It has a sign (+ or -, up or down) and a value (1/2 or 1, really n/2 which can end in .0 or .5, making it really integer or what they call half-integer — or 0 for the Higgs, and only the Higgs – is that why gravity is different than everything else, since the Higgs field provides mass? Why am I so tickled by the idea that the Higgs was found much later than everything else, just like the number zero was?) A fermion is a particle with half-integer spin. Fermions are all the things we already though of as particles, like protons and electrons. Bosons have integer spin, and are “force-carrying particles” which mediate quantum force fields like electromagnetism, that’s the photon – ordinary light, and the strong nuclear force that holds protons and neutrons together in a nucleus.
The Pauli Exclusion Principle says that any number of bosons can hang out together in the same quantum state (position, velocity, and spin up/down,) but fermions can’t. So you can arbitrarily put as many photons in the same place and at the same time as you want and they’ll all just chillax together according to Bose-Einstein statistics. But you can’t do that with electrons. Pauli developed it to explain the experimentally derived groupings on the periodic table.
All this was consistent with what I knew, but then along comes a new factoid about Helium. He4 is the classic, alpha particle-with-electrons form that you almost always see. 2 protons and 2 neutrons. It turns out, that He4 acts like a Boson, presumably because two halfs make a whole. That is, when you have the same number of gyroscopes spinning left and right, it’s like you don’t have any gyroscopes at all. Why doesn’t this make atoms on the periodic table alternate between one kind of thing and another as they whole nucleus shifts from being a Boson to a Fermion? Why don’t isotopes alternate the same way? Maybe they do, but we can’t tell because almost every time we interact with the world in any way, it’s with electromagnetism: Sight, sound, touch, taste, virtually all of chemistry. So whatever might be alternating we just don’t notice…
The thing about this two fermions make a boson thing that’s interesting is, in a two-dollar term, Bose-Einstein Condensates. So you take atoms like Helium 4 that act like bosons, and you cool them waaaaaay down to around the temperature of the colder parts of interstellar space, and suddenly they start acting one, giant particle, with a single, shared quantum state, the way a laser beam does. This is cool because we get ridiculously useful behavior out of them now, like super-conductivity, super-fluidity, mag-lev trains. Essentially it’s “frictionless” motion, no energy loss. 10%-20% of electric grid power is lost to heat from resistance just in the wires themselves, let alone all the transformers, etc. Superconductors completely exclude magnetic fields, so even a big, heavy train won’t bottom out if you arrange superconducting magnets correctly.
I knew some of that, but then quantum computing comes along and they start doing things I didn’t know were possible. They can make a pretty large BEC with a grid of lasers, then prod specific locations in the grid and change the state of just that bit. That hadn’t occurred to me, I thought they would all just either hang out at the lowest energy state, or it would stop being a BEC. It turns out you can excite them just a little, without destroying quantum entanglement. This is huge because that’s exactly how quantum computers work. You prepare a specific, entangled quantum state as an input, feed it into circuitry that does classical, logic-gate type stuff to it (flip spin up to spin down someplace, or w/e,) and you get out a new quantum state that’s your answer – almost instantly, and with a known probability of being correct.
The thing this paper shows that draws comparison between black holes and BECs, and is most exciting for quantum computing, is that really interesting things happen at the quantum critical point, which is the phase transition temperature at which ordinary matter becomes a BEC. Like the freezing point of water.
Theorists know how to calculate how much information the black hole must be able to store: the amount is quantified in the black hole’s entropy and proportional to the horizon surface area. They have also found that black holes can redistribute or ‘scramble’ information very quickly. And finally, they know the pace at which information must escape from the black hole in order to avoid conflicts with quantum mechanics.
Starting in 2012, Dvali explored these various attributes and discovered, to his surprise, that certain types of Bose-Einstein condensates share their essential properties with black holes. To act like a black hole, the condensate must linger at a transition point – its so-called quantum critical point – where extended fluctuations span through the fluid just before the quantum behaviour collapses. Such a quantum-critical condensate, Dvali calculated, has the same entropy, scrambling capacity and release time as a black hole… ‘Somebody can say this is a coincidence, but I consider it extremely strong evidence – mathematical evidence that is – that black holes genuinely are Bose-Einstein condensates,’ he says.
ibid.
This means two things, one, that you can study quantum-critical BECs and maybe learn about black holes, and two, that, since black holes are the most efficient, most dense information storage and processing devices we can imagine, and they act like quantum-critical BECs, that’s probably where we should look for some interesting advances in quantum computing.
Man, I had to look up a lot of things to make sense of this article, but it was worth it. I love this stuff 🙂 I hope that, if anyone gets this far, it means you found something interesting in here, too.