jack

https://www.scottaaronson.com/blog/?p=4317

I feel like Scott's FAQ needs its own FAQ

Q. So, I heard on twitter there was some big news about quantum computing. Is that for bullshit?
A. Until now I've basically assumed all big announcements about quantum computing are bullshit and haven't been proved wrong yet.
Q. And this one?
A. Scott Aaronson thinks its for real and he's generally right about this sort of thing and not prone to quantum bullshit.
Q. So... wtf is "quantum supremacy"
A. This sounded like super bullshit to me, but according to wikipedia, it's a term for a quantum computer which can solve a problem no existing non-quantum computer can.
Q. So... that happened?
A. Scott Aaronson thinks so. The official publication hasn't happened yet.
Q. And this is... out of nowhere?
A. It sounds like no, actually, just that the number of qubits in quantum computers was slowly growing until through some engineering brilliance they reached the point of being able to do non-trivial calculations. But having a quantum computer which is actually better than a classical computer at SOMETHING is still pretty impressive.
Q. So... better at what?
A. Um... some contrived problem made up to specifically show that there's something quantum computers can do and classic computers can't.
Q. Oh. But, like, it really is, a problem you can try and solve on a classic computer and fail and try on a quantum computer and succeed?
A. Apparently so.
Q. Apparently?
A. That's basically the situation. No-one can PROVE you can't do it on a classical computer: no-one's even proved large travelling salesman problems or other NP-complete/NP-hard problems are impossible for classical computers yet. But no-one expects otherwise.
Q. Any other big caveats?
A. Apparently this particular problem is probabilistic, you sample the result N times and show it's more-likely-than-chance in the right answer.
Q. And how do you know what the right answer is? Is this a hard-to-find-each-to-check thing?
A. That's what everyone hopes to reach in future, but sadly no, apparently this is a "solve it in seconds on a quantum computer, then simulate the quantum algorithm in months of giant compute clusters on classical processors, check the results match"
Q. But then you CAN do it on a non-quantum computer. Wasn't the point to find a problem you can't?
A. Yeah. But (a) with this method, if they build a quantum computer even slightly bigger, it would be unmatchable, but then they wouldn't have any way of checking the answer and (b) if the method works and it is seconds vs months, everyone agrees that is quantum computers doing something useful.
Q. So, does this break crypto?
A. Not for a while yet. They'll need a fair bit bigger quantum computers to make that practical.
Q. But those are coming?
A. I don't know, but it sounds like it.
Q. And that breaks all crypto?
A. Of course not.
Q. It breaks all crypto we use in real life at the moment?
A. No.
Q. But?
A. It would break MOST crypto we use at the moment. Anything that lets you set up secure crypto without secretly sharing a key in advance.
Q. Wait, not just RSA, other systems too?
A. Apparently the same factoring works there too?
Q. But someone will come up with some crypto which quantum computers don't help against?
A. As I understand it, we expect that from a theoretical point of view, but people haven't actually got round to it yet.
Q. Do the NSA have a bigger quantum computer?
A. I really don't know. I think installing spyware everywhere is probably easier. But they're filled with ethics-flexible maths nerds who'd probably WANT to build a big quantum computer.
Q. So what are the next steps after this?
A. Quantum computer with more bits. Solving a less contrived problem or finding a problem to solve that can actually be checked. Working out how many extra quantum bits you need to account for errors from losing the coherence of your qubits (10% more? 1000000% more? somewhere between?). Eventually, getting a computer that can run Shur's factoring algorithm, and breaking existing cryptosystems in practice. Find a problem that's actually useful -- not sure what that is, but modelling some physical processes?

Last post, I decided that what's "really there" for fundamental particles is typically a quantum thing, specifically, a probability wave of possible values a particle can have which appears to collapse into one particular place only when its interacted with.

However, this "collapse" sounds very suspicious. If two different particles emitted from the same particle decay (or something?) are known to have opposite spins, but not what those are, do you get all the usual wavelike behaviour, can each self-interfere, etc? Yes, of course. And yet, when you finally measure them, lo, the spins are still conveniently opposite.

Something that looks like collapsing to a single answer seems to happen, because when we measure them, we always do get a single answer. But that's not an event. If you measure one, does a spooky force reach out across the room to force the other to collapse at the same time? Does it collapse the value you measure, but still allow other properties of the particle to continue being multiple? That looks awfully like what happens, but it should seem wrong to start with, even before you ask "if you measure one particle, does the other know to wait until you interact with it, but store the answer you're going to find until then" and "if you measure them both a long way apart, does the collapse rush faster than the speed of light (aka backwards in time) to make sure both answers agree with each other?"

Any theory involving particles "knowing" or "waiting" or "choosing" depending on how you measure them sounds very unlike physics.

And yet, the particles go on behaving like probability waves until you measure them, and if they came from a shared source, then when you measure them, they DO agree. Just as if this spooky shit was happening. What might be going on?

Hypothesis 1

Whenever one particle collapses, a spooky force travels faster than the speed of light to the other particle, and then hangs around telling it what value it will have when it's finally measured.

This *works*, but hopefully you can see why it doesn't seem correct.

Hypothesis 2

Just like hypothesis 1, but we try to avoid thinking about it. This is not really satisfying, but it works and is a pragmatic default for many physicists. (Sort of Copenhagen interpretation?)

Hypothesis 3

Even while a particle is still smeared out across a probability of many potential positions/values, it has a hidden property which tells it how it's *going* to collapse when something interacts with it. Like, not necessarily "hidden", but basically some sort of determinism.

This is roughly Hidden variables interpretation (right?)

This would be fairly satisfactory except that it turns out it's impossible.

This is not very mysterious or controversial, but involves more simple probability than I can manage to wade through. Look up the EPR paradox or the Bell inequality. The idea is, you choose something like polarisation angle that could be measured at many different angles. You randomly choose to measure at different angles for two particles known to have opposite polarisation. There are various correlations between the probabilities when you measure the two particles at an angle to each other (the detectors neither parallel nor orthogonal). You can prove that no possible hidden value would make all those correlations true at once, but QM does and that's what's actually observed.

I can't really prove this to myself, let alone anyone else, but AFAIK no reputable physicists doubt that it's correct, only maybe what it means, so I'm willing to accept it as true.

There are still edge cases, like, people argue whether the experiments have ABSOLUTELY DEFINITELY proved this spooky collapse effect would have to go faster than the speed of light, rather than going at a possible speed (but depending what exact moment sets it off, etc). But I don't find any of that very persuasive. A spooky collapse effect which is triggered by measuring a particle and goes at the speed of light or below, while not ABSOLUTELY DEFINITELY ruled out, doesn't sound at all likely. I don't think anyone seriously expects that if they make the distance apart in those measurements a bit bigger, they'll suddenly get difference results: that's not how you expect physics to happen.

Hypothesis 4

Those weird quantum probability waves don't only exist for tiny particles, they happen just the same for everything including macroscopic objects, humans, etc, but you can't observe the effects except for tiny things (because to see interference you need something isolated from other particles, and you need to be able to detect its wavelength, which is way too small for anything bigger than a molecule).

I'm still working on understanding *why*, if that's true, it produces the effects we see. But most physicists, even ones who don't like this line of reasoning, seem to agree that it *would*.

This makes everything above non-mysterious. How does the collapse effect move around? It doesn't. Every "collapse" is just another probability thing of a scientist (and all the other macroscopic stuff) interacting with a particle and becoming two never-interacting possible scientists, one observing A, one observing B. We know both happen. We know, when we measure things light-hours apart and then compare notes, that we will be comparing notes with the version of the other scientist who observed the opposite polarisation to what we saw, while our shadow twin will be comparing notes with the other scientist's shadow twin.

The multiple non-interacting versions of the macroscopic world are called "many worlds" or "parallel universes" which admittedly makes them sound very implausible.

It seems like, this leaves some things to ponder, but resolves a very large part of the things people find mysterious. And yet, many physicists really don't like it. I need to read the bits of Scott Aaron's book about different interpretations[1], because I trust him to know more about this than me and he doesn't seem convinced.

Footnote [1]

The hypotheses above are called interpretations. I don't know if my ones exactly map onto the real ones. The name is because they all predict the same results, and yet seem quite different.

You can argue, "they're the same", but I don't quite agree. See for instance space outside our light cone -- we have no way of observing it, so the hypotheses "it's got physics just like ours but with different stuff there" and "it's all purple unicorns" are both possible, and yet, the first one seems a lot more like actual reality.

In both cases, it sort of doesn't matter, but you can imagine (a) which answer is most plausible, most useful, easiest to work with, or least ridiculous (b) if we're wrong and there IS some difference, which one would actually be found to be the one that exists.

Hypothesis 1: Electrons are tiny objects that have a specific position

Evidence: If you bounce something off an electron it hits the electron in one place. For all the talk of "in multiple places at once", you never shoot something at an electron, it bounces off the electron, and it bounces off the electron *somewhere else*.

Evidence: There's always a particular number of electrons. You never have two and a half electrons.

Hypothesis 2: Electrons are waves

Evidence: If you have an electron "orbiting" an atom, it's not at a particular place, it's smeared out over a whole sphere (or sphere-ish shape?) round the electron aka "an electron shell". Indeed, if you have two electrons in an electron shell, I don't know if you can even tell them apart, just that there's two. In metal, ALL the electrons are ALL OVER. They really don't have a particular position.

Evidence: If you fire one at a corner of an object, they diffract round it (is that right??)

Evidence: If you fire one through one or two narrow slits, you get interference bands, where "electron from here" and "electron from *here*" combine to give a dark band of "no electrons detected". This happens to waves. It does not happen to objects.

Hypothesis 3

This takes longer to explain. Imagine you have an object, but its position isn't certain, you're doing a calculation like, "if there's an x% chance it's here, and a y% chance it's there, and it bounces off this, then it might be anywhere along this line with a chance proportional to the distance..." etc. We do that all the time instinctively. But we mostly expect that the object actually *is* in one particular place, we just don't know what it is.

Suppose that instead of a mathematical convenience, what an electron *actually is* is a probability distribution like that, except for:

(a) When something interacts with it, it interacts with one point in the distribution chosen with the relative likelihood of that point, and from then on only that matters. Except if the other particle is of uncertain distribution too, then you get a probability distribution over both of them, until you actually check at least one of them.

(b) The probability distribution changes obeying equations which mostly describe a particle moving in a straight line (or a curve according to a force acting on it), except that it's all continuous, and if you have a sharp corner, the probability spreads out round it (as if the particle's path was bending).

(c) The probability not only has a magnitude, it has a direction (usually represented as a complex number, where the actual probability is the magnitude). If two probabilities have opposite signs, they cancel out. And it changes as it moves, analogous to wave oscillating, eg. light consisting of electric field waxing while a magnetic field wanes, etc.

The third point (c) is par for the course for waves: waves almost always involve something oscillating in both directions away from a rest point. But it's very spooky to see with things that look like particles: if there's a 5% chance of an electron hitting this particular point on a screen having gone through slit A, and a 5% chance of an electron hitting this particular point having gone through slit B, what's the chance of it hitting that point at all? Well, it might be 10% or it might be 0% or it might be somewhere between, depending

Evidence: Everything above in both previous hypotheses

Evidence: Everything behaves like a particle even if you didn't expect it (eg. light has photons)

Evidence: Everything behaves like a wave even if you didn't expect it (eg. you can fire small molecules through slits and see them do wave-like things like interference).

Evidence: The cancelling-out thing. You can construct this out of specific particles with clearly defined values (qubits) in building a quantum computer, and this is exactly how you find probabilities behaving. (Right?)

Correct me?

Is (b) really true? That's what it looks like from what I've read. But is that basically accurate?

If not, where have I gone wrong?

If so, it seems such an obvious "this is how we know these probability thingies actually exist" why isn't it front and centre in more explanations?

Is the description of probabilities right?

Conclusions

Hopefully I will think myself through some more examples. But this is the major point to get your head around first with quantum mechanics.

I think everyone would say the first two hypotheses are more natural. But they don't fit the evidence. The third hypothesis fits ALL the evidence, even though the hypothesis itself looks screwy.

And as far as I can tell, physicists still argue about which parts of this are actually there, and which are mathematical descriptions of something else, but agree that if you take Hypothesis 3 and just assume everything works like that, then you get all the right answers.

This is a bit earlier in the sequence than I'd intended but I wanted to rant about it.

What is so-called quantum teleportation?

Imagine you have a small particle. If this were a classical world, you could measure everything about it (it's speed, it's spin, etc), and then use a bunch of fiddly experiments to recreate one (or more) new copies of it that had all those same properties. Of course, it's *practically* impossible, to scan the state of millions of particles so this actually only happens to single particles (or we mass-manufacture consumer goods, but we don't try and make sure they all have corresponding atoms in the same place in each).

As we live in a quantum world, you can't "measure everything about it". Electrons don't exist at a particular point, they exist as a wave of possibility in a sphere round an atom, and only when another particle interacts with them, does it interact with them at one particular place on that sphere. Each photon isn't "in a particular place", even if you have a single photon you have a very very very faint beam of light and if you repeat the experiment, you find "places a photon hits" and "places the beam of light would cover" are the same thing. If you have a qubit made up of a single atom, you can measure its value as 0 or 1, or send it through a quantum logic gate, and find out about the parts of its state you can't measure directly *instead* but you can't do both.

Hence, in a quantum world, even in theory, it's weirder to construct a new particle the same as an existing particle, because you can't "measure everything, and then move the new particle so it has all those values".

So you *can't* make multiple copies.

What can you do

However, it turns out, there *is* a way of making an exact copy of a particle's property. You create two other objects (photons?) with opposite values for polarisation or something, even though you can't measure what that value is. (aka "an entangled pair", although all "entangled" means is "they have the opposite polarisation even if you don't know what it is"). You interact the original with that one and measure some values. Those values don't tell you what the property is (because if it WAS one particular thing, you'd have destroyed the information you were trying to copy). But you can apply them to a new particle via the second entangled particle. And you don't know what the state *is*, the original particle no longer has it, but the new one does.

That is, "You might imagine that you could copy a quantum electron the same way you could copy a classical particle by measuring the values and applying them to a new electron. But you can't, that's actually a meaningless concept. Knowing that, you might give up. But there's a way to do sort-of do that."

Specifically, "quantum teleportation" means "there's a special and fiddly way you can construct a new particle exactly the same as an old particle, but only EXACTLY ONE, and it destroys the original state". As in, you can do SOME of what you'd expect to be able to do to a classical particle, but not all of it.

What doesn't it mean?

What doesn't it mean? Firstly, it means "teleportation of quantum", not "teleportation by means of quantum". It doesn't give you some magic way of scanning macroscopic objects or reconstructing them elsewhere. It just means that, if you happened to already have one, you might be able to copy quantum states too.

Secondly, nothing anyone cares about day-to-day is encoded in quantum states. It might matter for quantum computers. Maybe for quantum cryptography. Certain scientific experiments. That sort of thing.

If you actually cared about quantum states, this might be exciting. Suppose brains encoded what they did in something like a quantum computer. Then startrek teleportation would only be normally impossible because you can't scan a human like that, not logically impossible. However, brains don't do anything of the sort[1].

If you care about startrek-teleporting a human, you probably want to end up with the same DNA molecule. But you probably don't need each atom to have the same quantum state. So it doesn't really matter.

Takeaways

A: Startrek is awesome, right?
B: Yeah.
A: But teleporting people is impossible right?
B: Pretty much. I suppose there might be some way discovered, but it doesn't seem very practical.
A: But, doesn't quantum say something about this?
B: Oh right. Yes, it says if you care about replicating all the quantum states in the transportee, you can only have one source (which is destroyed) and one copy.
A: That seems fair. That's how it works in startrek.
B: Well, it rules out "lets keep a backup of our most valuable engineers and seconds in command". Which did happen in startrek but only by accident.
A: Oh yeah, I guess.
A: So, *do* I care about replicating the quantum states in the transportee?
B: No, not really.
A: So quantum doesn't really change the answer?
B: No.
A: What about "quantum teleportation". Doesn't that let you... teleport people?
B: No. It just means, you CAN do the up-to-one perfect-quantum-states copy (assuming you have a way of teleporting people at all).
A: So why do people keep writing news articles about it?
B: Because it sounds startrek-y.
B: And to be fair, is relevant for how QM works.

Footnote 1

How do I know that? Well, I might be wrong. But firstly, maintaining atoms in a particular quantum state which can encoded a qubit used for quantum computing needs a whole bunch of vacuums and stuff. MAYBE brains could do that, but it seems unlikely. Sorry Penrose, I know you're a genius and I'm not, but I don't believe you.

Secondly, quantum computers have certain distinguishing features. They're about the same as classical computers for most problems. Notably, most every-day stuff. Also, NP-complete problems they're not significantly better. However, they ARE better than normal calculations for some specific things, like factoring numbers with thousands of digits, and other maths problems which share some features in common with that. If you look at a human brain, do you think, "boy, that's optimised for simple but powerful heuristics used for catching balls, recognising objects, and social interaction, but is mediocre at factorising incredibly large numbers"? Or the reverse?

Thirdly, there's no reason to think brains DO have quantum information used in any particular way. If they did... it wouldn't change anything significant. It wouldn't make the free will argument any different. It wouldn't give them a magical insight into parallel universes (as awesome as Anathem makes it sound). So why would you think that?