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This week on Radio New Zealand National I talked about the strange world of quantum computing and its more surprising implications. Read on for my notes…

Q: Quantum computing?

A: Strange-sounding, isn’t it? Quantum physics is easily the strangest branch of science. Its all about small things like electrons and photons. It seems that when we start doing experiments on individual electrons and photons they just don’t behave like larger objects do.

Q: How so?

A: It is deeply strange. Everything is what is called quantized. You find that the properties these objects are restricted to a few choices for no very good reasons. For instance, electrons in atoms can have only a few specific energy levels – the levels depend on the type of the atom – rather than any number you can think of, as you would expect in the world we are used to. And there’s the famous uncertainty principle that says that we can’t actually know everything about a particle – its almost as though the act of looking at it changes it, which is pretty much the case. And there’s the Pauli exclusion principle which says that no two electrons in an atom can be in the same state. Nobody knows why but it appears to be true. And then there’s problem that started the whole of quantum off – particles seem to be in one place at once, as you’d expect, but they also act as though they are waves that everywhere at once. Richard Feynman, one of the greatest physicists ever to have lived, said that no-one understands quantum physics.

Q: If no-one understands it how is it useful?

A: It is because we can exploit what we do know. Perhaps the most useful effect is so-called tunneling. Tunneling says that an electron or some other object of that size might cross a barrier that you’d think would stop it. Let’s think of an analogy. If you have a cat locked in a room, and there’s no way for it to get out, you can be certain that it will be there when you come back. Put an electron in a box, and it might or might not be there you come back – and we know the probability. If you put a hundred electrons in that box, we know how many will be there when you come back. Try that with cats and all hundred would still be there, although there might be a fair bit of fur lying around!

Q: The electron does behave strangely…

A: Quite. The rules for really small things are not the same as they are for large objects like cats, people or buildings.

Q: How small do things have to be to behave like this?

A: Each of us might have 10^26 electrons in our bodies – that’s a one followed by 26 zeros. That’s how small we are talking. We are composed of these tiny things that observe such strange rules, but the strangeness happens only on the tiny scale and we can’t see it. By quantum rules, it’s perfectly possible that this microphone might just suddenly leap a metre to the left – each of its constituent particles could do exactly that at the same time – but the probability is ludicrously low because there are so many particles which would all have to do it at once. So you the strange quantum picture of what happens to very small things quite consistent with the classical view of objects moving under Newton’s laws that we are used to.

Q: Classical?

A: A scientist’s way of sneering at a theory which we know to be only part of the truth.

Q: You just used the word “theory”. Is all this just a theory?

A: Yes and no – a scientist uses the term theory to mean a set of rules which explain what you can observe in the world around you. Quantum is a theory, relativity is a theory, Newton’s Laws are a theory – it just means a system of explaining things that actually works. Any kind of theory that has been around for more than a few years is likely to be pretty solid, because its easy to disprove theories that don’t work and impossible to prove theories that do work. Successful theories tend to build on and extend theories that have gone before, like Einstein built relativity onto Newton’s Laws. Quantum theory is built on Newton, too, and there are great labours going to merge it with relativity.

Q: OK, so small things behave oddly. What has that got to do with computers?

A: Computers work by manipulating electrons. That’s the crux of the matter. And as computers get more and more powerful, they do this getting their parts smaller and smaller, which means that they are dealing with relatively few electrons in any given part.

Q: This is all inside the silicon chips, right?

A: Yes, exactly. If you take cover off a modern PC you’ll see somewhere in the middle what looks like a group of metal cooling fins with a fan attached. Underneath that is the chip which drives your computer. They get hot, which is why all the ironmongery is attached. Older, slower machines often have the processor chip plainly visible. Now inside that chip are hundreds of millions of components. The size of these components gets smaller every year as manufacturers try to squeeze more onto the chip. Currently the scale of these components is about 0.1 micron, and a micron is a millionth of a metre.

At that size you are manipulating small numbers of electrons and quantum rules very definitely apply.

Q: How do you design things to work with such strange rules?

A: It’s pretty specialized stuff as you can imagine. There is some serious mathematical heavy lifting involved. One of the leading people in this area is a New Zealander called Professor Michael Kelly. He works at Cambridge University in England – he taught me some of this stuff when I was an undergraduate. I think he comes back to Wellington from time to time.

All modern computers use quantum effects in their chips because they have to – there’s no ignoring them at that scale. But there are some really “out there” possibilities that quantum offers if you go looking for trouble, so to speak.

Q: Like what?

A: Another one of the amazingly strange things that quantum theory predicts is that things can be in many states at once – as though an electron were in many places at once, but the act of looking at it forces it to choose as it were and from then on its only where you saw it. This bizarre behaviour is what drives the Schrodinger’s Cat thought experiment. Schrodinger – who incidentally was a strange character himself who did all his best work on weekends with his mistress in an alpine chalet, you have to wonder what she thought of him spending his time on quantum mechanics instead of on her – he said, let’s imagine we have a cat in a closed box and with the cat is a machine which will gas the cat if some quantum event happens. If we don’t look at the quantum object in question it is half in one state, half in the other. As soon as we look it is one or the other. The question is: before we open the box and look, is the cat alive or dead?

Q: If the cat’s in a closed box it will suffocate!

A: Well, yes, but what Schrodinger was getting at was a way to magnify a quantum event with all its attendant weirdness into the domain that you and I inhabit. So quantum theory would seem to say that the cat is both alive and dead until we look inside the box, then it’s one or the other.

Q: What does happen if you try the experiment?

A: I don’t think it would be ethical to try it! Anyway, this weird way in which quantum objects can be many things at once – it’s called superposition by the way – can be harnessed to solve a problem which has bedeviled mathematicians for centuries – prime numbers. More correctly, it can be used in theory to factorise large numbers which is nearly the same thing. Now that’s a big problem in some quarters, because – you remember how we talked about how we use codes on the Internet a few months ago?

Q: Yes – weren’t prime numbers involved there?

A: Yes, the difficulty of factorizing large numbers is the cornerstone of some of the codes in use on the Internet today. And there are signs that a quantum computer can be used to do that job using something called Shor’s algorithm, although no one’s managed to build one yet.

Q: And the implications if they do build one?

A: Quite a lot actually – the codes we use for e-commerce are suddenly insecure and that’s a problem, but one I expect we could cover for that by switching to a new cryptosystem based on something different – there’s a technology called elliptic curves which could be used.

Q: How does that work?

A: It relies on a class of mathematical functions that are very easy to write down and fiendishly hard to solve. There is a vague relationship to the mathematical description of an ellipse, which is where the name came from.

But the real problem if someone makes a working quantum computer would be the amount of secret material – really secret, government classified national security material that has been broadcast in the past and recorded by people who would love to know what it said.

Q: Are there people out there really collected coded radio signals?

A: Absolutely there are. We are talking government-to-government stuff here, and they have a lot of resources, and if any of them have succeeded in cracking the prime-number based codes they certainly aren’t about to tell you or me.

Links

As always, you can discuss this broadcast at it.gen.nz.

A introduction to quantum mechanics at Wikipedia, and an article about the strange Erwin Schrodinger. Also an interview with the brilliant Oxford mathematician Roger Penrose as he describes the broad sweep of modern phyisics.

An article about quantum computing and a description of how one might one day be used to break codes

Wikipedia on elliptic curves that might one day replace prime number based codes.