An Animation About Quantum Computers

https://github.com/jeffwass/Squankum

The video doesn't realy describe what quantum computation is but it rather describes what feature of QM makes quantum computers different from classical computers (superposition and quantum correlations) and why is it so difficult to build or use a quantum computer (decoherence, and the fact that you can't observe or clone the "registers" at intermediate stages in a computation).

The video addresses the notion of quantum computing quite obliquely. I would expect this to be the first of a multi-part series where this is explored in more depth (especially given the attention it's receiving).

We can't. Nobody knows how to measure a wavefunction. Instead, what you measure is one of the eigenvalues of a linear operator that acts on a wavefunction (which particular eigenvalue? You can't always predict this; hence the randomness in QM). For each "observable" you want to measure (position, momentum, spin), there is a specific linear operator associated with it. For instance, in position-space, the position operator is just the identity operator.

If you haven't taken linear algebra, I can clarify this further.

When a measurement is made, the wave function, which gives the probability of finding the system in any particular state, "collapses" so all the probability mass is on the state you just measured.

If you keep measuring the system quickly (relative to the time it would take to change significantly) you actually stop if from evolving the way it would have if you'd left it alone, as if you dropped a ball and kept staring at it and it dangled in the air instead of falling.

The reason it's difficult to know the precise situation of a photon, in-flight, is because it's been emitted from a moving target, whose precise state is difficult to control perfectly: a live atom.

Without having perfect control of the atom that sends off the spinning, oscillating particle, we have a hard time discerning the exact circumtances of the spin/oscillation imparted upon it. We can hazard guesses, but when we're right, it's only because we get lucky. Not because we controlled it.

EDIT: The reason is there are two factors driving the emission:

1. The external behavior of the electon shells

2. The internal nuclear behavior of the protons and neutrons (which do not behave simply as a clump of spherical marbles, the nucleus is it's own volatile, nebulous construct)

And, oh yeah... 3. Any other random cosmological events that might sail in from outer space (literally), as fortuitous signals

A qubit exists in multiple states until measured. When you entangle multiple qubits together, each one increases the power of the system exponentially. Quantum computers are only good for certain kinds of problems like factoring large prime numbers. Luckily quantum systems are good at things classic computers aren't, and vice versa. You have to state your "question" in such a way that it causes the overall state of the quantum system to resolve on your answer.

I know my answer isn't much better. I only have a high level understanding with none of the math behind it. There's good videos if you search and watch a few times to get the concepts.

I can't remember the exact scenario that was explained to me, but it was something like this. Imagine the Traveling Salesman problem. You want the best route. But with a regular computer, it might take thousands of years to calculate the best route. With a quantum computer, if you structure the measurement correctly (this is how you "program" a quantum computer) then only the best route is what the system decoheres to.

There was also something about light and how if you had the right filter, only the answer gets through. I really forgot the details of that one, but maybe it'll help.

The state of the computer is a vector of complex amplitudes (one entry per possible answer, n qubits -> 2^n possible answers). The operations of the computer correspond to unitary matrix multiplications against the state vector. An entry's probability of being the result is the squared length of its final amplitude.

I try to explain it better here: http://twistedoakstudios.com/blog/Post2644_grovers-quantum-s...

Conversely, a quatum computer is very useful to solve such problems, think of: genetic algorithms, Monte-Carlo, etc. It is expected to do way better than classical computers. That doesn't necessarily make the simple problems easy on a quantum computer. Asking it the sort of question you did is not a measure of it's usefulness.

Since I'm not an expert on this, my aswer might be a little loose, but that's the basic idea.

We can't be sure (even though Luboš Motl disagrees). The universe may not be intrinsically random if superdeterminism is true. However, this isn't a popular idea in physics; in fact Gerard t'Hooft is the only Nobel prize winner I can think of that supports this idea.

Local hidden variable theories have almost all been ruled out by experiment in the last few decades (the same kind of theory Einstein was trying to find). There's still some loopholes, but, eh...

Colbeck and Renner have written a pretty powerful paper that given the assumption that measurements can be chosen freely, no extension of QM can have improved predictive power than the current theory of QM, regardless of whether this randomness "comes" from somewhere. Here's the paper: http://arxiv.org/abs/1005.5173

Bell's theorem (http://en.wikipedia.org/wiki/Bell's_theorem) and the tests around it show this to be false, things just don't act like there's a variable we simply don't know.

TL;DR: (edit) ignore the rest of this and just go read a lot on Bell's Theorem and the Double Slit Experiment. Both demonstrate concretely the essence of the weirdness.

(I'll leave the rest below just to keep me honest about my ignorance.) it's a provably special state where randomness allows it to have the needed characteristics for the math to work at all. [1]

Also disclaimer: I'm not a PhD physicist, just a BS in engineering physics. This is merely how I cope with the idea.

Think of it like this: given time, chaotic systems become unpredictable and noisy. An electron whizzing around an atom doesn't need much time before it's state is utterly unpredictable at any measurable level (Heisenberg Uncertainty assures this must happen eventually, and pretty fast it turns out).

So what if we isolate that little electron from the outside world? Then even the universe becomes uncertain, and must assume ANY possible state is valid and happening at once, blurring them together based on how likely each is given the last known observation! Otherwise the next observation could be contradictory to expectations, and seg fault the universe (perhaps just locally). This way though, the universe can always say "well I thought it could have been that" and be correct, even if it only thought it really unlikely.

But until the universe interacts with the state then, once coherence [2] sets in only probability can hint at what state it is in. Thus it is random in the before-the-fact sense like the probability before rolling a die, as opposed to an after-the-fact sense like a coin that is already flipped yet hidden.

And - here's the catch - the math needs to treat it as unknown. To label the parts of an unlabeled system will break the algebra! And if a distribution of states is unknown in a mathematically precise ignorance, this is indistinguishable from true randomness. Such pure conceptual states are rare in our messy universe (at least observationally), but they do exist and can be proven to exist in the same way a one time pad can be proven to be cryptographically secure.

Thanks for being my duck, I needed to think about something interesting today!

[1] Perhaps the most amazing bit is that if it weren't random, then it would act differently, since the distribution of observations would vary from the expected random field after enough observations. And this has been done! Study the double slit experiment deeply, as it really is a fantastic empirical example of why interfering via observation adjusts our interpretation of the results. [2]This term is jargon here, like quark colors. It's not coherence like a laser's.

In the video they relate this randomness to the fact that qubits live in a superposition of states, in contrast to bits, which can be either 1 or 0, but not both. This means that when you measure a qubit, you would still obtain 1 OR 0, but you will obtain each with certain probability. So, how is this different to just picking a random bit and then measuring it? You could fabricate a way of picking those classical bit that yield the same distribution than the qubit.

We find a difference in one of the very first experiments that highlighted the quantum nature of the microscopic world; the double slit experiment: you have two screens, one with 2 small holes and the other is placed behind that. Then you send a bunch of classical particles through the punctured screen and you receive the counts on the screen behind it. Then you have a distribution of places where those particles hit. Then you do the same with quantum particles this time. You obtain a different pattern (this is important, is different to the classical pattern). This pattern is called "diffraction" pattern and means there was a wave like interaction between the particles. So now you try to do the same experiment with quantum particles, but sending them one by one, so no classical-like interaction could exist. Amazingly, you find the same diffraction pattern. This means one particle can "interact" with itself. The way physicists explain this is by allowing quantum states to exists on this superposition states which induces intrinsic randomness due to the fact that when measured, each particle could only have travelled through one of the slits, or each qubit (after measurement) can only be 1 OR 0, but not both.

This difference between classical and quantum description of nature goes deeper, and makes mechanisms as entanglement and teleportation possible. "Bell inequalities" are a great example of of some other, related ways in which both differ.

Quantum randomness has a quality that makes it hard to explain in other ways. The results of measurements can't be made up on the spot, because they need to correlate with remote measurements. They also can't be stored ahead of time, because of how the correlation depends on which measurement is performed.

http://math.ucr.edu/home/baez/quantum/