The video really doesn't do a good job of explaining how a quantum computer can work. They just hit the basic high points because this video is intended for a general rather than specific audience.

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.

To substantiate your point: Essentially, quantum computing is useful for problems that could take help from a large degree of parallelization. Quantum mechanics has an inherent parallelization at it heart. Otoh, simulating that amount of parallelization with classical resources will be exponentially complex.

This is a VERY common misconception, and is not a good intuition for how quantum computing is different than classical.

A better intuition, in my opinion, is computing with "un-flipped" coins, except with funny complex-valued probabilities of heads vs tails instead of real values between 0.0 and 1.0. Because the probabilities are complex-valued, they interact in ways that can seem a bit counter-intuitive, (it makes sense it is counter-intuitive, because how many quantities do we deal with day-to-day that are described with complex numbers?) These interactions can provide some algorithmic speed up on some nicely structured problems.

It's not always obvious what these problems are, and it doesn't relate to do whether the problem is highly-parallel. My intuition for "quantum-friendly" is if a problem involves some kind of periodicity, or Fourier-like frequency analysis, then perhaps you'll see a quantum speedup. But it's important to remember the coins don't somehow "try every flip possible" to find the answer you're looking for -- if they did that you'd be able to solve NP problems in constant time.

I agree that the superposition with complex probability amplitudes (fundamental quantum randomness) is different from just statistical randomness of trying every possibility. I fact, this is one of the notions which is being used to verify whether the D-Wave computer (as a black box) is "truly quantum".

1. I don't quite see what periodicity has to do with the speedup. Could you elaborate on that?

2. "...if they did that you'd be able to solve NP problems in constant time." Again, please explain. In QM, the answer you calculate is actually the weighted sum over all possibilities... so the way I see it, it does cover every possible path. That answer might not be useful in telling you which is the shortest single path, but if you were an electron traversing a graph and wanted to optimize your travel, you'd do exactly what the quantum computer says and traverse all paths! The classical notion of "best path" might be trickier to deduce from a quantum computer. Maybe I'm addressing something tangential to what you're saying.

Re 1. Periodicity: The quantum Fourier transform is an operation that reflects information about a quantum state into the the phases of the amplitudes. Quantum phase information is exactly where quantum computing differs from classical probabilistic computing, so it makes sense that this technique might show up in places where quantum computing beats classical. For example: Shor's factorization of integers makes direct use of the quantum Fourier transform. I mention periodicity only as an example of a sort of problem where the Fourier transform might be useful. This is as an alternative intuition to what quantum computers are "good at" to combat the notion that "quantum computing is good for parallel problems."

Re 2. "covering all paths": I don't have a problem interpreting quantum superposition as inhabiting all possible states. However, classical probabilistic computing also can be interpreted this way: an un-flipped coin is both heads and tails until the flipping happens. But probabilistic computing doesn't give us faster-than-classical speedup, therefore it's not just the "existing in all states at once" that buys us the speedup: it's the unique kind of math we can do on these states because our amplitudes are unitary-complex, not positive-real.

You understand this distinction, so I perhaps shouldn't have adopted the tone I did (sorry!). The leap between "superposition involves a complex-valued combination of several states" and "tries all answers at once so is very fast" is a very common leap made in popular science articles and is the kind of misconceptions that I think the "quantum computers are good at parallel" intuition encourages. Just because a quantum state is a superposition doesn't mean we get to, for free, observe and evaluate all those states and pick out the one we like. We can sometimes arrange things in such a way that the quantum phases interact non-classically to leverage the structure of some problems to reveal information that isn't available to classical algorithms.

Periodicity information, via the quantum Fourier transform, is an example of one way to arrange things to extract information that would be more expensive to calculate classically.

Pfft, anyone can factor large prime numbers :)

I can do it right now, for ANY arbitrary large prime P.

.......thinking....

P and 1 are the factors!

Quantum computing is sortof like... destructively interfering all the non-solutions so the only likely measurement results are solutions.

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...

The visualization for complex product is amazing!

Haven't seen the video yet, but I'll take a shot at your question. To my knowledge, the original motivation of a "quantum computer" was to simulate quatum mechanical systems (leading back to Feynman's lectures on computation). Simulating quantum (or other kinds of random) events with classical resources (conventional computers) is a hard problem in the sense that it's exponentially more complex than a classical problem.

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.

This was my question too, I don't understand how you can begin to make a computer out of something with - as they explained - intrinsic randomness. And I didn't quite understand, how, if we can't see or ask the computer how it did something, how we can be certain of its answer or know that we've built something that does what we want.

You can know the probability that the algorithm will output the correct answer. If the probability of a correct response is > 50%, all you have to do is run the algorithm multiple times to get within, say, 99.99% certainty that the most-commonly reported answer is correct.

Thank you, this makes sense