what are the benefits of quantum computing?

Answer 1

Speed Size Less Heat More Storage Any other questions?

Answer 2

Quantum computing uses the randomness of quantum mechanics to "simultaneously" preform a large number of computations at once. It's like having the parallel computing power of an large number of computers. This lets us take problems that were previously computationally intractable (like factoring very very large prime numbers, which is the key to breaking certain widely used forms of encryption) and make them tractable. In other words, the complexity of the solution to some problems would explode using traditional solutions methods as the problem became larger. However, with quantum computing even as the problem becomes larger, the solution method grows in complexity much more slowly. That is, problems that would take thousands of years to solve on traditional computers might only take a few days on a quantum computer. Keep in mind that this is the major push for quantum computers. It has nothing to do with their size or their heat or any other strange factors like that. For a long time, quantum computers are going to be the size of MRI machines and probably only used by scientists (to do things like, strangely enough, simulating other quantum systems).

Maybe it will help to explain a little bit of what's going on.

Quantum mechanics tells us that particles exist not as discrete elements but as probability distributions. These distributions do not "collapse" into a single realization until observed.

To setup an example, imagine the diffraction pattern you see on a wall when you shine a laser through a small slit. You should see a pattern on the wall that is dim on the left and gradually gets brighter until the center after which it gets dim again. This pattern actually reflects the probability distribution predicted by quantum mechanics. When you send a single photon through that slit, it will randomly show up somewhere in that pattern. However, there is a higher probability that it will show up in the center of the pattern. That's why when you send a flood of photons through the slit (as in a laser beam) you see a bright spot at the center that gets progressively lighter as you move farther out from the center. The slit "spreads out" the quantum mechanical probability function. (so in classical mechanics, a "light wave" is being diffracted by the slit; in quantum mechanics, a "probability wave" is being diffracted by the slit)

Now, before the photon is observed at the wall, what path does it take? In "reality," it takes all paths at once. The photon is not a discrete element that moves "through" the slit. The photon doesn't "exist" in that discrete form until it collapses at the point of observation to one spot governed by the probability distribution. (in fact, if you tried to "measure" which "path" the photon took with some detector at the slit, the diffraction pattern would disappear; the slit would stop "spreading" the distribution out because the photon would "enter existence" at the slit instead of the wall and there would be no probability distribution for the slit to spread out)

So that's the key. Particles following probability distributions can be interpreted as traveling multiple paths simultaneously.

Now, another spooky aspect of quantum mechanics (that is actually also simply due to probability) is that particles can be "entangled" so that their outcomes are correlated. In other words, they both have completely random outcomes, but once one "collapses" the other will necessarily also collapse to some related outcome.

What entanglement does is allow us to setup relationships between particles. It allows us to couple things together. This is what really lets us do computation.

By joining lots of entangled particles that all simultaneously exist in multiple states, we are able to do computations. Keep in mind that we can't touch each of the particles directly because we want to prevent them from "collapsing" onto one realization. The entanglement lets us join the fates of similar particles without determining that fate. This lets us force the combination of entangled to do the computations we WANT them to do, and their randomness lets them do multiple computations simultaneously. Eventually, we "observe" their state in a special way and they "collapse" to a useful result. That collapse happens very quickly. It's basically a zillion computations in an instant.

Usually that result isn't enough to solve all of our problems. We usually still need to do more work, some of which may involve more runs through the quantum machine and some of which may involve traditional computers; however, the work we have to do is FAR less than the work we'd have to do with a traditional computer.

And as we learn more about quantum computing, the less work we'll have to do with traditional computers when the quantum computers finish, so that makes things even faster.

Answer 3

The computers are much faster and capable...Check howstuffworks:
http://computer.howstuffworks.com/quantum-computer.htm