Let's take some time to think more about quantumness, and why we need quantum error correction to protect it.
Double Slit Experiment
One good example of a quantum effect comes from the so-called double slit experiment. This is shown in the following picture (from here).
You have a screen with two holes in: the double slit. You then take an electron gun, which is just something that fires electrons, and aim it between the two holes.
If electrons behave as we sometimes imagine they do, as little balls, they would just crash into the screen. Then they'd probably bounce off somewhere random and never be seen again. It would be a rather boring effect. But that's not what happens.
Let's put another screen behind the slits: the observing screen. This one shows us whenever an electron hits it. With this we find that at least some electrons do actually get through.
This fact alone doesn't contradict our assumption that they just behave like balls. Maybe it's just that the gun doesn't fire straight, and has a bit of a random spread. If this were true, we would expect to find electrons hitting the observing screen in two places, one behind one slit and one behind the other.
But that's not what happens. Instead we will see a more complicated pattern. In fact, we will see the kind of interference pattern that one usually expects from a wave passing through two slits. Like in the following picture (from here).
How do we explain this? Maybe the electrons going through one hole are affecting the ones going through the other, and that's what causes the wave like effect. If this is true, it would not happen if we only fired one electron at a time. Then it would always just be one electron through one hole, and there would be none of this wavy nonsense.
But that's not what happens. If we fire one electron at a time, we still get the same pattern! To make sense of this, we need more information. Let's put a detector next to both of the slits. When an electron passes them, the detectors will see it. They'll tell us which slit each electron went through, and we can try to figure out what is going on.
Once we put the detectors in, the interference pattern disappears. Now the electrons only hit the observing screen behind the two slits. They no longer behave in a strange wavy way. They behave as if they were balls!
What exactly is going on here? By doing experiments like this, and thinking hard about the results, physicists came up with the answer: quantum mechanics.
Quantum mechanics tells us that the electrons don't make decisions until they need to. If left undisturbed, they won't decide whether to go through one slit or the other. They will just go through both. At the same time.
Once an electron has gone through a slit, it has to pick which direction to travel in. Should it go straight? A little to the left? A little to the right? Again, it doesn't decide. It just goes in all the possible directions at the same time.
Between the slits and the observing screen there are many possible paths that the electron could be travelling through.They spread out like waves from the two slits. Some of the paths coming from one slit overlap with those from the other. The indecisive electron can then have multiple different and contrdictory histories that could bring it to each place. Understandably, this affects it. It turns out that these crossing paths affect each other just like waves would. And that's why we end up with the wavy interference pattern.
This doesn't happen when we look at which slit the electrons pass through, because we force the electron to decide early on. There is only one electron, so it can only be seen by one detector or the other. Once it has been seen to go through one of the slits, all the paths through the other become impossible, and the interference effect is cancelled.
An electron passing through two slits isn't the only thing that has these strange quantum effect of doing multiple contradictory things at once. Electrons also have a property called spin. If we measure its spin, we can only get two possible results: up and down. But we can also see effects just as strange as in the double split experiment, which tell us that the spin can also be up and down at the same time. They can also travel at multiple different speeds at the same time. And its not just electrons that do strange quantum things. All other particles do to. In fact, there's no reason to believe that we aren't governed by the same quantum mechanical laws. It's just that we are always scuffling along the floor and bashing into the air and getting hit by light. The effect is that we are constantly being measured by our surroundings, and don't get the chance to harness our quantumness. Only the tiniest of particles do.
These quantum effects aren't just fun to look at. They are useful too.
Suppose we have a more complicated situation, with lots of particles all affecting each other in quantum ways. In theory, quantum mechanics can tell us what will happen. In practice, though, the maths gets big and complicated. Even the world's best supercomputer would need to run for the age of the universe to figure out problems that don't even have that many quantum particles in.
Even though our computers find these problems complicated, the quantum particles themselves obviously don't. They work out what they are supposed to be doing instantly. So can we harness the quantumness to make a new kind of computer, that can do quantum maths easily? This is the idea behind quantum computers.
Normal computers are build from a set of basic operations called logic gates. These do basic little bits of maths. Using lots of them you can build up any maths, play Mariokart and surf the internet. Some jobs need more logic gates than others. Quantum mechanics is something that needs too many very easily, so the computer takes too long.
With a quantum computer we would use quantum gates. These would also do basic little bits of maths, but maths that is more suited to quantum mechanics. These would need to be built out of particles that naturally behave in a quantum way. They will be more tricky to build, which is why we can't go and buy ourselves a quantum computer already. But once we have them, solving quantum mechanical problems will be easy.
There are also other kinds of problem that normal computers find it hard to chew on, like factoring numbers and working out the best route for a travelling salesman. These need a huge amount of normal logic gates to solve, but some can be done with only a few quantum gates. Having a quantum computer will allow us reduce the time needed to solved them immensely, getting it down from the age of the Universe to that of a Mayfly. Then we'll be able to do a whole bunch of important and useful research across the sciences.
Our quantum gates really need our particles to be behaving in a quantum way. They need the freedom to do multiple things at once, without stuff bumping into them and messing it up. Otherwise it will be just like when we put the detectors next to the slit, the quantum effects will be gone. This job of protecting the quantumness and making sure everything runs smoothly is exactly what we need quantum error correction for. So let's get back to that.