What is a correct and simple definition of quantum physics? Is it correct to define Quantum Physics as the study of Physics in sub-atomic scale? Does Quantum Physics studies something else other than sub-atomic phenomena?
 A: Quantum physics is a probability theory where probability amplitudes appear. Any phenomenon where probability amplitudes appear is a quantum phenomenon, whether it is microscopic or macroscopic. The probability amplitudes unify the particle and wave classical limits into one object, and they probably apply to all objects, microscopic and macroscopic.
A: The unique way the human kind has got to determine if an effect needs quantum mechanics to be described consists in calculating the action (cf. wikipedia) and comparing it with Planck's constant. If it is much bigger, there is no need of quantum mechanics; if it is on the same order, you will need QM to describe that effect.
The action being much bigger than Planck's constant does not mean that QM cannot be used. Bohr used to think that the macroscopic and microscopic worlds were fundamentally different, but such examples as quantum levitation (which is macroscopic - see Wikipedia) suggest that describing fundamentally was a synonym of describing with QM.
A: Is it correct to define Quantum Physics as the study of Physics in sub-atomic scale? No.
Does Quantum Physics studies something else other than sub-atomic phenomena? Yes.
Take artificial atoms or superconducting flux qubits as examples.
What is a correct and simple definition of quantum physics? A correct and simple definition: "quantum physics" is a collection of models of physical phenomena which use the mathematics of "Hilbert space" to make operational predictions for the outcomes of laboratory experiments.  Which physical phenomena?  Well, whatever ones we can make good predictions for.
A: Short answer: It is the physics of small scales or high energies.
Long answer: Don't listen to Short-answer Jim, he doesn't know what he's talking about. (He's also a few rings short of Saturn, if you know what I mean)
The simplest way I can think of correctly defining quantum physics is that it is the combination of our best and most correct theories of physics that does not include General Relativity.
There are two relevant and important classes of physics for this explanation: classical physics and quantum physics.
Physicists are people too. If we can achieve our goals equally well through two different methods, we are going to pick the method that is easier for us to use. That being said, it should come as no surprise that the theories we choose to use for any given task are generally the simplest theories that effectively suit the needs of that task.
Quantum physics is generally accepted as the more correct version of physics compared to classical physics. That is, classical physics is mostly wrong. However, classical physics is usually correct enough that, for most everyday applications, you wouldn't notice the difference between the quantum and classical results. Technically speaking, it is possible for you to do absolutely everything using only quantum physics (except anything involving GR) and you would get much more accurate results; however, quantum physics is so much more complex than classical that it becomes extremely impractical to use. If classical physics gives you an answer that is correct enough, it makes sense to use it. We use quantum physics only when classical physics will not give us a good enough result. This tends to be true more often when dealing with extremely small scales or with extremely high energies. That is why many people often tell you that quantum physics is the physics of small scales or high energies. They are wrong. Quantum physics covers everything except GR and it is simply our most correct theories of physics to date.
That said, we know quantum physics is incomplete. We know it is not totally correct. That is why you will also hear some physicists say that physics breaks down on even smaller scales or at even higher energies. They don't mean that literally. There is no scale or energy level where physics actually does not apply. What they mean is that the theories we have, like classical physics on the quantum scale, are not correct enough to use. We don't know yet the theories that are correct enough to use outside the quantum limits. But even though we can't say what the physics is, we know the physics still works on those scales.
That is the simplest way I can define quantum physics.
A: Here's how I've tried to give a sense of quantum physics.
It doesn't take you very far in understanding all the implications, but it's a start.
First, let's understand the word "amplitude".
Think of an incandescent light bulb, like an automobile light bulb.
When you put positive twelve volts across it, like from the car battery, it glows with its full wattage, say 60 watts.
If instead, you put an older-style 6 volt car battery across it, it only glows with 1/4 of its full wattage, 15 watts.
Now each battery can be reversed, putting negative voltage across the light bulb, and you get the same result.
So think of amplitude as the voltage, which goes as the square root of the power. The amplitude can have a sign, positive or negative, but the power is always positive and always varies as the square of the amplitude.

Think of a coin. You flip it into the air, and you don't yet know if it will land "Heads".
You know the probability of Heads is 0.5, assuming it's a fair coin.
Now, in the quantum world we think of that probability, 0.5, like the power of the light bulb.
What's actually underneath is an amplitude of 0.707, which when squared gives you 0.5.
That amplitude could be positive, or it could be negative.
(It could actually be something in-between, if it's a complex number, but you can read up about that.)

Now, the coin's in the air, so you don't know how it's going to come out, yet,
but you do know with certainty (P = 1) it will be either heads or tails, nothing else.
The way you know that is by adding up the probabilities of the different outcomes.
0.5 + 0.5 = 1.
But in the quantum world, you don't add probabilities.
You add amplitudes.
Since the amplitudes have signs, they might cancel each other out, or they might reinforce.
So with a quantum coin, the probability that you'll get something is the square of the sum of the amplitude for Heads, plus the amplitude for Tails.
That sum could be -1.414, +1.414, 0 (or anywhere in between if amplitudes are complex).
Therefore the probability of even seeing the coin land is somewhere between 0 and 2.

OK, now you're confused (and so am I).
How could you flip a coin and see it land twice or not at all, let alone somewhere in between?
To answer this, we gotta go to the double-slit experiment.
Instead of flipping a coin we are shooting little electron or photon bullets through two parallel slits, the Heads slit and the Tails slit, and they hit a screen on the other side.
If they worked like normal bullets, you would expect to see them pile up under each slit.
However, they are quantum bullets so they don't do that.
Instead, they pile up in places where they shouldn't land at all (in the center), and they completely avoid other places, for no apparent reason.
So here's how some smart guys explained it.
They don't say the bullet has a probability of going through one slit or the other,
they say is has an amplitude of going through one slit or the other.
Those amplitudes are numbers, but not only that, they're always changing.
They are waves, in fact.
Then when those amplitude waves come together, they interfere, just like water waves.
Where they cancel out, you get zero probability (no bullets).
Where they reinforce, you get excess probability, so excess bullets,
because the bullets that don't end up in the sparse places end up in the dense places.

So just to top off the confusion, you could say that when you flip that coin, the universe bifurcates, but unlike in "Back to the Future", those separate universes don't stay separate, they rejoin in the same way that water waves interfere,
and this is going on everywhere, all the time.
