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I am new to the Quantum Computer world. I understand the basics of Quantum mechanics and I have watched a few lectures on Quantum computers, Quantum gates and played a bit on IBM QC.

As far as I understand every qubit and every QC will output a probabilistic value. For example 1+1 could be

  1. 0
  2. 1
  3. 2

How can we do a deterministic simple computation like 1+1=2 via a quantum computer? and if we can, how can it be faster than a classical computer?

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There are quite a few ways to make an adder on QC. I recommend watching Circuit Sessions with Ali Javadi, demo notebook from the talk
so, a simple explanation, what makes a quantum computer faster than a classical computer in some hard problems, is always quantum resources, like

  • superposition(example like Hadamard gate in Deutsch–Jozsa algorithm where $N$qubit $= 2^n$ classical states),
  • entanglement(example like bell state), and
  • interference(example like Grover search amplitude amplification)

but may be you want to ask about gate time, but in mind that different types of quantum computers have their own advantages in application scenarios.

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