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Quantum computing is a special type of computing which utilizes quantum phenomena to perform operations on data. This is a new and active area of research in the real world and many experts believe it may revolutionize computing.
To help us understand what's special about quantum computing, let's look first at traditional computing.
Traditional computing is based on binary digital electronics which are made of transistors. The term binary refers to the fact that there are only two possible states: zero or one. Thus in traditional computing, data can only be encoded into binary digits, or bits, which are zero or one. Physically, this means the transistors are either switched off or on.
Quantum computers do not use bits, but rather, quantum bits, also called qbits or qubits. (Incidentally 'bit' is a misnomer here since it is a combination of the words binary and digit.) The important thing about qubits is they can have many more than two states because of quantum mechanical superposition.
Superposition is a fundamental principle of quantum mechanics. It comes from the underlying mathematics of quantum mechanics. This math states every particle is both a particle and a wave and thus can be represented by something called a wavefunction. Wavefunctions are described in terms of probabilities and have unusual properties. For example, because of wavefunctions, particles can be located in an unlimited number of places at the same time.
Probably the most famous example of superposition is the Schrodinger's Cat thought experiment. We put a cat inside a box with a small amount of radioactive substance and poison. It the radioactive substance decays, the poison vial breaks and the cat dies. If not, the cat lives. The point is before we look inside the box, the cat is considered to be in a superposition of an alive and a dead state. Once we look inside, the wavefunction collapses and one reality is instantiated. The cat must be alive or dead. Thus the act of observation is powerful; observation itself creates the outcome. Note we cannot observe the superposition itself--just the consequences of it.
Therefore, because of superposition, in quantum computers instead of two possible states there are an infinite number of possible states. Thus, quantum computers could work on millions of computations at once.
An operational quantum computer could be used to decrypt many of the current cryptographic systems--including those considered 'uncrackable' by conventional computers. Another application of quantum computers could be quantum database searches--which would be much faster than conventional methods.