What is Quantum Computing? (Part 3)

In classical computing, computer program consists of operations on conventional bits of 1 and 0. In Quantum Computing (QC), there are also operations on Qubits. Here I will introduced a few commonly used operations.

The first one is the NOT gate (X) or called NOT operator or bit flip operator. In terms of linear algebra, it is represented as a 2-by-2 matrix, where

If we apply X on |0> (by matrix multiplication), we will get |1>.

Another crucial operator is Hadamard (H), which enables us to take a qubit from a definite state into a superposition of 2 states.

If we apply H on state |0>, we will get 1/sqrt(2){ |0> + |1> }, which is the superposition of state |0> and |1>, that we have 50% getting 0, and 50% getting 1.

Operations can be cascaded. You can noticed that apply H operator twice will give the identity operator (I). H² = I

Sequences of operators can be represented as the circuit diagram of quantum gates. Here is an example circuit diagram found on the web (link).