In this section, we will discuss the XOR operator, which we will encounter frequently in future sections. In this part of the work, we will explore the XOR operator, which is applied to pairs of Boolean variables and is mathematically represented by ⊕, also known as “exclusive OR”. This binary operation plays a crucial role in the definition of Boolean functions and is highly significant in all quantum algorithms. The truth table for this operator is shown below:

x	y	x ⊕ y
0	0	0
0	1	1
1	0	1
1	1	0

The XOR operator holds a special place in quantum algorithms, as it plays an important role in defining the relationships and transformations between quantum bits (qubits).