Walsh–Hadamard Gate and Its Properties

Quantum computing would not be powerful if there is no superposition. Most of the quantum gates we have learned so far have classical counterparts and cannot be used to form superposition. In this chapter, we will discuss a very important gate, namely the Hadamard gate, which can form the superposition of quantum states and does not have any classical counterpart. We will study its properties and also how it forms a superposition state in multi-qubit cases. The derivations might seem difficult but are important to follow through so that you will be able to understand more difficult algorithms in the future.