# Building Quantum Circuits

Let's see how to build proper quantum circuits using the gates we've learned so far.

## We'll cover the following

## Equal superposition state

An important part of most quantum circuits is the equal superposition state. It gives us the power to represent an **exponential** number of states with respect to the number of qubits we have at our disposal.

How can we create a superposition state representing our whole qubit system? You might recall that the **Hadamard** gate $H$ is used to put one qubit in an equal superposition state. This is the key concept here. If we have **five** qubits at our disposal, applying the **Hadamard** gate $H$ on each qubit will enable us to generate a superposition of $2^5$ states. Let’s take a look at a simple example using only two qubits:

$H^{\otimes2}|00\rangle = H|0\rangle \otimes H|0\rangle$

$H^{\otimes2}|00\rangle = (\frac{1}{\sqrt{2}}|0\rangle + \frac{1}{\sqrt{2}}|1\rangle) \otimes (\frac{1}{\sqrt{2}}|0\rangle + \frac{1}{\sqrt{2}}|1\rangle)$

$H^{\otimes2}|00\rangle = \frac{1}2(|00\rangle + |01\rangle + |10\rangle + |11\rangle)$

As you can see, the state of our system has an equal chance of 25% to yield either of the states in the superposition upon measurement. Let’s have a look at the circuit diagram.

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