# Constructing Other States using "0" State on Quantum Computing

As you may know, the interface of IBM's Quantum Composer or Qiskit/QASM only lets us to "reset" a quantum bit to $|0\rangle$ state. However, it's a must to have use other states when designing a quantum circuit. In this blog post, I'll introduce you how to create those and their state vectors.

Please study the sphere below. It is called **Bloch Sphere** and lets us imagine how does quantum gates changes a state into another one. On z-axis, we have two classical states: $0$, $1$. On y-axis, we have two complex states: $i$, $-i$. At last, on x-axis, we have two sign states: $+$, $-$.

## Classical States

In quantum world, $|0\rangle$ and $|1\rangle$ are known as classical states. Since resetting operation directly creates a $|0\rangle$ state, we will be only investigating on creating $|1\rangle$ state.

To have $|1\rangle$, we should turn our $|0\rangle$ vector by $\pi$ radians either on x-axis. So, we'll use an *X gate* to convert it.

## Sign States

With using Hadamard gate, we can construct a superposition between $|0\rangle$ and $|1\rangle$ which also equivalent to $|+\rangle$ or $|-\rangle$ states.

To construct a $|+\rangle$, let us reset a qubit to $0$ and then apply a Hadamard gate to it.

To construct a $|-\rangle$, we need to input a $|1\rangle$ into Hadamard gate. Since we've already learned how to create each classic gate, let's implement it, and apply a H gate afterwards.

```
from qiskit import QuantumRegister, QuantumCircuit
from numpy import pi
qbit = QuantumRegister(1, 'q')
circuit = QuantumCircuit(qbit)
circuit.reset(qbit[0])
circuit.x(qbit[0])
circuit.h(qbit[0])
```

## Complex States

Complex states are the edges of Bloch Sphere on y-axis. To create a complex state, we may firstly create a sign state (as we previously learned) and then apply an **S gate **which rotates $\pi/2$ radians on x-y plane. Outputs of S gate are $|i\rangle$, $|-i\rangle$ when $|+\rangle$, $|-\rangle$ given, respectively.

Let's construct a $|+\rangle$ state, and apply S gate into it to have $|i\rangle$ state.

Now, it is the turn to construct a $|-i\rangle$ state.

As you see, we've constructed all the Quantum states using the single-input gates. I hope that helps!