# What is a qubit?

## Qubit

A qubit (or quantum bit) is the quantum mechanical analogue of a classical bit. In classical computing the information is encoded in bits, where each bit can have the value zero or one. In quantum computing the information is encoded in qubits. A qubit is a two-level quantum system where the two basis qubit states are usually written as $\left\lvert 0 \right\rangle$ and $\left\lvert 1 \right\rangle$. A qubit can be in state $\left\lvert 0 \right\rangle$, $\left\lvert 1 \right\rangle$ or (unlike a classical bit) in a linear combination of both states. The name of this phenomenon is superposition. This video from the QuTech Academy explains some basic qubit properties.

## Single-qubit computational basis states

The two orthogonal z-basis states of a qubit are defined as:

• $\vert 0\rangle$
• $\vert 1\rangle$

When we talk about the qubit basis states we implicitly refer to the z-basis states as the computational basis states.

The two orthogonal x-basis states are:
$\vert +\rangle =\frac{\vert 0\rangle + \vert 1\rangle}{\sqrt{2}}$ $\vert -\rangle =\frac{\vert 0\rangle - \vert 1\rangle}{\sqrt{2}}$

The two orthogonal y-basis states are:
$\vert R\rangle =\frac{\vert 0\rangle + \imath \vert 1\rangle}{\sqrt{2}}$ $\vert L\rangle =\frac{\vert 0\rangle - \imath \vert 1\rangle}{\sqrt{2}}$

The basis states are located at opposite points on the Bloch sphere representation of the state of a single qubit.