qubits

Qubit is a short-hand for quantum bit.

Unlike classical bits ¹, which has the state space of , qubits’ state is a subset of a two-dimensional vector space. For instance, a possible state of qubits is .

The Computational Basis States

There are two special quantum states which correspond to the 0 and 1 states of a classical bit: the unit basis vectors. People like to write them in the special bra-ket notation:

We call those special states and “computational basis state.”

States of a Qubit

A general quantum state the entries can be complex numbers.

Also, quantum states have the normalization constraint: the sum of the squares of the amplitudes constraint to . i.e. for ,

In summary, the quantum state of a qubit is a vector of unit length in a two-dimensional complex vector space known as state space.

Measuring a Qubit

See: measuring a qubit

References

• Quantum computing for the very curious

Footnotes

1. “classical” in “classical bits” comes from “classical mechanics” ↩