Quantum Operations and Quantum Circuits

Baby's First Quantum Circuit

In quantum computation, it is common to use quantum circuits to visualize the interaction between (sometimes many different) quantum states and quantum operators.

This is also known as the circuit model of computation.

For example, applying the Pauli $Z$ gate (aka operator) on a qubit $\ket{\psi}=\alpha\ket{0}+\beta\ket{1}$ would be represented as:

Note this diagram flows left to right, that is, we read it in the following order:

1. We start off with a qubit $\ket{\psi} = \alpha\ket{0} + \beta\ket{1}$.
2. We then apply the Pauli $Z$ gate to the qubit, i.e. $Z\ket{\psi}$.
3. We then have the output state $Z\ket{\psi} = \alpha\ket{0} - \beta\ket{1}$.

We call the lines in the circuit quantum wires, and quantum circuits in most quantum algorithms typically involve many quantum wires, because the algorithm involves many qubits.

However, for now, we are focusing just on single qubit quantum circuits, so we can understand the basic building blocks, and build up from there.

Simplest possible quantum circuit

...