Quantum circuit complexity, by quantifying the minimal size of any circuit that implements a given unitary, is closely related to computational notions of complexity. The latter quantify the difficulty of solving a given computational task with a quantum computer and determine quantum complexity classes.

Quantum circuits are the most straightforward analogue of classical computers: wires connect gates which manipulate qubits. The transformation made by the gates is always reversible: this is a remarkable departure from classical computers. The circuit description uses simple diagrams to represent connections.

Circuit depth is the count of time steps needed to execute all the gates in a quantum circuit. One time step is the time it takes to execute one gate. If N gates can be executed in parallel, then only one time step is needed. But if N gates need to be executed sequentially, then N time steps are needed.

The easiest way to do this is to have some extra qubits that are your output qubits and, for each of the qubits we've prepared so far and each of the output qubits, either add a CNOT between the two or don't.