3. Quantum gates

3.1 Quantum gates on a single qubit

A quantum gate is an operator that transforms one quantum system into another. It is an elementary quantum circuit operating on a number of qubits. Quantum gates are the building blocks of quantum circuits.

A quantum gate is the quantum equivalent of a classical logic gate. In a classical computer, logic gates perform operations on bits (0 or 1) to perform calculations. In a quantum computer, quantum gates operate on qubits, which can be in a superposition of states.

A quantum gate enables unitary operations to be performed on these qubits, i.e. transformations that preserve the norm of the state vector, and, unlike many conventional logic gates, quantum gates are also reversible, i.e. their operation...