What is Hadamard Gate?

A fundamental single-qubit gate that transforms a basis state into an equal superposition, mapping |0⟩ to (|0⟩+|1⟩)/√2 and |1⟩ to (|0⟩−|1⟩)/√2.

What category does Hadamard Gate belong to?

Hadamard Gate is a Gates & Circuits concept in quantum computing.

Hadamard Gate — Quantum Computing Glossary

The Hadamard gate (H) is one of the most important gates in quantum computing, serving as the primary tool for creating superposition from classical basis states. It maps |0⟩ to the equal superposition (|0⟩+|1⟩)/√2 (also written |+⟩) and |1⟩ to (|0⟩−|1⟩)/√2 (also written |−⟩). Applying the Hadamard gate twice returns the qubit to its original state, making it self-inverse (H² = I).

On the Bloch sphere, the Hadamard gate performs a 180-degree rotation around the axis halfway between x and z. It is a member of the Clifford group and can be efficiently simulated classically when combined only with other Clifford gates. However, when combined with the T gate, the Hadamard gate becomes part of a universal gate set capable of approximating any quantum operation to arbitrary precision.

The Hadamard gate appears at the beginning of almost every quantum algorithm. In Grover's search algorithm, Hadamard gates applied to all qubits create the uniform superposition that initializes the search. In the quantum Fourier transform (used in Shor's algorithm), Hadamard gates alternate with controlled phase gates. In quantum error correction, Hadamard gates switch between the X and Z bases, enabling measurement of different error syndromes. The ubiquity of the Hadamard gate makes its high-fidelity implementation a basic requirement for any quantum computing platform.