Hadamard Operator

The Hadamard operator (often denoted **H**) is a single-qubit quantum gate that creates an equal superposition of |0⟩ and |1⟩. It transforms basis states as **H|0⟩ = (|0⟩ + |1⟩)/√2** and **H|1⟩ = (|0⟩ − |1⟩)/√2**. Mathematically, it’s represented by the matrix **(1/√2)·[[1, 1], [1, −1]]**, which both rotates and reflects the qubit state on the Bloch sphere.