Quantum Computing Questions
The Hadamard gate is a fundamental quantum gate that operates on a single qubit. It is represented by the matrix:
1/sqrt(2) * [[1, 1], [1, -1]]
When applied to a qubit in the state |0⟩ or |1⟩, the Hadamard gate transforms it into a superposition state, represented as:
H|0⟩ = 1/sqrt(2) * (|0⟩ + |1⟩)
H|1⟩ = 1/sqrt(2) * (|0⟩ - |1⟩)
The Hadamard gate is often used in quantum algorithms, such as the quantum Fourier transform and the creation of entangled states. It plays a crucial role in quantum computing by enabling the manipulation and measurement of quantum states.