Bonaparte Quantum Logic

Hadamard Gates

The Hadamard gate is a fundamental single-qubit gate in quantum computing. It transforms basis states into superpositions, enabling interference effects that are central to quantum algorithms.

Action on States:

  • |0⟩ → (|0⟩ + |1⟩)/√2 = |+⟩
  • |1⟩ → (|0⟩ - |1⟩)/√2 = |−⟩

Circuit: |0⟩ → H

H|0⟩

Figure A: Hadamard gate creates superposition - measurement gives random 0 or 1.

Ready to run - Hadamard creates superposition, measurement gives random 0 or 1

Bloch Sphere Representation

|ψ⟩
Z
|0⟩
|1⟩
X
|-⟩
|+⟩
Y
|-i⟩
|i⟩

The Hadamard gate rotates |0⟩ from the north pole to the equator at |+⟩ = (|0⟩ + |1⟩)/√2