garden/unitary-operator.md

Unitary Operator

• quantum-computing
• a matrix `\mathcal{U}` operating on a quantum-state to produce another quantum-state
  • maps unit vectors to unit vectors
  • norm
• other equivalent definitions:
  • columns of `\mathcal{U}` are orthonormal
  • rows of `\mathcal{U}` are orthonormal
  • `\mathcal{U}^{-1} = \mathcal{U}^\dagger = \overline{\mathcal{U}^\intercal} = \overline{\mathcal{U}}^\intercal`
  • preserves norm
  • preserves inner-product