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]]
  • bounded [[linear-operator]] that is both an [[isometry]] and a [[coisometry]]