12 lines
495 B
Markdown
12 lines
495 B
Markdown
# Unitary Operator
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- [[quantum-computing]]
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- a matrix $`\mathcal{U}`$ operating on a [[quantum-state]] to produce another [[quantum-state]]
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- maps unit vectors to unit vectors
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- [[norm]]
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- other equivalent definitions:
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- columns of $`\mathcal{U}`$ are [[orthonormal]]
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- rows of $`\mathcal{U}`$ are [[orthonormal]]
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- $`\mathcal{U}^{-1} = \mathcal{U}^\dagger = \overline{\mathcal{U}^\intercal} = \overline{\mathcal{U}}^\intercal`$
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- preserves [[norm]]
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- preserves [[inner-product]]
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