u-gate
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| u-gate [June 12, 2026 at 22:58] – Ivan Janevski | u-gate [June 13, 2026 at 03:13] (current) – external edit 127.0.0.1 | ||
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| # Unitary gate | # Unitary gate | ||
| - | **U gate** is the most general single-qubit unitary gate, parameterized by three real angles $\theta$, $\phi$, $\lambda$. Every single-qubit unitary (up to global phase) can be expressed as $U(\theta, \phi, \lambda)$ for some choice of these angles, making it the canonical representation of a single-qubit gate. | + | **Unitary |
| $$U(\theta, \phi, \lambda) = \begin{pmatrix}\cos\dfrac{\theta}{2} & -e^{i\lambda}\sin\dfrac{\theta}{2}\\[8pt] e^{i\phi}\sin\dfrac{\theta}{2} & e^{i(\phi+\lambda)}\cos\dfrac{\theta}{2}\end{pmatrix}$$ | $$U(\theta, \phi, \lambda) = \begin{pmatrix}\cos\dfrac{\theta}{2} & -e^{i\lambda}\sin\dfrac{\theta}{2}\\[8pt] e^{i\phi}\sin\dfrac{\theta}{2} & e^{i(\phi+\lambda)}\cos\dfrac{\theta}{2}\end{pmatrix}$$ | ||
u-gate.1781305085.txt.gz · Last modified: by Ivan Janevski