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--- r-gate [May 22, 2026 at 21:23] – Ivan Janevski
+++ r-gate [Unknown date] (current) – removed - external edit (Unknown date) 127.0.0.1
@@ Line 1: / Line 1: @@
-# R-gate
-Those are operators:
-$$R_x(\theta) = e^{-i\theta X/2}$$
-$$R_y(\theta) = e^{-i\theta Y/2}$$
-$$R_z(\theta) = e^{-i\theta Z/2}$$
-After applying the exponential map $e^A = 1 + A + A^2 / 2 + \cdots$ and $X^2 = Y^2 = Z^2 = I$:
-$$R_x(\theta) = \cos\left(\frac{\theta}{2}\right)I + i\sin\left(\frac{\theta}{2}\right)X$$
-$$R_y(\theta) = \cos\left(\frac{\theta}{2}\right)I + i\sin\left(\frac{\theta}{2}\right)Y$$
-$$R_z(\theta) = \cos\left(\frac{\theta}{2}\right)I + i\sin\left(\frac{\theta}{2}\right)Z$$