# cirq.ops.phase_flip

Returns a PhaseFlipChannel that flips a qubit's phase with probability p

if p is None, return a guaranteed phase flip in the form of a Z operation.

This channel evolves a density matrix via:

$$\rho \rightarrow M_0 \rho M_0^\dagger + M_1 \rho M_1^\dagger$$

#### With:

\begin{aligned} M_0 =& \sqrt{p} \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} \\ M_1 =& \sqrt{1-p} \begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix} \end{aligned}

p the probability of a phase flip.

ValueError if p is not a valid probability.