Phase Gate P(λ) | Arbitrary Diagonal Phase Rotation
Quick Technical Answer:
The Phase gate P(λ) imparts a continuous phase shift of e^{iλ} exclusively to the |1⟩ state while preserving |0⟩. It is equivalent to an Rz rotation up to a global phase of e^{iλ/2}.
Formula / Unitary:
P(\lambda) = \begin{pmatrix} 1 & 0 \\ 0 & e^{i\lambda} \end{pmatrix} = e^{i\lambda/2} R_z(\lambda)
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Frequently Asked Questions
What special cases arise from P(λ)?
P(π) = Pauli-Z, P(π/2) = S gate, and P(π/4) = T gate.