controlledU
ControlledU, often written as CU, is a two-qubit quantum gate that applies a unitary operation U to a target qubit conditioned on the control qubit being in the state 1. When the control qubit is 0, the target qubit is left unchanged. Formally, CU = |0⟩⟨0| ⊗ I + |1⟩⟨1| ⊗ U, where I is the identity on the target qubit.
In the standard computational basis {|00⟩, |01⟩, |10⟩, |11⟩}, CU has a block-diagonal form: CU = diag(I,
Special cases illustrate the concept: if U = X (the Pauli-X gate), CU becomes the CNOT gate; if
Applications and significance: controlled-U gates are fundamental for constructing conditional operations in quantum circuits. They are
Implementation: In practice, CU can be synthesized from native single-qubit gates and two-qubit entangling gates (such
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