  We give a simple, closed-form formula, what we call the Deflation Identity,
for converting any 2-qubit circuit with exactly two controlled-U's (and some
1-qubit rotations) into an equivalent circuit with just two CNOTs (and some
1-qubit rotations). We also give two interesting applications of the Deflation
Identity; one to "opening and closing a breach" in a quantum circuit, the other
to the CS decomposition of a 2-qubit operator.

Quantum Physics