When is first-order Trotterization exact?

Question: Let H=A+B. Under which condition is the first-order product formula e^(−itA)e^(−itB) exactly equal to e^(−it(A+B)) for every real t? A) A and B commute B) A and B have the same eigenvalues but different eigenvectors C) The operator norms of A and B are both less than one D) A and B are each sums of Pauli operators Correct: A Explanation: If A and B commute, their exponentials combine exactly. When they do not commute, Baker–Campbell–Hausdorff terms involving commutators and nested commutators generate product-formula error. Topic: advanced quantum computing / Hamiltonian simulation / Trotterization