No Quantum Utility from Hadron Masses? No, Quantum Utility from Hadron Masses!

Is there a quantum utility in establishing the masses of hadrons? Here we show that the best response is that of Farr\'es, Cap\'o, and Davis: perhaps, perhaps, perhaps. This is interesting given the general case that particle physics demands quantum computers. For stable hadrons, classical LQCD has achieved sub-percent precision with no sign problem, and quantum computers offer no advantage. For resonances, the Maiani-Testa theorem is an obstruction that quantum simulation is immune to. For nuclei, Wick contractions and signal-to-noise are genuine classical barriers. Underlying these cases is a unified picture connecting the sign problem to Wigner negativity and T gate cost. This manuscript was drafted from extensive interaction with \textsc{Claude}.