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

TL;DR

This paper argues that quantum computers currently offer no advantage in determining hadron masses due to classical methods' effectiveness and fundamental quantum simulation limitations, highlighting the connection to sign problems and Wigner negativity.

Contribution

It provides a comprehensive analysis of the limitations of quantum computing in hadron mass determination, linking classical barriers to quantum resource costs and sign problems.

Findings

Classical LQCD achieves high precision without quantum advantage.

Quantum simulation faces fundamental obstructions like the Maiani-Testa theorem.

Sign problems and Wigner negativity are key barriers to quantum utility.

Abstract

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}.