This paper introduces a computational complexity framework for quantum experiments, called Quantum Algorithmic Measurements (QUALMs). QUALMs combine black-box quantum algorithms with interactive protocols to study experimental problems in quantum many-body physics. The authors demonstrate a provable exponential speedup for coherent QUALMs compared to incoherent ones in distinguishing time-independent from time-dependent Hamiltonians and determining system dynamics' symmetry classes.

Dorit Aharonov, Jordan Cotler, Xiao-Liang Qi