  The imminent era of error-corrected quantum computing urgently demands robust
methods to characterize complex quantum states, even from limited and noisy
measurements. We introduce the Quantum Attention Network (QuAN), a versatile
classical AI framework leveraging the power of attention mechanisms
specifically tailored to address the unique challenges of learning quantum
complexity. Inspired by large language models, QuAN treats measurement
snapshots as tokens while respecting their permutation invariance. Combined
with a novel parameter-efficient mini-set self-attention block (MSSAB), such
data structure enables QuAN to access high-order moments of the bit-string
distribution and preferentially attend to less noisy snapshots. We rigorously
test QuAN across three distinct quantum simulation settings: driven hard-core
Bose-Hubbard model, random quantum circuits, and the toric code under coherent
and incoherent noise. QuAN directly learns the growth in entanglement and state
complexity from experimentally obtained computational basis measurements. In
particular, it learns the growth in complexity of random circuit data upon
increasing depth from noisy experimental data. Taken to a regime inaccessible
by existing theory, QuAN unveils the complete phase diagram for noisy toric
code data as a function of both noise types. This breakthrough highlights the
transformative potential of using purposefully designed AI-driven solutions to
assist quantum hardware.
