Attention to Quantum Complexity

Abstract

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.