Hardware-efficient learning of quantum many-body states*

Recent developments in quantum learning theory have established that a modest number of randomized measurements suffices to learn exponentially many properties of a quantum many-body system. However, implementing the appropriate randomized measurements requires universal local control over individual qubits, which is unavailable in many experimental platforms. Here, we generalize the framework of classical shadow tomography to systems where control over individual qubits and measurement capabilities are limited. Employing techniques from learning theory, we provide a general framework and specific algorithms for hardware-efficient learning with rigorous guarantees. We numerically demonstrate the effectiveness of our algorithms through the example of estimating energy densities in a U(1) lattice gauge theory with limited control. We also combine our framework with techniques from unsupervised learning to establish that certain topological states of matter can be distinguished even with very limited measurement capabilities.