Entanglement-enhanced learning of quantum noise at scale

Learning unknown processes affecting a quantum system reveals underlying physical mechanisms and enables suppression, mitigation, and correction of unwanted effects. Generally, learning quantum processes requires exponentially many measurements. We show how entanglement with an ideal auxiliary quantum memory can provide an exponential advantage in learning certain quantum processes. In practice, though, quantum memory and entangling operations are always noisy and introduce errors, making the advantage of using noisy quantum memory unclear. To address these challenges, we introduce error-mitigated entanglement-enhanced learning and show, both theoretically and experimentally, that even with noise, entanglement with auxiliary quantum memory combined with error mitigation considerably enhances the learning of quantum processes.