Entanglement-enhanced learning of quantum processes at scale

Learning unknown processes affecting a quantum system reveals underlying physical mechanisms and enables suppression, mitigation, and correction of unwanted effects. Describing a general quantum process requires an exponentially large number of parameters. Measuring these parameters, when they are encoded in incompatible observables, is constrained by the uncertainty principle and requires exponentially many measurements. However, for Pauli channels, having access to an ideal quantum memory and entangling operations allows encoding parameters in commuting observables, thereby exponentially reducing measurement complexity. 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, there is a separation in efficiency between learning Pauli channels with and without entanglement with noisy quantum memory. We demonstrate our protocol's efficacy in examples including hypothesis testing with up to 64 qubits and learning inherent noise processes in a layer of parallel gates using up to 16 qubits on a superconducting quantum processor. Our protocol provides accurate and practical information about the process, with an overhead factor of $1.33 \pm 0.05$ per qubit, much smaller than the fundamental lower bound of 2 without entanglement with quantum memory. Our study demonstrates that entanglement with auxiliary noisy quantum memory combined with error mitigation considerably enhances the learning of quantum processes.