K-body Pauli error estimation

Learning the Pauli error rates of arbitrary channels remains an important aspirational aim for multi-qubit devices. Such information is vital in error mitigation as well as the design of codes and bespoke decoders for error correction, especially as quantum devices inch towards full error correcting thresholds. Clearly it is not possible to learn (or even represent) the full Pauli error channel for devices much larger than, say, 20 qubits. In order to maintain efficiency, existing protocols require some assumptions, typically assuming the Pauli channel is sparse or k-local. Recently Flammia and O'Donnell showed how to recover all Pauli error terms of an arbitrary Pauli error channel to a precision of epsilon using population recovery techniques. Here we build on that work, seeking to retain a practical implementation but removing measurement error and increasing relative precision; albeit at the cost of limiting the recovery to Pauli error terms that act non-trivially on only k or fewer qubits.