  Error-mitigation techniques such as probabilistic error cancellation and
zero-noise extrapolation benefit from accurate noise models. The sparse
Pauli-Lindblad noise model is one of the most successful models for those
applications. In existing implementations, the model decomposes into a series
of simple Pauli channels with one- and two-local terms that follow the qubit
topology. While the model has been shown to accurately capture the noise in
contemporary superconducting quantum processors for error mitigation, it is
important to consider higher-weight terms and effects beyond nearest-neighbor
interactions. For such extended models to remain practical, however, we need to
ensure that they can be learned efficiently. In this work we present new
techniques that accomplish exactly this. We introduce twirling based on Pauli
rotations, which enables us to automatically generate single-qubit learning
correction sequences and reduce the number of unique fidelities that need to be
learned. In addition, we propose a basis-selection strategy that leverages
graph coloring and uniform covering arrays to minimize the number of learning
bases. Taken together, these techniques ensure that the learning of the
extended noise models remains efficient, despite their increased complexity.
