  Noise in pre-fault-tolerant quantum computers can result in biased estimates
of physical observables. Accurate bias-free estimates can be obtained using
probabilistic error cancellation (PEC), which is an error-mitigation technique
that effectively inverts well-characterized noise channels. Learning correlated
noise channels in large quantum circuits, however, has been a major challenge
and has severely hampered experimental realizations. Our work presents a
practical protocol for learning and inverting a sparse noise model that is able
to capture correlated noise and scales to large quantum devices. These advances
allow us to demonstrate PEC on a superconducting quantum processor with
crosstalk errors, thereby providing an important milestone in opening the way
to quantum computing with noise-free observables at larger circuit volumes.
