  Using near-term quantum computers to achieve a quantum advantage requires
efficient strategies to improve the performance of the noisy quantum devices
presently available. We develop and experimentally validate two efficient error
mitigation protocols named "Noiseless Output Extrapolation" and "Pauli Error
Cancellation" that can drastically enhance the performance of quantum circuits
composed of noisy cycles of gates. By combining popular mitigation strategies
such as probabilistic error cancellation and noise amplification with efficient
noise reconstruction methods, our protocols can mitigate a wide range of noise
processes that do not satisfy the assumptions underlying existing mitigation
protocols, including non-local and gate-dependent processes. We test our
protocols on a four-qubit superconducting processor at the Advanced Quantum
Testbed. We observe significant improvements in the performance of both
structured and random circuits, with up to $86\%$ improvement in variation
distance over the unmitigated outputs. Our experiments demonstrate the
effectiveness of our protocols, as well as their practicality for current
hardware platforms.
