  Reducing measurement errors in multi-qubit quantum devices is critical for
performing any quantum algorithm. Here we show how to mitigate measurement
errors by a classical post-processing of the measured outcomes. Our techniques
apply to any experiment where measurement outcomes are used for computing
expected values of observables. Two error mitigation schemes are presented
based on tensor product and correlated Markovian noise models. Error rates
parameterizing these noise models can be extracted from the measurement
calibration data using a simple formula. Error mitigation is achieved by
applying the inverse noise matrix to a probability vector that represents the
outcomes of a noisy measurement. The error mitigation overhead, including the
the number of measurements and the cost of the classical post-processing, is
exponential in $\epsilon n$, where $\epsilon$ is the maximum error rate and $n$
is the number of qubits. We report experimental demonstration of our error
mitigation methods on IBM Quantum devices using stabilizer measurements for
graph states with $n\le 12$ qubits and entangled 20-qubit states generated by
low-depth random Clifford circuits.
