Perturbative readout-error mitigation for near-term quantum computers

Readout errors on near-term quantum computers can introduce significant error to the empirical probability distribution sampled from output of a circuit. These be mitigated by classical postprocessing given access an experimental \emph{response matrix} that describes associated with measurement each computational basis state. However, resources required characterize complete response matrix and compute corrected scale exponentially in number qubits $n$. In this work, we modify standard inversion techniques using two perturbative approximations significantly reduced complexity bounded when likelihood high order bitflip events is strongly suppressed. Given characteristic rate $q$, our first method recovers all-zeros bitstring $p_0$ sampling only small subspace before inverting readout resulting relative speedup $\text{poly}\left(2^{n} / \big(\begin{smallmatrix} n \\ w \end{smallmatrix}\big)\right)$, which motivate simplified model for approximation incurs $O(q^w)$ some integer $w$. We then provide generalized technique efficiently recover full distributions limit. approximate correction may greatly accelerate near term computing applications.