  The readout error on the near-term quantum devices is one of the dominant
noise factors, which can be mitigated by classical post-processing called
quantum readout error mitigation (QREM). The standard QREM method applies the
inverse of noise calibration matrix to the outcome probability distribution
using exponential computational resources to the system size. Hence this
standard approach is not applicable to the current quantum devices with tens of
qubits and more. We propose two efficient QREM methods on such devices whose
computational complexity is $O(ns^2)$ for probability distributions on
measuring $n$ qubits with $s$ shots. The main targets of the proposed methods
are the sparse probability distributions where only a few states are dominant.
We compare the proposed methods with several recent QREM methods on the
following three cases: expectation values of GHZ state, its fidelities, and the
estimation error of maximum likelihood amplitude estimation (MLAE) algorithm
with modified Grover iterator. The two cases of the GHZ state are on real IBM
quantum devices, while the third is by numerical simulation. The proposed
methods can be applied to mitigate GHZ states up to 65 qubits on IBM Quantum
devices within a few seconds to confirm the existence of a 29-qubit GHZ state
with fidelity larger than 0.5. The proposed methods also succeed in the
estimation of the amplitude in MLAE with the modified Grover operator where
other QREM methods fail.
