  Noise in quantum hardware remains the biggest roadblock for the
implementation of quantum computers. To fight the noise in the practical
application of near-term quantum computers, instead of relying on quantum error
correction which requires large qubit overhead, we turn to quantum error
mitigation, in which we make use of extra measurements. Error extrapolation is
an error mitigation technique that has been successfully implemented
experimentally. Numerical simulation and heuristic arguments have indicated
that exponential curves are effective for extrapolation in the large circuit
limit with an expected circuit error count around unity. In this article, we
extend this to multi-exponential error extrapolation and provide more rigorous
proof for its effectiveness under Pauli noise. This is further validated via
our numerical simulations, showing orders of magnitude improvements in the
estimation accuracy over single-exponential extrapolation. Moreover, we develop
methods to combine error extrapolation with two other error mitigation
techniques: quasi-probability and symmetry verification, through exploiting
features of these individual techniques. As shown in our simulation, our
combined method can achieve low estimation bias with a sampling cost multiple
times smaller than quasi-probability while without needing to be able to adjust
the hardware error rate as required in canonical error extrapolation.
