  The approximate state estimation and the closely related classical shadows
methods allow for the estimation of complicated observables with relatively few
shots. As these methods make use of random measurements that can symmetrise the
effect of readout errors, they have been shown to permit simplified approaches
to readout error mitigation which require only a number of samples that scales
as $\mathcal{O}(1)$ with increasing numbers of qubits. However, these
techniques require executing a different circuit at each shot, adding a
typically prohibitive amount of latency that prohibits their practical
application. In this manuscript we consider the approximate state estimation of
readout-mitigated expectation values, and how to best implement that procedure
on the Rigetti quantum computing hardware. We discuss the theoretical aspects
involved, providing an explicit computation of the effect of readout error on
the estimated expectation values and how to mitigate that effect. Leveraging
improvements to the Rigetti control systems, we then demonstrate an efficient
implementation of this approach. Not only do we find that we can suppress the
effect of correlated errors and accurately mitigate the readout errors, we find
that we can do so quickly, collecting and processing $10^6$ samples in less
than $1.5$ minutes. This development opens the way for practical uses of
methods with this type of randomisation.
