  Error mitigation will play an important role in practical applications of
near-term noisy quantum computers. Current error mitigation methods typically
concentrate on correction quality at the expense of frugality (as measured by
the number of additional calls to quantum hardware). To fill the need for
highly accurate, yet inexpensive techniques, we introduce an error mitigation
scheme that builds on Clifford data regression (CDR). The scheme improves the
frugality by carefully choosing the training data and exploiting the symmetries
of the problem. We test our approach by correcting long range correlators of
the ground state of XY Hamiltonian on IBM Toronto quantum computer. We find
that our method is an order of magnitude cheaper while maintaining the same
accuracy as the original CDR approach. The efficiency gain enables us to obtain
a factor of $10$ improvement on the unmitigated results with the total budget
as small as $2\cdot10^5$ shots.
