  We consider the problem of estimating quantum observables on a collection of
qubits, given as a linear combination of Pauli operators, with shallow quantum
circuits consisting of single-qubit rotations. We introduce estimators based on
randomised measurements, which use decision diagrams to sample from probability
distributions on measurement bases. This approach generalises previously known
uniform and locally-biased randomised estimators. The decision diagrams are
constructed given target quantum operators and can be optimised considering
different strategies. We show numerically that the estimators introduced here
can produce more precise estimates on some quantum chemistry Hamiltonians,
compared to previously known randomised protocols and Pauli grouping methods.
