Adaptive estimation of quantum observables

The accurate estimation of quantum observables is a critical task in science. With progress on the hardware, measuring system will become increasingly demanding, particularly for variational protocols that require extensive sampling. Here, we introduce measurement scheme adaptively modifies estimator based previously obtained data. Our algorithm, which call AEQuO, continuously monitors both estimated average and associated error considered observable, determines next step this information. We allow overlap non-bitwise commutation relations subsets Pauli operators are simultaneously probed, thereby maximizing amount gathered AEQuO comes two variants: greedy bucket-filling algorithm with good performance small problem instances, machine learning-based more favorable scaling larger instances. configuration determined by these subroutines further post-processed order to lower estimator. test our protocol chemistry Hamiltonians, provides estimates improve all state-of-the-art methods various grouping techniques or randomized measurements, thus greatly lowering toll measurements current future applications.