Adaptive estimation of quantum observables

TL;DR

AEQuO is an adaptive measurement scheme for quantum observables that optimizes data collection, improving accuracy and reducing measurement costs in quantum experiments, especially for chemistry Hamiltonians.

Contribution

The paper introduces AEQuO, a novel adaptive measurement protocol that dynamically adjusts measurement strategies based on ongoing data, enhancing efficiency over existing methods.

Findings

AEQuO improves error estimates compared to state-of-the-art methods.

AEQuO reduces the number of measurements needed in quantum experiments.

AEQuO performs well on chemistry Hamiltonians, demonstrating practical advantages.

Abstract

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