Adaptive estimation of quantum observables
- URL: http://arxiv.org/abs/2110.15339v6
- Date: Fri, 20 Jan 2023 00:36:23 GMT
- Title: Adaptive estimation of quantum observables
- Authors: Ariel Shlosberg, Andrew J. Jena, Priyanka Mukhopadhyay, Jan F. Haase,
Felix Leditzky, Luca Dellantonio
- Abstract summary: 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.
We test our protocol on chemistry Hamiltonians, for which AEQuO provides error estimates that improve on all state-of-the-art methods.
- Score: 4.567122178196833
- License: http://creativecommons.org/licenses/by/4.0/
- 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.
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