Foundations for Bayesian inference with engineered likelihood functions for robust amplitude estimation

We present mathematical and conceptual foundations for the task of robust amplitude estimation using engineered likelihood functions (ELFs), a framework introduced by Wang et al. [PRX Quantum 2, 010346 (2021)] that uses Bayesian inference to enhance the rate of information gain in quantum sampling....

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Bibliographic Details
Published in:Journal of mathematical physics 2022-05, Vol.63 (5)
Main Authors: Koh, Dax Enshan, Wang, Guoming, Johnson, Peter D., Cao, Yudong
Format: Article
Language:English
Subjects:
Amplitudes
Bayesian analysis
Circuits
Foundations
Parameter estimation
Physics
Robustness (mathematics)
Statistical inference
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Summary:We present mathematical and conceptual foundations for the task of robust amplitude estimation using engineered likelihood functions (ELFs), a framework introduced by Wang et al. [PRX Quantum 2, 010346 (2021)] that uses Bayesian inference to enhance the rate of information gain in quantum sampling. These ELFs, which are obtained by choosing tunable parameters in a parametrized quantum circuit to minimize the expected posterior variance of an estimated parameter, play an important role in estimating the expectation values of quantum observables. We give a thorough characterization and analysis of likelihood functions arising from certain classes of quantum circuits and combine this with the tools of Bayesian inference to give a procedure for picking optimal ELF tunable parameters. Finally, we present numerical results to demonstrate the performance of ELFs.
ISSN:0022-2488
1089-7658
DOI:10.1063/5.0042433