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arXiv · 2006.09349

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

Dax Enshan Koh·Guoming Wang·Peter D. Johnson·Yudong Cao
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Abstract

We present mathematical and conceptual foundations for the task of robust amplitude estimation using engineered likelihood functions (ELFs), a framework introduced in 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.

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Dax Enshan Koh, Guoming Wang, Peter D. Johnson, Yudong Cao. 2020-06-16. Foundations for Bayesian inference with engineered likelihood functions for robust amplitude estimation. https://doi.org/10.1063/5.0042433

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