用工程似然函数进行鲁棒幅度估计的贝叶斯推断的基础
Foundations for Bayesian inference with engineered likelihood functions for robust amplitude estimation
摘要：
我们提出了使用工程似然函数（ELF）进行鲁棒幅度估计任务的数学和概念基础，这是Wang等人[PRX Quantum 2，010346（2021）]中引入的一种框架，使用贝叶斯推断来提高量子采样中的信息增益率。这些ELF是通过在参数化量子线路中选择可调参数以最小化被估计参数的期望后验方差而获得的，在量子可观测量的期望值估计中起着重要的作用。我们给出了一个彻底的表征和分析的似然函数所产生的某些类的量子电路，并结合这与贝叶斯推断的工具，给出一个程序，挑选最佳ELF可调参数。最后，我们提出了数值结果来证明ELF的性能。
英文摘要：
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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