Noisy quantum amplitude estimation without noise estimation

TL;DR

This paper introduces a method to accurately estimate quantum amplitudes in noisy quantum systems without needing to estimate the noise parameters, improving efficiency and robustness.

Contribution

It applies the theory of nuisance parameters and parameter orthogonalization to isolate the target amplitude estimation from noise estimation in quantum systems.

Findings

The proposed estimator performs well in numerical simulations.

Experimental validation on a superconducting quantum device shows effectiveness.

The method simplifies amplitude estimation in noisy quantum environments.

Abstract

Many quantum algorithms contain an important subroutine, the quantum amplitude estimation. As the name implies, this is essentially the parameter estimation problem and thus can be handled via the established statistical estimation theory. However, this problem has an intrinsic difficulty that the system, i.e., the real quantum computing device, inevitably introduces unknown noise; the probability distribution model then has to incorporate many nuisance noise parameters, resulting that the construction of an optimal estimator becomes inefficient and difficult. For this problem, we apply the theory of nuisance parameters (more specifically, the parameter orthogonalization method) to precisely compute the maximum likelihood estimator for only the target amplitude parameter, by removing the other nuisance noise parameters. That is, we can estimate the amplitude parameter without estimating the noise parameters. We validate the parameter orthogonalization method in a numerical simulation and study the performance of the estimator in the experiment using a real superconducting quantum device.