Quantum amplitude estimation from classical signal processing

TL;DR

This paper introduces a novel quantum amplitude estimation method that leverages classical signal processing techniques, specifically DOA estimation algorithms, to achieve improved query complexity and robustness.

Contribution

It maps quantum amplitude estimation to classical DOA estimation, enabling the use of existing signal processing algorithms for more efficient quantum measurement processing.

Findings

Achieves a worst-case sequential query complexity of ~4.3/ε.

Achieves a parallel query complexity of ~0.26/ε at 95% confidence.

Outperforms previous quantum amplitude estimation methods by 16 times in query complexity.

Abstract

We demonstrate that the problem of amplitude estimation, a core subroutine used in many quantum algorithms, can be mapped directly to a problem in signal processing called direction of arrival (DOA) estimation. The DOA task is to determine the direction of arrival of an incoming wave with the fewest possible measurements. The connection between amplitude estimation and DOA allows us to make use of the vast amount of signal processing algorithms to post-process the measurements of the Grover iterator at predefined depths. Using an off-the-shelf DOA algorithm called ESPRIT together with a compressed-sensing based sampling approach, we create a phase-estimation free, parallel quantum amplitude estimation (QAE) algorithm with a worst-case sequential query complexity of $\sim 4.3/\varepsilon$ and a parallel query complexity of $\sim 0.26/\varepsilon$ at 95% confidence. This performance is statistically equivalent and a $16\times$ improvement over Rall and Fuller [Quantum 7, 937 (2023)], for sequential and parallel query complexity respectively, which to our knowledge is the best published result for amplitude estimation. The approach presented here provides a simple, robust, parallel method to performing QAE, with many possible avenues for improvement borrowing ideas from the wealth of literature in classical signal processing.