Iterative Quantum Amplitude Estimation

TL;DR

The paper introduces Iterative Quantum Amplitude Estimation (IQAE), a new quantum algorithm that achieves quadratic speedup over classical methods without relying on quantum phase estimation, reducing qubit and gate requirements.

Contribution

IQAE is a novel variant of QAE that eliminates the need for QPE, simplifying implementation and improving efficiency, with rigorous analysis and empirical validation.

Findings

IQAE achieves quadratic speedup over classical Monte Carlo.

IQAE requires fewer samples than previous QAE variants.

Empirical results show IQAE outperforms other methods by orders of magnitude.

Abstract

We introduce a new variant of Quantum Amplitude Estimation (QAE), called Iterative QAE (IQAE), which does not rely on Quantum Phase Estimation (QPE) but is only based on Grover's Algorithm, which reduces the required number of qubits and gates. We provide a rigorous analysis of IQAE and prove that it achieves a quadratic speedup up to a double-logarithmic factor compared to classical Monte Carlo simulation. Furthermore, we show with an empirical study that our algorithm outperforms other known QAE variants without QPE, some even by orders of magnitude, i.e., our algorithm requires significantly fewer samples to achieve the same estimation accuracy and confidence level.