Real Quantum Amplitude Estimation

TL;DR

The paper introduces Real Quantum Amplitude Estimation (RQAE), an iterative quantum algorithm that detects the sign of amplitudes, offering a quadratic speedup over traditional sampling methods, supported by theoretical and numerical validation.

Contribution

It presents RQAE, a novel amplitude estimation algorithm sensitive to amplitude signs with controllable amplification, extending the capabilities of existing quantum algorithms.

Findings

Achieves quadratic speedup over unamplified sampling

Provides explicit control over amplification policy

Validated through numerical experiments

Abstract

We introduce the Real Quantum Amplitude Estimation (RQAE) algorithm, an extension of Quantum Amplitude Estimation (QAE) which is sensitive to the sign of the amplitude. RQAE is an iterative algorithm which offers explicit control over the amplification policy through an adjustable parameter. We provide a rigorous analysis of the RQAE performance and prove that it achieves a quadratic speedup, modulo logarithmic corrections, with respect to unamplified sampling. Besides, we corroborate the theoretical analysis with a set of numerical experiments.