Accelerated Quantum Amplitude Estimation without QFT

TL;DR

This paper introduces a quantum amplitude estimation algorithm that outperforms previous methods by eliminating the need for the Quantum Fourier Transform, achieving lower complexity and faster classical computation, with proven correctness.

Contribution

The paper presents a new quantum amplitude estimation algorithm that does not rely on QFT and offers improved quantum and classical computational efficiency.

Findings

Quantum amplitude estimation without QFT is feasible.

The algorithm achieves $O(1/\varepsilon)$ quantum complexity.

Tighter bounds on complexity are supported by computer-assisted estimates.

Abstract

We put forward a Quantum Amplitude Estimation algorithm delivering superior performance (lower quantum computational complexity and faster classical computation parts) compared to the approaches available to-date. The algorithm does not relay on the Quantum Fourier Transform and its quantum computational complexity is of order $O(\frac{1}{\varepsilon})$ in terms of the target accuracy $\varepsilon>0$. The $O(\frac{1}{\varepsilon})$ bound on quantum computational complexity is also superior compared to those in the earlier approaches due to smaller constants. Moreover, a much tighter bound is obtained by means of computer-assisted estimates for the expected value of quantum computational complexity. The correctness of the algorithm and the $O(\frac{1}{\varepsilon})$ bound on quantum computational complexity are supported by precise proofs.