Modified Grover operator for amplitude estimation

TL;DR

This paper introduces a modified Grover operator for quantum amplitude estimation that enhances accuracy and robustness under noise, outperforming conventional methods especially with simple measurement strategies.

Contribution

It proposes a novel modified Grover operator for amplitude estimation that improves accuracy and noise resilience, approaching quantum Fisher information limits.

Findings

Quadratic improvement in estimation accuracy with the modified operator

Outperforms conventional methods under depolarizing noise

Achieves near ultimate quantum Fisher information accuracy with simple measurements

Abstract

In this paper, we propose a quantum amplitude estimation method that uses a modified Grover operator and quadratically improves the estimation accuracy in the ideal case, as in the conventional one using the standard Grover operator. Under the depolarizing noise, the proposed method can outperform the conventional one in the sense that it can in principle achieve the ultimate estimation accuracy characterized by the quantum Fisher information in the limit of a large number of qubits, while the conventional one cannot achieve the same value of ultimate accuracy. In general this superiority requires a sophisticated adaptive measurement, but we numerically demonstrate that the proposed method can outperform the conventional one and approach to the ultimate accuracy, even with a simple non-adaptive measurement strategy.