Single-shot quantum neural networks with amplitude estimation

TL;DR

This paper introduces a single-shot quantum neural network framework using amplitude estimation, significantly reducing sampling errors and improving inference efficiency on quantum hardware.

Contribution

It integrates quantum amplitude estimation into QNNs, enabling single-shot inference with lower error, a novel approach to overcoming quantum sampling bottlenecks.

Findings

AE-based QNN inference achieves $ ext{O}(1/N)$ error with a single shot.

The approach improves noise robustness and training feasibility.

Quantum algorithms can enhance the efficiency of quantum models.

Abstract

Quantum neural networks (QNNs) suffer from a fundamental sampling bottleneck since quantum measurements are probabilistic, requiring many circuit executions to estimate outputs with sufficient accuracy. Conventional Monte-Carlo (MC) inference exhibits an $\mathcal{O}(1/\sqrt{N})$ sampling error, rendering QNN inference and training costly on near-term quantum hardware, especially where each shot requires expensive qubit generation. This work introduces a "single-shot" QNN framework by integrating quantum amplitude estimation (AE) into the readout stage. By embedding a trained QNN as a state-preparation oracle within AE, outputs are estimated through coherent interference rather than repeated sampling. We demonstrate that AE-based QNN inference achieves an $\mathcal{O}(1/N)$ error even with a single shot. We further analyze noise robustness and training feasibility, showing that AE can be a powerful primitive for overcoming the sampling overhead of QNNs. This highlights that when the model itself is quantum, quantum algorithms can enhance the computation efficiency.