# Tangible reduction in learning sample complexity with large classical samples and small quantum system

## TL;DR

This paper demonstrates that a classical-quantum hybrid approach can significantly reduce the number of samples needed for learning in noisy quantum systems by leveraging large classical datasets with small quantum devices.

## Contribution

It introduces a hybrid architecture that reduces sample complexity and enhances noise immunity in quantum learning tasks, suitable for NISQ devices.

## Key findings

- Hybrid oracle's noise immunity improves query success rate
- Sample complexity is reduced in PAC learning framework
- Large classical data can be effectively embedded with small quantum systems

## Abstract

Quantum computation requires large classical datasets to be embedded into quantum states in order to exploit quantum parallelism. However, this embedding requires considerable resources. It would therefore be desirable to avoid it, if possible, for noisy intermediate-scale quantum (NISQ) implementation. Accordingly, we consider a classical-quantum hybrid architecture, which allows large classical input data, with a relatively small-scale quantum system. This hybrid architecture is used to implement an oracle. It is shown that in the presence of noise in the hybrid oracle, the effects of internal noise can cancel each other out and thereby improve the query success rate. It is also shown that such an immunity of the hybrid oracle to noise directly and tangibly reduces the sample complexity in the probably-approximately-correct learning framework. This NISQ-compatible learning advantage is attributed to the oracle's ability to handle large input features.