Quantum-classical reinforcement learning for decoding noisy classical parity information

TL;DR

This paper introduces a quantum-classical reinforcement learning approach to efficiently decode noisy classical parity information, outperforming classical algorithms in sample complexity and robustness, especially when data is generated by classical oracles.

Contribution

It presents a novel quantum-classical reinforcement learning algorithm that reduces sample complexity for decoding noisy parity functions from classical data, bridging quantum advantages with practical classical data sources.

Findings

Quantum-classical RL outperforms classical algorithms in sample efficiency.

The method is robust to quantum circuit noise and classical noise.

Simulations up to 12-bit strings demonstrate practical advantages.

Abstract

Learning a hidden parity function from noisy data, known as learning parity with noise (LPN), is an example of intelligent behavior that aims to generalize a concept based on noisy examples. The solution to LPN immediately leads to decoding a random binary linear code in the presence of classification noise. This problem is thought to be intractable classically, but can be solved efficiently if a quantum oracle can be queried. However, in practice, a learner is more likely to receive data from classical oracles. In this work, we show that a naive application of the quantum LPN algorithm to classical data encoded in an equal superposition state requires an exponential sample complexity. We then propose a quantum-classical reinforcement learning algorithm to solve the LPN problem for data generated by a classical oracle and demonstrate a significant reduction in the sample complexity. Simulations with a hidden bit string of length up to 12 show that the quantum-classical reinforcement learning performs better than known classical algorithms when the sample complexity, run time, and robustness to classical noise are collectively considered. Our algorithm is robust to any noise in the quantum circuit that effectively appears as Pauli errors on the final state.