Efficient algorithms for quantum information bottleneck

TL;DR

This paper introduces a fast, general algorithm for the quantum information bottleneck problem, enabling efficient extraction of relevant quantum information and demonstrating quantum advantage over classical systems.

Contribution

It presents a novel, efficient algorithm for the quantum information bottleneck, extending to broader problem variants and showing quantum systems can outperform classical ones.

Findings

The algorithm outperforms previous methods in speed and convergence.

It applies to a wider range of problems including the quantum deterministic information bottleneck.

Quantum systems can achieve better performance than classical counterparts in information bottleneck tasks.

Abstract

The ability to extract relevant information is critical to learning. An ingenious approach as such is the information bottleneck, an optimisation problem whose solution corresponds to a faithful and memory-efficient representation of relevant information from a large system. The advent of the age of quantum computing calls for efficient methods that work on information regarding quantum systems. Here we address this by proposing a new and general algorithm for the quantum generalisation of information bottleneck. Our algorithm excels in the speed and the definiteness of convergence compared with prior results. It also works for a much broader range of problems, including the quantum extension of deterministic information bottleneck, an important variant of the original information bottleneck problem. Notably, we discover that a quantum system can achieve strictly better performance than a classical system of the same size regarding quantum information bottleneck, providing new vision on justifying the advantage of quantum machine learning.