Efficient algorithms for quantum information bottleneck

Masahito Hayashi1,2,3,4 and Yuxiang Yang5

1Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen,518055, China
2International Quantum Academy (SIQA), Futian District, Shenzhen 518048, China
3Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen, 518055, China
4Graduate School of Mathematics, Nagoya University, Nagoya, 464-8602, Japan
5QICI Quantum Information and Computation Initiative, Department of Computer Science, The University of Hong Kong, Pokfulam Road, Hong Kong

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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.

Imagine that a large amount of data about the weather are generated. In order to predict tomorrow's weather, such a large amount of data is difficult to handle, and it is needed to extract essential information T from the original large data X. The information bottleneck realizes this objective of information extraction by minimizing a certain informational quantity.

The advent of the age of quantum computing calls for information bottleneck algorithms that work for quantum systems. In this work, we design such an algorithm that works generally when either (or both) of T and Y is a quantum system. Our algorithm excels in the speed and the definiteness of convergence compared with prior results. Remarkably, we found a genuine advantage of using a quantum system as the new database T, which suggests that quantum systems could be better at representing key features in machine learning.

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