Efficient algorithms for quantum information bottleneck

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.

arXiv commentaccepted by Quantum

References in corpus (22)

• Quantum Machine Learning
• Quantum algorithm for solving linear systems of equations
• Supervised learning with quantum enhanced feature spaces
• The information bottleneck method
• Quantum machine learning in feature Hilbert spaces
• An introduction to quantum machine learning
• Hamiltonian Simulation by Qubitization
• Data re-uploading for a universal quantum classifier
• Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics
• Supervised quantum machine learning models are kernel methods
• Generalization in Quantum Machine Learning: a Quantum Information Perspective
• Quantum Data Compression of a Qubit Ensemble
• Efficient compression of quantum information
• Hamiltonian Simulation by Uniform Spectral Amplification
• Computing Quantum Channel Capacities
• Optimal compression for identically prepared qubit states
• Efficient Quantum Compression for Ensembles of Identically Prepared Mixed States
• Convexity and Operational Interpretation of the Quantum Information Bottleneck Function
• Quantum Rate-Distortion Coding of Relevant Information
• Quantum Stopwatch: How To Store Time in a Quantum Memory
• Compression for quantum population coding
• Quantum Predictive Filtering

Cited by in corpus (6)

• Kerr-effect-based quantum logical gates in decoherence-free subspace
• Efficient Computation of the Quantum Rate-Distortion Function
• Generalized quantum Arimoto-Blahut algorithm and its application to quantum information bottleneck
• Iterative minimization algorithm on a mixture family
• Chernoff Information Bottleneck for Covert Quantum Target Sensing
• Disentangling quantum autoencoder