Extreme dimensionality reduction with quantum modelling

Abstract

Effective and efficient forecasting relies on identification of the relevant information contained in past observations -- the predictive features -- and isolating it from the rest. When the future of a process bears a strong dependence on its behaviour far into the past, there are many such features to store, necessitating complex models with extensive memories. Here, we highlight a family of stochastic processes whose minimal classical models must devote unboundedly many bits to tracking the past. For this family, we identify quantum models of equal accuracy that can store all relevant information within a single two-dimensional quantum system (qubit). This represents the ultimate limit of quantum compression and highlights an immense practical advantage of quantum technologies for the forecasting and simulation of complex systems.

arXiv comment6+3 pages, 3+1 figures

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• Statistical Complexity of Quantum Learning
• Quantifying Non-Markovianity in Open Quantum Dynamics
• Ticking-clock performance enhanced by nonclassical temporal correlations
• Quantum coarse-graining for extreme dimension reduction in modelling stochastic temporal dynamics
• Accuracy vs Memory Advantage in the Quantum Simulation of Stochastic Processes
• Reconstructing Non-Markovian Open Quantum Evolution From Multi-time Measurements
• Scalable quantum measurement error mitigation via conditional independence and transfer learning
• Provable superior accuracy in machine learned quantum models
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• Analysis of Quantum Image Representations for Supervised Classification
• Ideal stochastic process modeling with post-quantum quasiprobabilistic theories
• Quantum Dimension Reduction of Hidden Markov Models