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About this paper
Paul M. Riechers, Thomas J. Elliott
Researchers at the Beyond Institute for Theoretical Science (BITS) and the University of Manchester resolved the identifiability problem for classical, quantum, and 'post-quantum' models of classical stochastic processes, establishing that models are equivalent if they map to the same canonical Generalized Hidden Markov Model. They also derived a lower bound of d_min ≥ √ℓ_min for minimal quantum memory dimension, where ℓ_min is the minimal GHMM dimension, demonstrating a potential quadratic quantum advantage in some cases.
Key insights
- All diverse generative models (classical, quantum, 'post-quantum') can be mapped to a unique, minimal "standard Generalized Hidden Markov Model" (GHMM), which acts as a canonical form for comparison.
- Two models are observationally equivalent if and only if they generate identical probabilities for a finite set of past and future words, bounded by a maximal length related to the models' memory dimensions.
- Quantum models (QHMMs) have a fundamental lower bound on their memory dimension, d_min ≥ √ℓ_min, where ℓ_min is the dimension of the minimal GHMM for the process.
Summary by alphaXiv.
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