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Newton-Schulz Retraction-Based Inference Enables Hidden Quantum Markov Models to Outperform Classical HMMs — arXiv:2608.06554

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.06554
License (as archived): CC0-1.0
Archived: 2026-10-19T11:04:38.398Z
SHA-256 of the archived text: d83c718f8a6319e72119943a70440a4acea06a1d90bcb3a5b31dadb016a74022
Stable URL of this page: https://metraipolis.com/documento/dc_d7eab2bbdc2b

How to cite

Newton-Schulz Retraction-Based Inference Enables Hidden Quantum Markov Models to Outperform Classical HMMs — arXiv:2608.06554 — arXiv (en), https://arxiv.org/abs/2608.06554 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_d7eab2bbdc2b (Metraipolis archive dc_d7eab2bbdc2b, sha256 d83c718f8a6319e72119943a70440a4acea06a1d90bcb3a5b31dadb016a74022)

BibTeX

@misc{dcd7eab2bbdc2b,
  title = {Newton-Schulz Retraction-Based Inference Enables Hidden Quantum Markov Models to Outperform Classical HMMs — arXiv:2608.06554},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.06554},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_d7eab2bbdc2b; sha256 d83c718f8a6319e72119943a70440a4acea06a1d90bcb3a5b31dadb016a74022},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.06554. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Hidden Markov models (HMMs) are widely used probabilistic models for discrete sequential data but can be limited when hidden dynamics are complex. Hidden quantum Markov models (HQMMs) generalize HMMs by replacing probability vectors with density matrices and stochastic transitions with quantum operations, enabling richer latent representations. However, existing HQMM learning methods have not consistently outperformed Expectation--Maximization (EM)-trained HMMs on data not generated by quantum processes, limiting their practical applicability. We introduce NS-RIS, Newton--Schulz Retraction-based Inference on the Stiefel manifold, a scalable algorithm for learning trace-preserving HQMMs. NS-RIS uses Newton--Schulz orthogonalization to compute a polar-factor search direction while preserving Stiefel-manifold feasibility, avoiding costly matrix decompositions. We further establish a finite-time stationarity guarantee under standard assumptions on smoothness, stochastic gradients, and finite Newton--Schulz accuracy. Empirically, NS-RIS provides the first benchmark evidence that an HQMM can significantly outperform an EM-trained HMM on data not generated by a quantum model. On synthetic HMM-generated benchmarks, NS-RIS outperforms both EM and the state-of-the-art HQMM method COSM, improving the evaluation metric by an average of 38.5% and by up to 50.6%. On a synthetic HQMM benchmark, it improves the test metric over COSM by 18.9% while reducing runtime by 12.0%. On the real-world Splice classification benchmark, NS-RIS also surpasses both EM and COSM in higher-dimensional latent regimes, reducing mean classification error by 17.9% for latent dimension 6 and 14.9% for latent dimension 8 relative to COSM. These results move HQMMs beyond a theoretical generalization of HMMs and establish them as practical and expressive models for scientific sequence data.

Tema degli esploratori: statistica e scienza dei dati (retro-catalogo arXiv: annunci del 2026-08-10 in stat.ME).
Categorie arXiv: Machine Learning (cs.LG) ; Quantum Physics (quant-ph); Methodology (stat.ME).
Pagina del lavoro: https://arxiv.org/abs/2608.06554 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-19T11:02:56.770Z dalla pagina https://arxiv.org/catchup/stat.ME/2026-08-10?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).