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Probability-Preserving Transformer for the Time-Dependent Schr\"odinger Equation

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Computer Science > Machine Learning

arXiv:2608.15112 (cs)
[Submitted on 15 Aug 2026]

Title:Probability-Preserving Transformer for the Time-Dependent Schrödinger Equation

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Abstract:Solving the time-dependent Schrödinger equation (TDSE) via traditional numerical methods is computationally intensive. Transformer models offer a compelling alternative, but standard implementations rely on soft constraints that cannot rigorously guarantee probability conservation. Here, we introduce a Transformer architecture that enforces TDSE probability conservation as a hard constraint. The design intrinsically ensures unitarity across temporal evolution without requiring repeated retraining. Our empirical findings show that this hard-constraint approach is not only physically exact but also computationally superior to conventional soft-constraint methods.
Comments: 9 pages, 7 figures
Subjects: Machine Learning (cs.LG); Mathematical Physics (math-ph); Quantum Physics (quant-ph)
Cite as: arXiv:2608.15112 [cs.LG]
  (or arXiv:2608.15112v1 [cs.LG] for this version)
  https://doi.org/10.48550/arXiv.2608.15112
arXiv-issued DOI via DataCite (pending registration)

Submission history

From: Niaz Ali Khan Ph.D. [view email]
[v1] Sat, 15 Aug 2026 08:29:20 UTC (683 KB)
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