Compare Papers
Paper 1
Characterizing the Burst Error Correction Ability of Quantum Cyclic Codes
Jihao Fan, Min-Hsiu Hsieh
- Year
- 2026
- Journal
- IEEE Transactions on Information Theory
- DOI
- 10.1109/tit.2026.3659999
- arXiv
- -
No abstract.
Open paperPaper 2
Direct Variational Calculation of Two-Electron Reduced Density Matrices via Semidefinite Machine Learning
Luis H. Delgado-Granados, David A. Mazziotti
- Year
- 2026
- Journal
- arXiv preprint
- DOI
- arXiv:2603.05524
- arXiv
- 2603.05524
We introduce a data-driven framework for approximating the convex set of $N$-representable two-electron reduced density matrices (2-RDMs). Traditional approaches characterize this set through linear matrix inequalities that define its supporting hyperplanes. Here, we instead learn a vertex-based approximation to its boundary from molecular data and use this information to improve the set defined by low-order positivity constraints, without explicitly constructing higher-order conditions. The resulting semidefinite machine learning approach -- combining an input convex neural network with semidefinite programming -- drives a direct variational calculation of the 2-RDM with enhanced accuracy at computational cost comparable to two-positivity calculations. Applications to the potential energy curves of ${\rm C}_2^{2-}$, ${\rm N}_2$, and ${\rm O}_2^{2+}$ demonstrate these systematic improvements as well as close agreement with complete active space configuration interaction results. Overall, semidefinite machine learning interweaves data-driven boundary information with semidefinite positivity constraints to yield more accurate energies and 2-RDMs without explicit higher-order positivity conditions.
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