We develop quantum algorithms that construct block-encodings of solution matrices for continuous- and discrete-time algebraic Riccati equations (CAREs and DAREs), differential Riccati equations (DREs), and finite Riccati recursions. The Quantum Weighted Riesz Method, unifying four kinds of Riccati problems, constructs...
Jing-Yao Wang, Yan-Qiao Wang, Bo-Wen Li et al.· 0 citations
If each coordinate appears in only a small number of clauses, there is a quantum algorithm for strongly log-concave sampling using local queries using $\widetilde{O}(\sqrt{\kappa}d)$ local queries, where $\kappa$ is the condition number.
Hao, Huang, and Liu (STOC'26) recently showed that optimal quantum query complexity may require large workspace even for short-output problems, and asked whether a quantum query advantage over classical computation can itself require space. We resolve this question by exhibiting an explicit total Boolean function with...
A dimension-free version of the retained-energy form of the Mallat--Zeitouni conjecture is established, showing that the KL basis is within this factor of the optimal basis, and shows that the possible advantage of optimizing over all orthonormal bases vanishes as $d$ grows.
Minbo Gao, Zheng-Feng Ji, Cheng-Hua Liu· 0 citations
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