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Non-orthogonal quantum eigensolver [U. Baek et al., PRX Quantum 4, 030307 (2023)] is a promising algorithm for solving the electronic structure problem of quantum chemistry using early-fault-tolerant quantum computers. In this algorithm, each element of...

A longstanding open question in algorithm design is whether "combinatorial" matrix multiplication algorithms -- avoiding Strassen-like divide-and-conquer -- can achieve truly subcubic runtime $n^{3-\delta}$. We present an $O(n^{2.89})$-time exact algorithm...