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Brand\~ao and Svore very recently gave quantum algorithms for approximately solving semidefinite programs, which in some regimes are faster than the best-possible classical algorithms in terms of the dimension $n$ of the problem and the number $m$ of constraints, but worse in terms of various other parameters.
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Joran van Apeldoorn, András Gilyén, Sander Gribling, and Ronald de Wolf · 2017
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Quantum speed-ups for solving semidefinite programs
Fernando G. S. L. Brandão and Krysta M. Svore · 2017
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Andrew M. Childs, Robin Kothari, and Rolando D. Somma · 2017
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Quantum algorithms for Gibbs sampling and hitting-time estimation
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