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Near-Optimal Lower Bounds For Convex Optimization For All Orders of Smoothness
We study the complexity of optimizing highly smooth convex functions.
Optimal learning of quantum Hamiltonians from high-temperature Gibbs states
In the appendix, we show that virtually the same algorithm can be used to learn $H$ from a real-time evolution unitary $e^{-it H}$ in a small $t$ regime with similar sample and time complexity.
Unambiguous DNFs and Alon-Saks-Seymour
We exhibit an unambiguous k-DNF formula that requires CNF width $\tilde{\Omega}(k^2)$, which is optimal up to logarithmic factors.
Computational Complexity
Simulating Hamiltonian dynamics with a truncated Taylor series
We describe a simple, efficient method for simulating Hamiltonian dynamics on a quantum computer by approximating the truncated Taylor series of the evolution operator.
Quantum Physics
Easy and hard functions for the Boolean hidden shift problem
We study the quantum query complexity of the Boolean hidden shift problem.
