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Easy and hard functions for the Boolean hidden shift problem
We study the quantum query complexity of the Boolean hidden shift problem.
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
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
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.
Near-Optimal Lower Bounds For Convex Optimization For All Orders of Smoothness
We study the complexity of optimizing highly smooth convex functions.
