We revisit the connection between boosting algorithms and hard-core set constructions discovered by Klivans and Servedio. We present a boosting algorithm with a certain smoothness property that is necessary for hard-core set constructions: the distributions it generates do not put too much weight on any single example. We then use ... more >>>

Statistical query (SQ) learning model of Kearns (1993) is a natural restriction of the PAC learning model in which a learning algorithm is allowed to obtain estimates of statistical properties of the examples but cannot see the examples themselves. We describe a new and simple characterization of the query complexity ... more >>>

We prove the following surprising result: given any quantum state rho on n qubits, there exists a local Hamiltonian H on poly(n) qubits (e.g., a sum of two-qubit interactions), such that any ground state of H can be used to simulate rho on all quantum circuits of fixed polynomial size. ... more >>>