Lior Eldar

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The local Hamiltonian problem plays the equivalent role of SAT in quantum complexity theory. Understanding the complexity of the intermediate case in which the constraints are quantum but all local terms in the Hamiltonian commute, is of importance for conceptual, physical and computational complexity reasons. Bravyi and Vyalyi showed in 2003 [8], using(More)
Recent results by Harrow et. al. [2], and by Ta-Shma [5], suggest that quantum computers may have an exponential advantage in solving a wealth of linear algebraic problems, over classical algorithms. Building on the quantum intuition of these results, we step back into the classical domain, and explore its usefulness in designing classical algorithms. We(More)
Computing the eigenvectors and eigenvalues of a given Hermitian matrix is arguably one of the most well-studied computational problems. Yet despite its immense importance, and a vast array of heuristic techniques, there is no algorithm that can provably approximate the spectral decomposition of any Hermitian matrix in asymptotic bit-complexity o(n 3).(More)
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