Local Hamiltonians in Quantum Computation

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In this thesis, I investigate aspects of local Hamiltonians in quantum computing.

• First, I focus on the Adiabatic Quantum Computing model, based on evolution with a time dependent Hamiltonian.
• I show that to succeed using AQC, the Hamiltonian involved must have local structure, which leads to a result about eigenvalue gaps from information theory.
• I also improve results about simulating quantum circuits with AQC.