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Quantum and Classical in Adiabatic Computation

Andrew Green, UCL

The aim of this seminar is to provide a conceptual framework in which to separate quantum and classical effects in adiabatic computation using open systems. I will do so by starting from physics-inspired classical optimization algorithms and gradually incorporating the effects of quantum mechanics; first local superposition and then entanglement.

The result is a matrix product/tensor network model of adiabatic computation. This picture allows a geometrical interpretation of a key constraint on the performance of an adiabatic computation – whether the entirety of the adiabatic path through Hilbert space is physically accessible when coupled to environmental dissipation. Using this, we formulate a set of tests aimed at quantifying the amount of quantum entanglement in a putative quantum adiabatic computation. In passing, I will discuss recent progress on developing a field theory of matrix product states.