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Some new constructions for Local Hamiltonian and universal adiabatic quantum computing

Peter Love, Haverford College

(Session 8 : Saturday from 4:00-4:30)

Abstract. The difficulty of finding the ground state energy of a Hamiltonian is formalized in quantum complexity theory through the problem Local Hamiltonian. Various restrictions of the form of the Hamiltonians in this problem have been studied, including, inter alia, restricted locality and geometry of couplings, coupling strengths, interaction types and stoquasticity of the Hamiltonians. Concomitantly, such results typically tell us which physical Hamiltonians are capable of realizing universal quantum computation adiabatically. In this talk I will describe some new results on the problem Local Hamiltonian that allow universal adiabatic quantum computation in stoquastic Hamiltonians, restrict the form of the Hamiltonian required, and reduce (but do not eliminate) the need for perturbative gadgets. I will discuss the implications of these results for the design of universal adiabatic quantum computers.