Analysis and limitations of modified circuit-to-Hamiltonian constructions
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Peer-reviewed
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Abstract
Feynman's circuit-to-Hamiltonian construction connects quantum computation
and ground states of many-body quantum systems. Kitaev applied this
construction to demonstrate QMA-completeness of the local Hamiltonian problem,
and Aharanov et al. used it to show the equivalence of adiabatic computation
and the quantum circuit model. In this work, we analyze the low energy
properties of a class of modified circuit Hamiltonians, which include features
like complex weights and branching transitions. For history states with linear
clocks and complex weights, we develop a method for modifying the circuit
propagation Hamiltonian to implement any desired distribution over the time
steps of the circuit in a frustration-free ground state, and show that this can
be used to obtain a constant output probability for universal adiabatic
computation while retaining the
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2521-327X