Analysis and limitations of modified circuit-to-Hamiltonian constructions

Understand

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.