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We show that it is possible to use a classical computer to efficiently simulate the adiabatic evolution of a quantum system in one dimension with a constant spectral gap, starting the adiabatic evolution from a known initial product state.
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We ignore error due to the finite numerical precision of real number arithmetic on a computer. Such error can be taken into account straightforwardly if desired
Cited in the paper.
The same exponent, ω \omega , up to to constant factors, appears in 1darea and here, because both constructions start with state with non-zero overlap with the ground state and bootstrap this to construct a state with a better overlap
Cited in the paper.
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