A forward-backward time evolution filter (cos^k((H-e_s)t)) is used to amplify a chosen eigenstate, with LCU and Monte Carlo implementations, applied to molecular and topological Hamiltonians.
In fact, the superposition of the forward and backward time evolution in the QESDS algorithm forms a cosine filtering operator, whose peak is determined by the energy-shift es
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A Time-Symmetric Quantum Algorithm for Direct Eigenstate Determination
A forward-backward time evolution filter (cos^k((H-e_s)t)) is used to amplify a chosen eigenstate, with LCU and Monte Carlo implementations, applied to molecular and topological Hamiltonians.