Overlapped grouping enables linear-in-terms variance reduction for quantum energy estimation via a new repacking algorithm, with numerical gains growing with problem size.
Proof.Since eachP i has±1outcomes,Var(P i) = 1− ⟨Pi⟩2 ≤1, hence D(ψ) = X i c2 i Var(Pi)≤ X i c2 i =∥c∥ 2 2
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Overlapped groupings for quantum energy estimation: Maximal variance reduction and deterministic algorithms for reducing variance
Overlapped grouping enables linear-in-terms variance reduction for quantum energy estimation via a new repacking algorithm, with numerical gains growing with problem size.