New adaptive quantum gradient estimation variants (Method I and Method II) achieve O~(N^{k/2})/epsilon state-preparation queries for fermionic k-RDMs, and a sine-state amplitude estimation circuit is shown to be near-optimal in mean squared error.
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Comprehensive Study on Heisenberg-limited Quantum Algorithms for Multiple Observables Estimation
New adaptive quantum gradient estimation variants (Method I and Method II) achieve O~(N^{k/2})/epsilon state-preparation queries for fermionic k-RDMs, and a sine-state amplitude estimation circuit is shown to be near-optimal in mean squared error.