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Nearly Optimal Quantum Algorithm for Estimating Multiple Expectation Values

Nearly Optimal Quantum Algorithm for Estimating Multiple Expectation Values

Many quantum algorithms involve the evaluation of expectation values. Optimal strategies for estimating a single expectation value are known, requiring a number of state preparations that scales with the target error $ϵ$ as $\mathcal{O}(1/ϵ)$. In this Letter, we address the task of estimating the expectation values of $M$ different observables, …