Low depth algorithms for quantum amplitude estimation

We design and analyze two new low depth algorithms for amplitude estimation (AE) achieving an optimal tradeoff between the quantum speedup circuit depth. For β∈(0,1], our require xmlns:mml="http://www.w3.org/1998/Math/MathML">N=O~(1ϵ1+β) oracle calls to be called sequentially xmlns:mml="http://www.w3.org/1998/Math/MathML">D=O1−βϵ. These interpolate classical algorithm xmlns:mml="http://www.w3.org/1998/Math/MathML">(β=1β=0) achieve a xmlns:mml="http://www.w3.org/1998/Math/MathML">ND=O(1/ϵ2). bring speedups Monte Carlo methods closer realization, as they can provide with shallower circuits.The first (Power law AE) uses power schedules in framework introduced by Suzuki et al \cite{S20}. The works stretchy="false">] has provable correctness guarantees when log-likelihood function satisfies regularity conditions required Bernstein Von-Mises theorem. second (QoPrime Chinese remainder theorem combining lower estimates higher accuracy. discrete xmlns:mml="http://www.w3.org/1998/Math/MathML">β=q/k where xmlns:mml="http://www.w3.org/1998/Math/MathML">k≥2 is number of distinct coprime moduli used xmlns:mml="http://www.w3.org/1998/Math/MathML">1≤q≤k−1, fully rigorous proof. both presence depolarizing noise numerical comparisons state art algorithms.