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arXiv · 1912.05559

Iterative Quantum Amplitude Estimation

Dmitry Grinko·Julien Gacon·Christa Zoufal·Stefan Woerner
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Abstract

We introduce a new variant of Quantum Amplitude Estimation (QAE), called Iterative QAE (IQAE), which does not rely on Quantum Phase Estimation (QPE) but is only based on Grover's Algorithm, which reduces the required number of qubits and gates. We provide a rigorous analysis of IQAE and prove that it achieves a quadratic speedup up to a double-logarithmic factor compared to classical Monte Carlo simulation. Furthermore, we show with an empirical study that our algorithm outperforms other known QAE variants without QPE, some even by orders of magnitude, i.e., our algorithm requires significantly fewer samples to achieve the same estimation accuracy and confidence level.

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Dmitry Grinko, Julien Gacon, Christa Zoufal, Stefan Woerner. 2019-12-11. Iterative Quantum Amplitude Estimation. https://doi.org/10.1038/s41534-021-00379-1

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