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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.
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C. Zoufal, A. Lucchi, and S. Woerner, “Quantum generative adversarial networks for learning and loading random distributions,” npj Quantum Information , vol. 5, no. 1, pp. 1–9, 2019
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A. Montanaro, “Quantum speedup of monte carlo methods,” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences , vol. 471, no. 2181, p. 20150301, 2015
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P. Rebentrost, B. Gupt, and T. R. Bromley, “Quantum computational finance: Monte carlo pricing of financial derivatives,” Phys. Rev. A , vol. 98, p. 022321, Aug 2018. [Online]. Available: https://link.aps.org/doi/10.1103/PhysRevA.98.022321
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N. Stamatopoulos, D. J. Egger, Y. Sun, C. Zoufal, R. Iten, N. Shen, and S. Woerner, “Option pricing using quantum computers,” Quantum , vol. 4, p. 291, 2020
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Y. Suzuki, S. Uno, R. Raymond, T. Tanaka, T. Onodera, and N. Yamamoto, “Amplitude estimation without phase estimation,” Quantum Information Processing , vol. 19, no. 2, pp. 1–17, 2020
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S. Aaronson and P. Rall, “Quantum approximate counting, simplified,” in Symposium on Simplicity in Algorithms . SIAM, 2020, pp. 24–32
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