Accelerated Quantum Amplitude Estimation without QFT

Alet Roux; Tomasz Zastawniak

doi:10.48550/arXiv.2407.16795

Accelerated Quantum Amplitude Estimation without QFT

Alet Roux, Tomasz Zastawniak

Mathematics

Research output: Working paper

Abstract

We put forward a Quantum Amplitude Estimation algorithm delivering superior performance (lower quantum computational complexity and faster classical computation parts) compared to the approaches available to-date. The algorithm does not relay on the Quantum Fourier Transform and its quantum computational complexity is of order O(1/ε) in terms of the target accuracy ε>0. The O(1/ε) bound on quantum computational complexity is also superior compared to those in the earlier approaches due to smaller constants. Moreover, a much tighter bound is obtained by means of computer-assisted estimates for the expected value of quantum computational complexity. The correctness of the algorithm and the O(1/ε) bound on quantum computational complexity are supported by precise proofs.

Original language	English
Publisher	arXiv
DOIs	https://doi.org/10.48550/arXiv.2407.16795
Publication status	Published - 24 Jul 2024

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10.48550/arXiv.2407.16795

Cite this

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abstract = "We put forward a Quantum Amplitude Estimation algorithm delivering superior performance (lower quantum computational complexity and faster classical computation parts) compared to the approaches available to-date. The algorithm does not relay on the Quantum Fourier Transform and its quantum computational complexity is of order O(1/ε) in terms of the target accuracy ε>0. The O(1/ε) bound on quantum computational complexity is also superior compared to those in the earlier approaches due to smaller constants. Moreover, a much tighter bound is obtained by means of computer-assisted estimates for the expected value of quantum computational complexity. The correctness of the algorithm and the O(1/ε) bound on quantum computational complexity are supported by precise proofs.",

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