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arXiv · 2408.15938

Phase Coordinate Uncomputation in Quantum Recursive Fourier Sampling

Christoffer Hindlycke·Niklas Johansson·Jan-Åke Larsson
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Abstract

Recursive Fourier Sampling (RFS) was one of the earliest problems to demonstrate a quantum advantage, and is known to lie outside the Merlin--Arthur complexity class. This work contains a new description of quantum algorithms in phase space terminology, demonstrating its use in RFS, and how and why this gives a better understanding of the quantum advantage in RFS. Most importantly, describing the computational process of quantum computation in phase space terminology gives a much better understanding of why uncomputation is necessary when solving RFS: the advantage is present only when phase coordinate garbage is uncomputed. This is the underlying reason for the limitations of the quantum advantage.

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Christoffer Hindlycke, Niklas Johansson, Jan-Åke Larsson. 2024-08-28. Phase Coordinate Uncomputation in Quantum Recursive Fourier Sampling. https://doi.org/10.3390/e27060596

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