Solving Shift Problems and Hidden Coset Problem Using the Fourier Transform

Lawrence Ip

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arXiv · quant-ph/0205034

Solving Shift Problems and Hidden Coset Problem Using the Fourier Transform

Lawrence Ip

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Abstract

We give a quantum algorithm for solving a shifted multiplicative character problem over Z/nZ and finite fields. We show that the algorithm can be interpreted as a matrix factorization or as solving a deconvolution problem and give sufficient conditions for a shift problem to be solved efficiently by our algorithm. We also show that combining the shift problem with the hidden subgroup problem results in a hidden coset problem. This naturally captures the redundancy in the shift due to the periodic structure of multiplicative characters over Z/nZ.

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Lawrence Ip. 2002-05-07. Solving Shift Problems and Hidden Coset Problem Using the Fourier Transform. https://arxiv.org/abs/quant-ph/0205034

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