Solving Shift Problems and Hidden Coset Problem Using the Fourier Transform

Details Solving Shift Problems and Hidden Coset Problem Using the Fourier Transform Solving Shift Problems and Hidden Coset Problem Using the Fourier Transform

2002-05-07

arxiv.org/abs/quant-ph/0205034v1

Physics

Quantum Physics

15 pages

Scientific paper

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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