publication . Preprint . 2009

Quantum Fourier Transform Over Galois Rings

Zhang, Yong;
Open Access English
  • Published: 16 Apr 2009
Abstract
Galois rings are regarded as "building blocks" of a finite commutative ring with identity. There have been many papers on classical error correction codes over Galois rings published. As an important warm-up before exploring quantum algorithms and quantum error correction codes over Galois rings, we study the quantum Fourier transform (QFT) over Galois rings and prove it can be efficiently preformed on a quantum computer. The properties of the QFT over Galois rings lead to the quantum algorithm for hidden linear structures over Galois rings.
Subjects
arXiv: Mathematics::Number TheoryMathematics::Commutative Algebra
free text keywords: Quantum Physics
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