Quantum Fourier Transform Over Galois Rings

Preprint English OPEN
Zhang, Yong (2009)
  • Subject: Quantum Physics
    arxiv: Mathematics::Commutative Algebra | Mathematics::Number Theory

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.
  • References (13)
    13 references, page 1 of 2

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