Quantum Fourier Transform Over Galois Rings
Yong Zhang
TL;DR
This paper introduces a quantum Fourier transform over Galois rings, demonstrating its efficient implementation on quantum computers and enabling quantum algorithms for hidden linear structures within these rings.
Contribution
It develops the first quantum Fourier transform over Galois rings and proves its efficiency, paving the way for quantum algorithms in this algebraic setting.
Findings
QFT over Galois rings can be efficiently performed on quantum computers
The properties of the QFT enable quantum algorithms for hidden linear structures
Foundation for quantum error correction codes over Galois rings
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.
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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Coding theory and cryptography · Quantum Information and Cryptography