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Efficient Quantum Query Algorithms Detecting Hamming and Reed-Solomon Codes

Solve the problem of verifying Hamming and Reed-Solomon codes using quantum query algorithms. Compare quantum and classical complexity with significant improvements. Explore lower bounds for these codes.

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Efficient Quantum Query Algorithms Detecting Hamming and Reed-Solomon Codes

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  1. Efficient Quantum Query Algorithms Detecting Hamming and Reed-Solomon Codes Rubens Agadžanjans Juris Smotrovs

  2. Problem to be solved • Question: We have sequence of n bits x1, x2, …, xn. Does this sequence make a correct Hamming (or Reed-Solomon) code? • Use quantum query algorithms for detecting Hamming and Reed-Solomon codes • Compare quantum and classical query complexity

  3. Results • 25 % improvement with a quantum algorithm for the Hamming codes • 50% improvement for the Reed-Solomon codes (repeats the best previously known achievement) • Lower bounds for these codes

  4. Thank you!

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