Efficient Quantum Query Algorithms Detecting Hamming and ReedSolomon Codes

1
Efficient Quantum Query Algorithms Detecting
Hamming and Reed-Solomon Codes

• Rubens Agadanjans
• 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!