Optimal Merging in Quantum K-XOR and K-Sum Algorithms

Optimal Merging in Quantum K-XOR and K-Sum Algorithms

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Intro

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1 of 21

Intro

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Optimal Merging in Quantum K-XOR and K-Sum Algorithms

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  1. 1 Intro
  2. 2 Outline
  3. 3 Generalized Birthday Problem(s)
  4. 4 Applications
  5. 5 Wagner's algorithm in a single slide
  6. 6 An example with k = 4
  7. 7 Known quantum complexities
  8. 8 Previous exponents (with QAQM)
  9. 9 Quantum search
  10. 10 Classical merging as a sampling procedure
  11. 11 Depth-first traversal of Wagner's tree
  12. 12 Quantum merging
  13. 13 4-xor example
  14. 14 We have to re-optimize the tree
  15. 15 General strategy
  16. 16 Merging 4 lists with a single solution
  17. 17 Schroeppel and Shamir's 4-list method
  18. 18 From classical to quantum
  19. 19 Time complexity of this example
  20. 20 General comparison
  21. 21 Conclusion

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