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Efficient quantum algorithms for set operations.

Rehab Elgendy1, Ahmed Younes2,3, H M Abu-Donia4

  • 1Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt. rehabsaad@zu.edu.eg.

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Summary
This summary is machine-generated.

This study introduces four quantum algorithms for Boolean function set operations like Intersection and Union. These algorithms offer improved success probabilities for database systems and cryptography applications.

Keywords:
Amplitude amplificationDifferenceIncomplete superpositionIntersectionQuantum search algorithmSet operationsUnion

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Area of Science:

  • Quantum Computing
  • Computational Complexity
  • Boolean Functions

Background:

  • Boolean function analysis is crucial for database systems, cryptography, and collision problems.
  • Existing methods for set operations on Boolean functions have limitations in efficiency and applicability.

Purpose of the Study:

  • To propose novel quantum algorithms for performing set operations (Intersection, Difference, Union) on two Boolean functions.
  • To achieve a time complexity of for these quantum set operations.
  • To enhance the probability of success and applicability compared to existing techniques.

Main Methods:

  • Utilizing two stages of quantum amplitude amplification techniques.
  • Employing Younes et al.'s algorithm for quantum searching to prepare superpositions of the first Boolean function's truth set.
  • Implementing a modified Arima's algorithm with a quantum oracle for the second Boolean function to execute set operations.

Main Results:

  • Development of four distinct quantum algorithms for Boolean function set operations.
  • Achieving a time complexity of for Intersection, Difference, and Union.
  • Demonstrating a higher probability of success in general applications.

Conclusions:

  • The proposed quantum algorithms provide an efficient and robust method for set operations on Boolean functions.
  • These algorithms have significant potential for applications in database systems, cryptography, and collision problems.
  • The enhanced success probability and broader applicability represent a notable advancement over current techniques.