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15. Simon’s, Deutsch–Jozsa, and Bernstein–Vazirani Algorithms

  • 2026
  • OriginalPaper
  • Chapter
Published in:
Authors
Osama M. Raisuddin
Suvranu De
Published in
Quantum Computing for Engineers
Publisher
Springer Nature Switzerland

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Abstract

This chapter delves into three quantum algorithms—Deutsch-Jozsa, Bernstein-Vazirani, and Simon's—that showcase the exponential speedups quantum computers can achieve over classical ones. The Deutsch-Jozsa algorithm demonstrates an exponential speedup by determining whether a function is constant or balanced with a single query, leveraging quantum parallelism and superposition. The Bernstein-Vazirani algorithm reveals a hidden string with a linear speedup, showcasing the power of quantum oracles. Simon's algorithm, an instance of the Abelian Hidden Subgroup Problem, achieves an exponential speedup by finding a hidden string with quantum techniques. The chapter also touches on the Hidden Subgroup Problem, illustrating its significance in quantum computing and its potential applications, such as in Shor's algorithm for integer factorization. These algorithms not only highlight the computational advantages of quantum computing but also underscore the fundamental differences between quantum and classical computational complexity.
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previous chapter Limitations of Quantum Computers
next chapter The Quantum Computing Stack
Title
Simon’s, Deutsch–Jozsa, and Bernstein–Vazirani Algorithms
Authors
Osama M. Raisuddin
Suvranu De
Copyright Year
2026
Book
Quantum Computing for Engineers

Print ISBN: 978-3-032-03324-6

Electronic ISBN: 978-3-032-03325-3

Copyright Year: 2026

DOI
https://doi.org/10.1007/978-3-032-03325-3_15
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