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5. Information and Complexity Theory

  • 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 the theoretical foundations of computing, exploring the tractability of problems through the lens of complexity. It begins by examining classical decision problems and complexity classes, introducing the concept of decision problems and their classification based on time and space requirements. The chapter uses the traveling salesman problem to illustrate differences in problem complexities and introduces the concept of reducing a problem to another. It also discusses the classes P, NP, NP-complete, and NP-hard, and their relationships. The text then explores broader classes of decision problems, including PSPACE, EXPTIME, and EXPSPACE, and their nested relationships. Additionally, it introduces probabilistic and quantum complexity classes, such as BPP, PP, and BQP, and discusses their relationships with classical computing. The chapter concludes with a thought experiment, Maxwell's Demon, to illustrate the connection between information and physics, highlighting the implications of Landauer's principle on the physical aspects of computing.
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previous chapter An Overview of Practical Classical Computing
next chapter A Gentle Introduction to Quantum Mechanics
Title
Information and Complexity Theory
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_5
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