"Version: 20220701"--Title page verso.

Includes bibliographical references.

1. Introduction -- 1.1. Introduction

2. Overview figures for a method of understanding quantum computing -- 2.1. What quantum-gated computing needs in its algorithms -- 2.2. Every reversibility in quantum circuits is by virtue of exclusive OR -- 2.3. Equivalence of the circuits by virtue of superposition of qubits to be applied by Hadamard gates -- 2.4. Bases of quantum computing -- 2.5. Preparation toward Deutsch's algorithm using intuitive model of the quantum oracle Uf -- 2.6. Preparation with phase kickback toward Deutsch's algorithm using an intuitive model of the quantum oracle Uf -- 2.7. Deutsch's algorithm -- 2.8. Bernstein-Vazirani algorithm--general expression by eigenstate concept -- 2.9. Implementation of the phase oracle based on CNOT for the Bernstein-Vazirani algorithm -- 2.10. Implementation of the phase oracle based on CNOT for the Bernstein-Vazirani algorithm--secret string s = 101 case

3. Quantum key distribution based on a special Deutsch-Jozsa algorithm -- 3.1. Review of Deutsch's algorithm -- 3.2. Deutsch's algorithm with another input state -- 3.3. Deutsch's algorithm using the Bell state -- 3.4. Quantum key distribution based on Deutsch's algorithm -- 3.5. Review of the Deutsch-Jozsa algorithm -- 3.6. Special Deutsch-Jozsa algorithm -- 3.7. Special Deutsch-Jozsa algorithm with another input state -- 3.8. Special Deutsch-Jozsa algorithm using the GHZ state -- 3.9. Quantum key distribution based on the special Deutsch-Jozsa algorithm

4. Quantum communication based on the Bernstein-Vazirani algorithm in a noisy environment -- 4.1. Review of the Bernstein-Vazirani algorithm -- 4.2. Quantum communication based on the Bernstein-Vazirani algorithm -- 4.3. Error correction based on the Bernstein-Vazirani algorithm -- 4.4. Evaluating simultaneously many functions using many parallel quantum systems -- 4.5. Method for evaluating a multiplication operation using the generalized Bernstein-Vazirani algorithm -- 4.6. Bernstein-Vazirani algorithm in a noisy environment

5. Quantum communication based on Simon's algorithm -- 5.1. Review of Simon's algorithm -- 5.2. Quantum communication based on Simon's algorithm

6. Expansion of Deutsch's algorithm -- 6.1. Expansion of Deutsch's algorithm for determining all the mappings of a function -- 6.2. Deutsch's algorithm -- 6.3. Expansion of Deutsch's algorithm

7. Some theoretically organized algorithm for quantum computers -- 7.1. New type of quantum algorithm for determining the 21 mappings of a function -- 7.2. New type of quantum algorithm for determining the 22 mappings of a function -- 7.3. Example using a logical function -- 7.4. New type of quantum algorithm for determining the 2N mappings of a function -- 7.5. Relation between set-theoretic atoms and the result in section 7.2

8. Some multi-quantum computing on quantum gating computers beyond a von Neumann architecture -- 8.1. Quantum algorithm for determining all the mappings of two logical functions -- 8.2. Overview of the quantum algorithm -- 8.3. Orthogonal pairs -- 8.4. Quantum algorithm for determining all the mappings of all 16 two-variable functions

9. Quantum cryptography based on an algorithm for determining simultaneously all the mappings of a logical function -- 9.1. Quantum algorithm for determining all the two mappings of a logical function -- 9.2. Concrete example -- 9.3. Quantum algorithm for determining all the three mappings of a logical function -- 9.4. Concrete example -- 9.5. Quantum algorithm for determining all the 22 mappings of a logical function -- 9.6. Concrete example

10. Quantum cryptography based on an algorithm for determining a function using qudit systems -- 10.1. Quantum cryptography based on an algorithm for determining a function using qudit systems -- 10.2. Concrete example

11. Continuous-variable quantum computing and its applications to cryptography -- 11.1. Quantum cryptography based on an algorithm for determining a function using continuous-variable entangled states -- 11.2. Concrete example

12. Various new forms of the Bernstein-Vazirani algorithm beyond qubit systems -- 12.1. Algorithm for determining a bit string -- 12.2. Extension to a natural number string -- 12.3. Extension to an integer string -- 12.4. Extension to a complex number string -- 12.5. Extension to a matrix string

13. Creating genuine quantum algorithms for quantum energy-based computing -- 13.1. Quantum algorithm for determining a homogeneous linear function -- 13.2. Quantum algorithm for determining M homogeneous linear functions

14. Quantum algorithms for finding the roots of a polynomial function -- 14.1. Finding the roots of a polynomial function by using a bit string -- 14.2. Finding the roots of a polynomial function by using a natural number string -- 14.3. Finding the roots of a polynomial function by using an integer string

15. Quantum algorithm for rapidly plotting a function -- 15.1. Description of the algorithm

16. Efficient exact quantum algorithm for the parity problem of a function -- 16.1. Description of the algorithm

17. Necessary and sufficient condition for quantum computing -- 17.1. Necessary and sufficient condition for quantum computing

18. Toward practical quantum-gated computers -- 18.1. Quantum algorithm for storing all the mappings of a logical function -- 18.2. Toward practically mathematical evaluations -- 18.3. Concrete quantum circuits for addition of any two numbers

19. Computational complexity in quantum computing -- 19.1. Quantum algorithm for storing simultaneously all the mappings of three logical functions -- 19.2. Typical arithmetic calculations

20. Measurement theory in Deutsch's algorithm based on the truth values -- 20.1. The new measurement theory can satisfy observability -- 20.2. Wave function analysis -- 20.3. New measurement theory -- 20.4. The new measurement theory can satisfy controllability -- 21. Conclusions.

The book is a simplified version of the classical quantum basic gate theory like Deutsch-Jozsa algorithm, Deutsch algorithm, Bernstein-Vazirani algorithm, Grover search algorithm, Simon algorithm, etc with applications in cryptography and coding theory.

Students studying quantum computers and applications. Beginners in the domain. Experts for new perspectives to the standard conceptions in quantum computing with applications.

Also available in print.

Mode of access: World Wide Web.

System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader.

Koji Nagata received BS and MS degrees from Kyoto University and Tohoku University in 1996 and 2000, respectively. He graduated as PhD from The Graduate University of Advanced Sciences' PhD (School of Advanced Sciences) in March 2003.

Title from PDF title page (viewed on August 5, 2022).