Simplified quantum computing with applications /

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.

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Nagata, Koji (Autor), Do, Ngoc Diep (Autor), Farouk, Ahmed (Ph. D. in computer science) (Autor), Nakamura, Tadao (Ph. D. in electronics) (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : IOP Publishing, [2022]
Colección:IOP (Series). Release 22.
IOP series in coherent sources, quantum fundamentals, and applications.
IOP ebooks. 2022 collection.
Temas:
Quantum computing.
Quantum physics (quantum mechanics & quantum field theory)
Quantum science.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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.

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