Simplified Quantum Computing with Applications

PRELIMS.pdf
	Preface
	Acknowledgements
	Author biographies
		Koji Nagata
		Do Ngoc Diep
		Ahmed Farouk
		Tadao Nakamura
	Abstract
CH001.pdf
	Chapter 1 Introduction
		1.1 Introduction
		References
CH002.pdf
	Chapter 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
		Reference
CH003.pdf
	Chapter 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
CH004.pdf
	Chapter 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
CH005.pdf
	Chapter 5 Quantum communication based on Simon’s algorithm
		5.1 Review of Simon’s algorithm
		5.2 Quantum communication based on Simon’s algorithm
CH006.pdf
	Chapter 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
CH007.pdf
	Chapter 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
CH008.pdf
	Chapter 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
CH009.pdf
	Chapter 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
CH010.pdf
	Chapter 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
CH011.pdf
	Chapter 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
CH012.pdf
	Chapter 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
CH013.pdf
	Chapter 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
CH014.pdf
	Chapter 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
CH015.pdf
	Chapter 15 Quantum algorithm for rapidly plotting a function
		15.1 Description of the algorithm
CH016.pdf
	Chapter 16 Efficient exact quantum algorithm for the parity problem of a function
		16.1 Description of the algorithm
CH017.pdf
	Chapter 17 Necessary and sufficient condition for quantum computing
		17.1 Necessary and sufficient condition for quantum computing
CH018.pdf
	Chapter 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
		Reference
CH019.pdf
	Chapter 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
CH020.pdf
	Chapter 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
CH021.pdf
	Chapter 21 Conclusions