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Table of Contents
Intro
Preface to the Second Edition
Acknowledgments
Author biography
Dr Hafiz Md Hasan Babu
Acronyms
Outline placeholder
An overview of quantum circuits
Chapter 1 Quantum logic
1.1 Overview
1.2 Motivations towards quantum computing
1.3 The relationship between reversible and quantum logic
1.4 Quantum computers
1.5 The working principles of quantum computers
1.6 The evolution of quantum computers
1.7 Why pursue quantum computing?
1.8 Summary
Critical thinking questions
References
Chapter 2 Basic definitions of quantum logic
2.1 The quantum qubit
2.2 The quantum gate
2.2.1 The quantum Feynman gate
2.2.2 The quantum Tofolli gate
2.2.3 The quantum Fredkin gate
2.3 Garbage outputs
2.4 Constant inputs
2.5 Area
2.6 Power
2.7 Delay
2.8 Depth
2.9 Quantum cost
2.10 Quantum gate calculation complexity
2.11 Summary
Critical thinking questions
References
Chapter 3 The quantum qubit string comparator
3.1 Characteristics of a quantum comparator
3.2 The quantum magnitude comparator
3.3 The design of a quantum comparator
Guess
3.3.1 Example
3.4 Summary
Critical thinking questions
References
Chapter 4 The quantum full-adder and subtractor
4.1 The quantum adder
4.1.1 The quantum full-adder
4.2 The quantum subtractor
4.2.1 The quantum half-subtractor
4.2.2 The quantum full-subtractor
4.3 Summary
Critical thinking questions
References
Chapter 5 The quantum multiplexer and demultiplexer
5.1 The quantum multiplexer
5.1.1 The quantum 2-to-1 multiplexer
5.1.2 Quantum 4-to-1 multiplexer
5.1.3 The quantum 2n-to-1 multiplexer
5.2 The quantum demultiplexer
5.2.1 The quantum 1-to-2 demultiplexer
5.2.2 The quantum 1-to-4 demultiplexer
5.2.3 Quantum 1-to-2n demultiplexer
5.3 Summary.
Critical thinking questions
References
Chapter 6 The quantum adder circuits
6.1 The quantum carry skip adder
6.2 The quantum comparison circuit
6.3 The quantum 2-to-1 multiplier circuit
6.4 The design of a quantum carry skip adder
6.4.1 The four-qubit quantum carry skip adder
6.4.2 The n-qubit quantum carry skip adder
6.4.3 Calculation of the area and power of a quantum carry skip adder circuit
6.4.4 Complexity of the n-qubit quantum carry skip adder circuit
6.5 The quantum BCD adder
6.6 Summary
Critical thinking questions
References
Chapter 7 The quantum multiplier-accumulator
7.1 The importance of a quantum multiplier-accumulator
7.2 The quantum multiplication technique
7.3 Reduction of the garbage outputs and ancillary inputs of quantum circuits
7.4 The design of a quantum multiplier circuit
7.4.1 The quantum ANDing circuit
7.4.2 The quantum full-adder circuit
7.4.3 The n × n-qubit quantum multiplier
7.5 Accumulator
7.6 Summary
Critical thinking questions
References
Chapter 8 The quantum divider
8.1 Division algorithms
8.1.1 Classical integer division algorithms
8.1.2 Quantum integer division algorithms
8.2 The importance of the quantum divider
8.3 The tree-based quantum division technique
8.3.1 Definitions and properties of the division technique
8.3.2 The algorithm of the division technique
8.4 The design of a quantum divider circuit
8.4.1 A technique to minimize the number of ancillary inputs in the quantum circuit realization
8.4.2 The components of the quantum divider circuit
8.5 Summary
Critical thinking questions
References
Chapter 9 The quantum BCD priority encoder
9.1 The properties of a quantum encoder
9.2 The design of a quantum BCD priority encoder circuit
9.2.1 The quantum BCD priority encoder circuit.
9.2.2 Analysis of the properties of the encoder circuit
9.3 Summary
Critical thinking questions
References
Chapter 10 The quantum decoder
10.1 The characteristics of a quantum decoder
10.2 The design of a quantum decoder
10.2.1 The quantum decoder circuit
10.2.2 Analysis of the properties of the circuits
10.3 Summary
Critical thinking questions
References
Chapter 11 The quantum square root circuit
11.1 The properties of a quantum square root function
11.2 The design of a quantum square root circuit
11.2.1 The quantum adder/subtractor circuit
11.2.2 The quantum square root circuit
11.2.3 Analysis of the properties of the quantum circuit
11.3 Summary
Critical thinking questions
References
Chapter 12 Quantum latches and counter circuits
12.1 The properties of quantum latches
12.2 The design of quantum latches
12.2.1 The quantum SR latch
12.2.2 The quantum D latch
12.2.3 The quantum T latch
12.2.4 The quantum J-K latch
12.3 The properties of quantum counter circuits
12.4 The design of quantum counters
12.4.1 The quantum asynchronous counter
12.4.2 The quantum synchronous counter
12.5 Summary
Critical thinking questions
References
Chapter 13 The quantum controlled ternary barrel shifter
13.1 Ternary quantum gates
13.1.1 The quantum ternary Peres gate
13.1.2 The quantum ternary modified Fredkin gate
13.2 The properties of ternary quantum circuits
13.3 The quantum barrel shifter
13.3.1 Logical right shift
13.3.2 Arithmetic right shift
13.3.3 Right rotation
13.3.4 Logical left shift
13.3.5 Arithmetic left shift
13.3.6 Left rotation
13.4 The design of a quantum ternary barrel shifter
13.4.1 The optimized quantum ternary barrel shifter
13.4.2 The properties of the designed circuit
13.5 Summary.
Critical thinking questions
References
Chapter 14 Quantum RAM, quantum ROM, and quantum cache memory
14.1 The quantum n-to-2n decoder
14.2 The quantum memory unit
14.3 The construction procedure of QRAM
14.4 Quantum ROM
14.5 Quantum cache memory
14.6 Summary
Critical thinking questions
References
Chapter 15 The quantum arithmetic logic unit
15.1 The design of a quantum ALU
15.1.1 The first approach
15.1.2 The second approach
15.1.3 The third approach
15.2 Summary
Critical thinking questions
References
Chapter 16 Quantum programmable logic devices
16.1 The quantum programmable array logic
16.1.1 The design procedure and working principles of quantum PAL
16.1.2 The importance and applications of quantum PAL
16.2 The quantum programmable logic array
16.2.1 The design procedure and working principles of quantum PLAs
16.2.2 The importance and applications of quantum PLAs
16.3 The quantum complex programmable logic device
16.3.1 The design procedure and working principles of quantum CPLDs
16.3.2 The importance and applications of quantum CPLD
16.4 The quantum field-programmable gate array
16.4.1 The design procedure and working principles of quantum FPGAs
16.4.2 The importance and applications of FPGAs
16.5 Summary
Critical thinking questions
References
Chapter 17 The quantum processor circuit
17.1 Introduction
17.2 Basic definitions
17.3 The block diagram of a quantum processor
17.4 The basic components of a quantum processor
17.4.1 The quantum RAM
17.4.2 The quantum instruction register
17.4.3 The quantum program counter
17.4.4 The quantum decoder
17.4.5 The quantum multiplexer
17.4.6 The quantum arithmetic logic unit
17.4.7 The quantum accumulator
17.5 Applications
17.6 Summary
Critical thinking questions.
References
Chapter 18 Applications of quantum computing technology
18.1 Optimization
18.1.1 The Roswell Park Cancer Institute
18.1.2 Volkswagen group
18.1.3 Recruit Communications
18.2 Machine learning
18.2.1 QxBranch
18.2.2 Los Alamos National Laboratory
18.2.3 NASA
18.3 Biomedical simulations
18.4 Financial services
18.5 Computational chemistry
18.6 Logistics and scheduling
18.7 Cyber security
18.8 Circuit, software, and system fault simulation
18.9 Weather forecasting
18.10 Summary
Critical thinking questions
References
Outline placeholder
An overview of quantum fault-tolerant circuits
Chapter 19 Quantum fault-tolerant circuits
19.1 The need for quantum fault-tolerant circuits
19.2 The fault-tolerant quantum adder
19.2.1 The fault-tolerant full-adder
19.3 The fault-tolerant multiplier
19.3.1 The fault-tolerant signed multiplier
19.4 The quantum fault-tolerant integer divider
19.4.1 The restoring division algorithm
19.4.2 The subtractor module
19.4.3 The conditional addition operation module
19.4.4 Quantum restoring integer division circuitry
19.5 Summary
Critical thinking questions
References
Outline placeholder
An overview of quantum-dot cellular automata
Chapter 20 Quantum-dot cellular automata
20.1 Fundamentals of QCA circuits
20.1.1 Area
20.1.2 Delay
20.1.3 Kink energy
20.1.4 Power
20.1.5 Overall cost
20.2 The QCA cell
20.3 Information and data propagation
20.4 Basic QCA elements and gates
20.4.1 The QCA majority voter
20.4.2 The QCA AND gate
20.4.3 The QCA OR gate
20.4.4 The QCA NOT gate
20.4.5 The QCA wire
20.5 The QCA clock
20.5.1 Special cell arrangements and symmetric cells
20.5.2 The NOT gate clock zones
20.5.3 The majority voter clock zones
20.6 Summary.
Critical thinking questions.
Preface to the Second Edition
Acknowledgments
Author biography
Dr Hafiz Md Hasan Babu
Acronyms
Outline placeholder
An overview of quantum circuits
Chapter 1 Quantum logic
1.1 Overview
1.2 Motivations towards quantum computing
1.3 The relationship between reversible and quantum logic
1.4 Quantum computers
1.5 The working principles of quantum computers
1.6 The evolution of quantum computers
1.7 Why pursue quantum computing?
1.8 Summary
Critical thinking questions
References
Chapter 2 Basic definitions of quantum logic
2.1 The quantum qubit
2.2 The quantum gate
2.2.1 The quantum Feynman gate
2.2.2 The quantum Tofolli gate
2.2.3 The quantum Fredkin gate
2.3 Garbage outputs
2.4 Constant inputs
2.5 Area
2.6 Power
2.7 Delay
2.8 Depth
2.9 Quantum cost
2.10 Quantum gate calculation complexity
2.11 Summary
Critical thinking questions
References
Chapter 3 The quantum qubit string comparator
3.1 Characteristics of a quantum comparator
3.2 The quantum magnitude comparator
3.3 The design of a quantum comparator
Guess
3.3.1 Example
3.4 Summary
Critical thinking questions
References
Chapter 4 The quantum full-adder and subtractor
4.1 The quantum adder
4.1.1 The quantum full-adder
4.2 The quantum subtractor
4.2.1 The quantum half-subtractor
4.2.2 The quantum full-subtractor
4.3 Summary
Critical thinking questions
References
Chapter 5 The quantum multiplexer and demultiplexer
5.1 The quantum multiplexer
5.1.1 The quantum 2-to-1 multiplexer
5.1.2 Quantum 4-to-1 multiplexer
5.1.3 The quantum 2n-to-1 multiplexer
5.2 The quantum demultiplexer
5.2.1 The quantum 1-to-2 demultiplexer
5.2.2 The quantum 1-to-4 demultiplexer
5.2.3 Quantum 1-to-2n demultiplexer
5.3 Summary.
Critical thinking questions
References
Chapter 6 The quantum adder circuits
6.1 The quantum carry skip adder
6.2 The quantum comparison circuit
6.3 The quantum 2-to-1 multiplier circuit
6.4 The design of a quantum carry skip adder
6.4.1 The four-qubit quantum carry skip adder
6.4.2 The n-qubit quantum carry skip adder
6.4.3 Calculation of the area and power of a quantum carry skip adder circuit
6.4.4 Complexity of the n-qubit quantum carry skip adder circuit
6.5 The quantum BCD adder
6.6 Summary
Critical thinking questions
References
Chapter 7 The quantum multiplier-accumulator
7.1 The importance of a quantum multiplier-accumulator
7.2 The quantum multiplication technique
7.3 Reduction of the garbage outputs and ancillary inputs of quantum circuits
7.4 The design of a quantum multiplier circuit
7.4.1 The quantum ANDing circuit
7.4.2 The quantum full-adder circuit
7.4.3 The n × n-qubit quantum multiplier
7.5 Accumulator
7.6 Summary
Critical thinking questions
References
Chapter 8 The quantum divider
8.1 Division algorithms
8.1.1 Classical integer division algorithms
8.1.2 Quantum integer division algorithms
8.2 The importance of the quantum divider
8.3 The tree-based quantum division technique
8.3.1 Definitions and properties of the division technique
8.3.2 The algorithm of the division technique
8.4 The design of a quantum divider circuit
8.4.1 A technique to minimize the number of ancillary inputs in the quantum circuit realization
8.4.2 The components of the quantum divider circuit
8.5 Summary
Critical thinking questions
References
Chapter 9 The quantum BCD priority encoder
9.1 The properties of a quantum encoder
9.2 The design of a quantum BCD priority encoder circuit
9.2.1 The quantum BCD priority encoder circuit.
9.2.2 Analysis of the properties of the encoder circuit
9.3 Summary
Critical thinking questions
References
Chapter 10 The quantum decoder
10.1 The characteristics of a quantum decoder
10.2 The design of a quantum decoder
10.2.1 The quantum decoder circuit
10.2.2 Analysis of the properties of the circuits
10.3 Summary
Critical thinking questions
References
Chapter 11 The quantum square root circuit
11.1 The properties of a quantum square root function
11.2 The design of a quantum square root circuit
11.2.1 The quantum adder/subtractor circuit
11.2.2 The quantum square root circuit
11.2.3 Analysis of the properties of the quantum circuit
11.3 Summary
Critical thinking questions
References
Chapter 12 Quantum latches and counter circuits
12.1 The properties of quantum latches
12.2 The design of quantum latches
12.2.1 The quantum SR latch
12.2.2 The quantum D latch
12.2.3 The quantum T latch
12.2.4 The quantum J-K latch
12.3 The properties of quantum counter circuits
12.4 The design of quantum counters
12.4.1 The quantum asynchronous counter
12.4.2 The quantum synchronous counter
12.5 Summary
Critical thinking questions
References
Chapter 13 The quantum controlled ternary barrel shifter
13.1 Ternary quantum gates
13.1.1 The quantum ternary Peres gate
13.1.2 The quantum ternary modified Fredkin gate
13.2 The properties of ternary quantum circuits
13.3 The quantum barrel shifter
13.3.1 Logical right shift
13.3.2 Arithmetic right shift
13.3.3 Right rotation
13.3.4 Logical left shift
13.3.5 Arithmetic left shift
13.3.6 Left rotation
13.4 The design of a quantum ternary barrel shifter
13.4.1 The optimized quantum ternary barrel shifter
13.4.2 The properties of the designed circuit
13.5 Summary.
Critical thinking questions
References
Chapter 14 Quantum RAM, quantum ROM, and quantum cache memory
14.1 The quantum n-to-2n decoder
14.2 The quantum memory unit
14.3 The construction procedure of QRAM
14.4 Quantum ROM
14.5 Quantum cache memory
14.6 Summary
Critical thinking questions
References
Chapter 15 The quantum arithmetic logic unit
15.1 The design of a quantum ALU
15.1.1 The first approach
15.1.2 The second approach
15.1.3 The third approach
15.2 Summary
Critical thinking questions
References
Chapter 16 Quantum programmable logic devices
16.1 The quantum programmable array logic
16.1.1 The design procedure and working principles of quantum PAL
16.1.2 The importance and applications of quantum PAL
16.2 The quantum programmable logic array
16.2.1 The design procedure and working principles of quantum PLAs
16.2.2 The importance and applications of quantum PLAs
16.3 The quantum complex programmable logic device
16.3.1 The design procedure and working principles of quantum CPLDs
16.3.2 The importance and applications of quantum CPLD
16.4 The quantum field-programmable gate array
16.4.1 The design procedure and working principles of quantum FPGAs
16.4.2 The importance and applications of FPGAs
16.5 Summary
Critical thinking questions
References
Chapter 17 The quantum processor circuit
17.1 Introduction
17.2 Basic definitions
17.3 The block diagram of a quantum processor
17.4 The basic components of a quantum processor
17.4.1 The quantum RAM
17.4.2 The quantum instruction register
17.4.3 The quantum program counter
17.4.4 The quantum decoder
17.4.5 The quantum multiplexer
17.4.6 The quantum arithmetic logic unit
17.4.7 The quantum accumulator
17.5 Applications
17.6 Summary
Critical thinking questions.
References
Chapter 18 Applications of quantum computing technology
18.1 Optimization
18.1.1 The Roswell Park Cancer Institute
18.1.2 Volkswagen group
18.1.3 Recruit Communications
18.2 Machine learning
18.2.1 QxBranch
18.2.2 Los Alamos National Laboratory
18.2.3 NASA
18.3 Biomedical simulations
18.4 Financial services
18.5 Computational chemistry
18.6 Logistics and scheduling
18.7 Cyber security
18.8 Circuit, software, and system fault simulation
18.9 Weather forecasting
18.10 Summary
Critical thinking questions
References
Outline placeholder
An overview of quantum fault-tolerant circuits
Chapter 19 Quantum fault-tolerant circuits
19.1 The need for quantum fault-tolerant circuits
19.2 The fault-tolerant quantum adder
19.2.1 The fault-tolerant full-adder
19.3 The fault-tolerant multiplier
19.3.1 The fault-tolerant signed multiplier
19.4 The quantum fault-tolerant integer divider
19.4.1 The restoring division algorithm
19.4.2 The subtractor module
19.4.3 The conditional addition operation module
19.4.4 Quantum restoring integer division circuitry
19.5 Summary
Critical thinking questions
References
Outline placeholder
An overview of quantum-dot cellular automata
Chapter 20 Quantum-dot cellular automata
20.1 Fundamentals of QCA circuits
20.1.1 Area
20.1.2 Delay
20.1.3 Kink energy
20.1.4 Power
20.1.5 Overall cost
20.2 The QCA cell
20.3 Information and data propagation
20.4 Basic QCA elements and gates
20.4.1 The QCA majority voter
20.4.2 The QCA AND gate
20.4.3 The QCA OR gate
20.4.4 The QCA NOT gate
20.4.5 The QCA wire
20.5 The QCA clock
20.5.1 Special cell arrangements and symmetric cells
20.5.2 The NOT gate clock zones
20.5.3 The majority voter clock zones
20.6 Summary.
Critical thinking questions.