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Introduction to Classical and Quantum Computing is for students who want to learn quantum computing beyond a conceptual level, but who lack advanced training in mathematics. The only prerequisite is trigonometry, and mathematics beyond that will be covered, including linear algebra. This book is suitable as a course textbook or for independent study.

The text begins with a significant overview of classical computing, from how they add numbers to their computational limits, and it mirrors many of the quantum computing topics that are covered later. Then, the investigation of quantum computing begins with a single qubit and quantum gates acting on it, first using geometry and elementary algebra, and later using linear algebra. Computer algebra systems are utilized, and code for both Mathematica and SageMath is included. After one qubit, multi-qubit systems are covered, including how quantum computers add numbers, universal gate sets, and error correction. After this, readers learn how to program quantum circuits on actual quantum processors using IBM Quantum Experience. Afterward, entanglement and quantum protocols are explored. Finally, quantum algorithms are examined, culminating in Shor's algorithm for factoring. Abundant use of the Quirk quantum simulator is used throughout. Finally, a short discussion of careers in quantum computing is provided, along with some possible technical topics to learn next.

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1 Classical Information and Computation

1.1 Bits
1.2 Logic Gates
1.3 Adders and Verilog
1.4 Circuit Simplification and Boolean Algebra
1.5 Reversible Logic Gates
1.6 Error Correction
1.7 Computational Complexity
1.8 Turing Machines
1.9 Summary

2 One Quantum Bit
2.1 Qubit Touchdown : A Quantum Computing Board Game
2.2 Superposition
2.3 Measurement
2.4 Bloch Sphere Mapping
2.5 Physical Qubits
2.6 Quantum Gates
2.7 Quantum Circuits
2.8 Summary

3 Linear Algebra
3.1 Quantum States
3.2 Inner Products
3.3 Quantum Gates
3.4 Outer Products
3.5 Summary

4. Multiple Quantum Bits
4.1 Entanglion: A Quantum Computing Board Game
4.2 States and Measurement
4.3 Entanglement
4.4 Quantum Gates
4.5 Quantum Adders
4.6 Universal Quantum Gates
4.7 Quantum Error Correction
4.8 Summary

5 Quantum Programming
5.1 IBM Quantum Experience
5.2 Quantum Assembly Language
5.3 Qiskit
5.4 Other Quantum Programming Languages
5.5 Summay

6 Entanglement and Quantum Protocols
6.1 Measurements
6.2 Bell Inequalities
6.3 Monogamy of Entanglement
6.4 Superdense Coding
6.5 Quantum Teleportation
6.6 Quantum Ket Distribution
6.7 Summary

7 Quantum Algorithms
7.1 Circuit vs Query Complexity
7.2 Parity
7.3 Constant cs BalancedFunctions
7.4 Secret Dot Product String
7.5 Secret XOR Mask
7.6 Brute-Force Searching
7.7 Discrete Fourier Transform
7.8 Phase / Eigenvalue Estimation
7.9 period of Modular Exponentiation
7.10 Factoring
7.11 Summary

8 Next Step
8.1 Careers in Quantum Computing
8.2 Technical Next Steps
8.3 Questions
8.4 Parting Words

Answers to Exercises

Index