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THE INTERACTIVE TEXTBOOK

# Introduction to
Quantum Computing 2026

From the first complex amplitude to reliable quantum computation.

A mathematical course you can read, question, and experiment with. Begin with ordinary algebra; build toward quantum information, algorithms, noise, and fault tolerance.

Begin Chapter 1 →How to use this book Resume reading →
25 Chapters
26 Working laboratories
120 Exercises with solutions
6 Integrated projects

START WITH A QUESTION

## One state. Three measurement bases.

For (2|0⟩ + 3i|1⟩)/√13, the Z, X, and Y bases reveal different probabilities. Change the amplitudes, sample measurements, and unfold every inner product.

Open the projection workbench →

## A continuous course

Each chapter has the same explanations, examples, notation, and exercises in the PDF and on this site. Laboratory links take you directly from the page to the experiment.

CHAPTERS 1–8

### Build the foundations

Probability, amplitudes, measurement, circuits, entanglement, and open systems.

1. Information, probability, and computation
2. Complex amplitudes and quantum states
3. Measurement and changes of basis
4. Gates, observables, and the Bloch sphere
5. Registers, circuits, and entanglement
6. Density matrices and subsystems
7. Bell correlations, teleportation, and dense coding
8. Noise channels, measurement data, and mitigation

CHAPTERS 9–15

### Understand the algorithms

Oracle interference, period finding, Fourier methods, Hamiltonian simulation, and variational techniques.

9. Oracle algorithms: Deutsch, Deutsch–Jozsa, and Bernstein–Vazirani
10. Simon's algorithm and hidden XOR structure
11. Grover search and amplitude amplification
12. Fourier transforms and phase estimation
13. Period finding and Shor's factoring algorithm
14. Hamiltonian simulation and modern algorithmic tools
15. Variational algorithms and their limits

CHAPTERS 16–20

### Make computation reliable

Classical simulation, stabilizer codes, decoding, logical operations, and resource budgets.

16. Classical simulation and the cost of representation
17. Stabilizers and quantum error correction
18. Surface codes and decoding
19. Fault-tolerant computation and modern codes
20. Resource estimation: from circuits to machines

CHAPTERS 21–25

### Connect theory to practice

Physical platforms, quantum networks, reproducible software, 2026 evidence, and integrated projects.

21. Physical qubits, control, and hardware benchmarks
22. Quantum networks, BB84, and post-quantum cryptography
23. Programming reproducible quantum experiments
24. Reading the experimental frontier in 2026
25. Integrated laboratories and a path to research

## A dated view of a changing field

Research cutoff: 5 September 2026. Experiments, theory, preprints, and company claims are identified separately. Hardware counts and resource estimates keep their assumptions and scope.

Read the scientific snapshot →