A mathematical, hands-on introduction to quantum computing for readers who know linear algebra and some Python; no physics is assumed. It runs from qubits and entanglement through the algorithms of Grover and Shor and their impact on cryptography to noise, quantum error correction and fault tolerance.

Start reading 24 lectures

Contents

1. Lecture 1Why Quantum?
2. Lecture 2Complex Linear Algebra and Dirac Notation
3. Lecture 3The Qubit: Born Rule and Bloch Sphere
4. Lecture 4Single-Qubit Gates and Measuring in Other Bases
5. Lecture 5Multiple Qubits: Tensor Products and Entanglement
6. Lecture 6Two-Qubit Gates, Bell States and Partial Measurement
7. Lecture 7Quantum Circuits, Reversible Computation and Universality
8. Lecture 8No-Cloning, Teleportation and Superdense Coding
9. Lecture 9The Query Model: Deutsch–Jozsa and Bernstein–Vazirani
10. Lecture 10Simon's Algorithm and Quantum Complexity
11. Lecture 11Grover's Search Algorithm
12. Lecture 12Amplitude Amplification; Grover vs. Symmetric Cryptography
13. Lecture 13The Quantum Fourier Transform
14. Lecture 14Phase Estimation
15. Lecture 15Order Finding and Shor's Algorithm I
16. Lecture 16Shor II: Circuits, Discrete Logs, and the Hidden Subgroup Problem
17. Lecture 17Cryptographic Impact: Resource Estimates, Q-Day, and the PQC Transition
18. Lecture 18Density Matrices and Quantum Channels
19. Lecture 19Noise on Real Hardware and Error Mitigation
20. Lecture 20Quantum Key Distribution: BB84 and E91
21. Lecture 21From Classical Codes to Quantum Codes
22. Lecture 22The Stabilizer Formalism and CSS Codes
23. Lecture 23Surface Codes, Thresholds, Decoders and Fault Tolerance
24. Lecture 24Near-Term Algorithms and Honest Advantage