This note maps the two source PDFs into the practical course path. Use [[Practical Quantum Information System]] for the teaching order, [[Roadmap]] for navigation, and [[Resources]] for course links, references, software, simulators, hardware, and fun project links. Use this page when you want to know which PDF chapter or lecture should sit beside a concept note. ## Source Roles > [!info] Primary technical spine > Scott Aaronson, *Introduction to Quantum Information Science Lecture Notes* (`qclec.pdf`) is the main source for the lecture sequence, definitions, algorithms, proofs, and homework-style derivations. > [!info] Companion perspective source > Scott Aaronson, *Quantum Computing since Democritus* (`7c581f75f258e9c36788c60cf45f3961.pdf`) is the companion source for conceptual framing, computational complexity context, skepticism of quantum computing, hidden variables, and the philosophical stakes of the subject. ## How To Use The Pair Read the lecture notes first when you need the formal object: state, gate, oracle, proof, or runtime. Read *Quantum Computing since Democritus* when you need the larger idea: why amplitudes are not ordinary probabilities, why BQP is not a blank check for NP-complete problems, why decoherence matters, or why fault tolerance is the right answer to the "analog computer" worry. For each concept note, the best study loop is: 1. read the concept note 2. read the matching `qclec.pdf` lecture section 3. read the companion Democritus chapter if listed below 4. answer the study questions without looking 5. run or sketch the practical lab ## Unit Map | Course unit | Primary `qclec.pdf` reading | Companion Democritus reading | Notes | | --- | --- | --- | --- | | Foundations and the Extended Church-Turing Thesis | Lectures 1-4 | Chapters 5-6, 9, 15 | [[concepts/Extended Church-Turing Thesis]], [[concepts/Probability Theory and Quantum Mechanics]], [[concepts/Basic Rules of Quantum Mechanics]], [[concepts/Quantum Gates and Circuits]] | | Multi-qubit states, mixed states, and entanglement | Lectures 5-11 | Chapters 9 and 14 | [[concepts/Pure vs. Mixed States]], [[concepts/Density Matrices and Partial Trace]], [[concepts/Separable vs. Entangled States]], [[concepts/Schmidt Decomposition]], [[concepts/Entanglement Entropy]] | | No-cloning, money, QKD, and communication | Lectures 7-10 | Chapters 8-10 | [[concepts/Bloch Sphere and No-Cloning Theorem]], [[concepts/Quantum Money and Quantum Key Distribution]], [[concepts/Superdense Coding]], [[concepts/Quantum Teleportation]], [[concepts/GHZ States, Entanglement Swapping, and Monogamy]] | | Interpretations, Bell, and certified randomness | Lectures 12-15 | Chapter 12 | [[concepts/Interpretations of Quantum Mechanics]], [[concepts/Bell's Inequality and CHSH]], [[concepts/Nonlocal Games]], [[concepts/Einstein-Certified Randomness]] | | Universal circuits and query algorithms | Lectures 16-24 | Chapters 10, 14, and 15 | [[concepts/Universal Gate Sets]], [[concepts/Quantum Query Complexity and Deutsch-Jozsa]], [[concepts/Bernstein-Vazirani and Simon's Algorithm]], [[concepts/Grover's Algorithm]], [[concepts/Quantum Complexity Theory]] | | Shor, QFT, and structured speedups | Lectures 19-21 | Chapters 10 and 15 | [[concepts/RSA, Period Finding, and Shor's Algorithm]], [[concepts/Quantum Fourier Transform]], [[concepts/Quantum Complexity Theory]] | | Hamiltonians and adiabatic ideas | Lectures 25-26 | Chapters 10 and 15 as context | [[concepts/Hamiltonians]], [[concepts/The Adiabatic Algorithm]] | | Error correction and stabilizers | Lectures 27-28 | Chapter 15 | [[concepts/Quantum Error Correction]], [[concepts/Stabilizer Formalism]] | ## Reading Priorities If time is short, prioritize the readings that change how you think: - `qclec.pdf`, Lectures 1-4: amplitudes, interference, measurement, and gates. - `qclec.pdf`, Lectures 6 and 11: density matrices, partial trace, Schmidt decomposition, and entropy. - `qclec.pdf`, Lectures 13-15: CHSH, nonlocal games, and certified randomness. - `qclec.pdf`, Lectures 22-24: Grover, BBBV, collision, Element Distinctness, and complexity boundaries. - `qclec.pdf`, Lectures 27-28: quantum error correction and Gottesman-Knill. - *Quantum Computing since Democritus*, Chapters 9, 12, 14, and 15: amplitudes as generalized probability, decoherence and hidden variables, the size of quantum states, and skepticism/fault tolerance. ## What To Extract Into Notes > [!question] What should be copied into the concept notes? >> [!answer] Do not copy long passages. Extract the durable study object: a definition, proof sketch, algorithmic runtime, warning, or lab idea. The notes should stay teachable and runnable, not become source transcripts. > [!question] When should the Democritus book change a note? >> [!answer] Use it when the note needs conceptual pressure: why a claim matters, what it does not imply, or how it fits into the larger complexity and interpretation debate. Keep formal derivations grounded in `qclec.pdf`. ## Public Reference Lanes Use [[Resources]] for the full link list. The most useful public reference lanes are: - formal lecture notes: `qclec.pdf`, O'Donnell, Watrous, Wong, and Mermin - conceptual commentary: *Quantum Computing since Democritus*, Shtetl-Optimized, IBM Quantum Blog, and Quantum Advantage Tracker - software practice: IBM Quantum/Qiskit, PennyLane, CUDA-Q, QuTiP, Classiq, and Q-CTRL - simulation and hardware: CHP, CUDA-Q, tensor networks, IBM Quantum, Braket, IonQ, Pasqal, QuEra, and Qiskit Metal