Use this page as the short navigation map of the course. For the full day-by-day teaching order, use [[Practical Quantum Information System]]. For source alignment with the two PDFs, use [[Source Reading Guide]]. For course links, references, simulators, and hardware pathways, use [[Resources]]. For a compact study surface, use [[Review Questions]]. For the runnable repo map, use [[Quantum Code Map]]. For the final project structure, use [[Final Capstone Workflow]]. ```mermaid flowchart TD A["Amplitudes, interference, and single-qubit mechanics"] --> B["Tensor products, density matrices, and entanglement"] B --> C["Communication, Bell, and cryptography"] C --> D["Algorithms, query models, and complexity"] D --> E["Hamiltonians, adiabatic methods, and noise"] E --> F["Error correction, stabilizers, and capstone work"] F --> G["Optional advanced extensions"] ``` ## Main Path Follow the main path in this order: 1. learn the concept from the note 2. read the matching source section from [[Source Reading Guide]] 3. answer the matching section in [[Review Questions]] 4. run the primary Qiskit lab 5. compare the same idea in Q#, CUDA-Q, QuTiP, or PennyLane when useful 6. compare ideal simulation, noisy simulation, and hardware if available 7. finish the homework by combining derivation and experiment analysis ## Reading Lanes Use the two PDFs in different ways. - `qclec.pdf`: formal lecture spine, derivations, algorithms, and proof sketches. - *Quantum Computing since Democritus*: conceptual companion for complexity, interpretation, skepticism, and why the formalism matters. - Concept notes: the teachable version that connects the source reading to labs and homework. ## Main Path Milestones 1. Understand amplitudes, interference, and the circuit model. Notes: [[concepts/Extended Church-Turing Thesis]], [[concepts/Probability Theory and Quantum Mechanics]], [[concepts/Basic Rules of Quantum Mechanics]], [[concepts/Quantum Gates and Circuits]] 2. Understand multi-qubit structure, mixed states, and entanglement. Notes: [[concepts/Separable vs. Entangled States]], [[concepts/Density Matrices and Partial Trace]], [[concepts/Pure vs. Mixed States]], [[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]], [[concepts/Schmidt Decomposition]], [[concepts/Entanglement Entropy]] 3. Understand communication, Bell nonlocality, and randomness. Notes: [[concepts/Interpretations of Quantum Mechanics]], [[concepts/Bell's Inequality and CHSH]], [[concepts/Nonlocal Games]], [[concepts/Einstein-Certified Randomness]] 4. Understand universal circuits, query complexity, and core algorithms. Notes: [[concepts/Universal Gate Sets]], [[concepts/Quantum Query Complexity and Deutsch-Jozsa]], [[concepts/Bernstein-Vazirani and Simon's Algorithm]], [[concepts/RSA, Period Finding, and Shor's Algorithm]], [[concepts/Quantum Fourier Transform]], [[concepts/Grover's Algorithm]], [[concepts/Quantum Complexity Theory]] 5. Understand Hamiltonians, adiabatic ideas, and physical modeling. Notes: [[concepts/Hamiltonians]], [[concepts/The Adiabatic Algorithm]] 6. Understand quantum error correction and the stabilizer formalism. Notes: [[concepts/Quantum Error Correction]], [[concepts/Stabilizer Formalism]] ## Core Concept Sequence Use this order when reviewing, teaching, or extending the notes: - Pure vs. Mixed States - Density Matrices and Partial Trace - Separable vs. Entangled States - Schmidt Decomposition - Von Neumann Entropy and Entanglement Entropy - Bell States, CHSH, and Nonlocal Games - No-Cloning, Teleportation, Superdense Coding, and QKD - QFT, Shor, and Grover - Noise, Error Correction, and Stabilizers ## Companion Code Repo The runnable course code should live in the companion repo [montekkundan/quantum-code](https://github.com/montekkundan/quantum-code). Use these repo layers the same way the LLM course uses `notebooks/`, `course_tools/`, and serious runtime files: - [[Quantum Code Map]] for the lecture-side map of notes to runnable code - [COURSE_MAP.md](https://github.com/montekkundan/quantum-code/blob/main/COURSE_MAP.md) for the lecture-to-code map - [notebooks/](https://github.com/montekkundan/quantum-code/tree/main/notebooks) for live walkthroughs and per-concept labs - [qcourse/](https://github.com/montekkundan/quantum-code/tree/main/qcourse) for tested concept-first helpers - [tests/](https://github.com/montekkundan/quantum-code/tree/main/tests) for regression checks and scientific invariants - [qsharp/](https://github.com/montekkundan/quantum-code/tree/main/qsharp) for selected Q# comparisons and resource-estimation exercises - [[Final Capstone Workflow]] and [capstone/](https://github.com/montekkundan/quantum-code/tree/main/capstone) for final project expectations The practical loop is note -> per-concept notebook -> helper module -> test. That loop is what keeps this from becoming a theory-only folder. ## Practical Tracks Keep the course anchored in real tools: - [IBM Quantum Learning and Qiskit](https://quantum.cloud.ibm.com/learning/en) for the primary lab path - [Microsoft Quantum and Azure Quantum](https://learn.microsoft.com/en-us/azure/quantum/) for Q# and provider workflows - [NVIDIA CUDA-Q](https://developer.nvidia.com/cuda-q) for hybrid and accelerated simulation - [QuTiP](https://qutip.org/) for Hamiltonians, density matrices, and open systems - [PennyLane demos](https://pennylane.ai/qml/demonstrations) for variational and QML extensions ## Optional Advanced Extensions Take the advanced track after the main path if you want the systems and research layer: - noise models and channels - error mitigation - quantum optimization - quantum machine learning - hardware-specific implementation pathways for superconducting, trapped-ion, and neutral-atom platforms - source-backed essays on quantum skepticism, BQP versus NP-complete problems, and the limits of extracting classical information from quantum states