Welcome to Quantum Knowledge — a curated guide to understanding quantum science, quantum computing, and related technologies. This repository gathers the best resources, explanations, and personal insights to help you learn quantum topics—whether you’re a beginner or brushing up on advanced concepts.
Feel free to contribute, edit, or expand any section!
- Quantum Vocab Cheat Sheet
- Linear Algebra
- Schrödinger's Equation
- Dirac Notation
- Quantum Physics
- Quantum Mechanics Basics
- Quantum Computing
- Useful Resources
- Quantum News Sources
- Quantum Sector Stocks to Watch
- How to Contribute
- See vocab cheat sheet for definitions of key terms in quantum science.
Linear algebra is the mathematical backbone of quantum computing. It helps describe quantum states, gates, and measurements.
| Concept | Description | Quantum Role |
|---|---|---|
| Vector | Ordered list of numbers | Represents quantum states (` |
| Matrix | Grid of numbers | Represents quantum gates |
| Inner Product | Measures similarity | Calculates probabilities |
| Tensor Product | Combines vectors | Builds multi-qubit systems |
| Eigenvalues/Eigenvectors | Special matrix properties | Describe measurements |
| Complex Numbers | Real + imaginary parts | Used in amplitudes |
| Unitary/Hermitian Matrices | Preserve norms / real eigenvalues | Define gates and observables |
- Essence of Linear Algebra – 3Blue1Brown
- Better Explained – Linear Algebra
- MIT OpenCourseWare
- A First Course in Linear Algebra – Free Textbook
- Linear Algebra Done Right (Book)
- Linear Algebra for Quantum Computing (YouTube)
The Schrödinger equation describes how quantum states evolve over time.
- Ψ(x, t): Wavefunction (state of the system)
- Ĥ: Hamiltonian operator (total energy)
- ħ: Reduced Planck’s constant
- Wikipedia: Schrödinger Equation
- Quantum Country – Schrödinger Equation
- MIT OpenCourseWare – Quantum Physics
- Video: Schrödinger’s Equation Explained
Dirac notation uses “kets” and “bras” to describe quantum states:
- Ket (
|ψ⟩): Represents a quantum state - Bra (
⟨ψ|): Represents the conjugate transpose of a quantum state - Bra–ket (
⟨ψ|ψ⟩): Inner product, describes probability amplitude
- Wikipedia: Bra–ket notation
- Quantum Country: Dirac Notation
- Qiskit Textbook
- MIT Lecture Notes
- Quantum Computing for the Determined (YouTube)
Quantum physics explores the behavior of matter and energy at the smallest scales.
- MIT Quantum Physics I – Video Lectures
- Quantum Physics for Beginners (Book)
- Khan Academy – Quantum Physics
- Quantum Physics Crash Course (YouTube)
Quantum mechanics describes the fundamental rules that govern particles at atomic and subatomic scales.
| Principle | Description |
|---|---|
| Superposition | A particle can exist in multiple states at once until measured |
| Entanglement | Two particles can be correlated so that measuring one affects the other instantly |
| Measurement | Observing a quantum system collapses it into a definite state |
| Uncertainty Principle | You can't precisely know both position and momentum: Δx·Δp ≥ ħ/2 |
| Wavefunction | A mathematical function that describes the quantum state of a system |
| Quantization | Energy levels are discrete, not continuous |
- Double-slit experiment – Demonstrates wave-particle duality
- Photoelectric effect – Shows light behaves as particles (photons)
- Stern-Gerlach experiment – Reveals quantum spin and measurement
- Bell’s inequality tests – Confirms quantum entanglement
- Quantum Mechanics and Path Integrals – Feynman & Hibbs
- Quantum Physics for Beginners – Alastair Rae
- The Feynman Lectures on Physics, Vol. 3
- Quantum Mechanics (MIT OpenCourseWare)
Quantum computing applies quantum mechanics to computation.
- Qubits: Quantum bits in superposition
- Quantum Gates: Operations on qubits
- Quantum Circuits: Sequences of gates
- Quantum Algorithms: Grover’s, Shor’s, Quantum Fourier Transform
- Qiskit Textbook
- IBM Quantum Playground
- Quantum Computing for the Determined (YouTube)
- Quantum Country
- Quantum Algorithm Zoo
- Microsoft Quantum Development Kit
- Quantum Country
- Qiskit Textbook
- IBM Quantum Playground
- Quantum Algorithm Zoo
- Microsoft Quantum Docs
- QuTiP: Quantum Toolbox in Python
- Quantum Computing Stack Exchange
- Quantum Open Source Foundation
- Quantum Machine Learning (Google)
Stay informed with these trusted quantum computing news platforms:
| Source | Description | Link |
|---|---|---|
| ScienceDaily – Quantum Computing | Breakthroughs from labs and universities | Link |
| MIT News – Quantum Computing | Academic and research updates | Link |
| The Quantum Insider | Industry, startups, and ecosystem news | Link |
| Quantum Computing Report | Funding, partnerships, and technical milestones | Link |
| Scientific American – Quantum Computing | Accessible articles on quantum theory and tech | Link |
- MSN Money & News – Quantum stock performance
- CNBC & NBC Business – Corporate quantum developments
- Quantum Daily – Industry analysis and investor news
Track companies leading the quantum computing revolution:
| Company | Ticker | Focus Area | Info Link |
|---|---|---|---|
| IBM | IBM | Quantum hardware/cloud | Yahoo Finance |
| IonQ | IONQ | Quantum hardware | Yahoo Finance |
| D-Wave Quantum | QBTS | Quantum annealing | Yahoo Finance |
| Rigetti Computing | RGTI | Quantum hardware | Yahoo Finance |
| Alphabet | GOOG | Quantum research | Yahoo Finance |
| Microsoft | MSFT | Quantum software | Yahoo Finance |
| Nvidia | NVDA | Quantum acceleration | Yahoo Finance |
Note: The quantum sector is emerging. Stocks can be volatile—do your own research and consult financial experts.
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- Add new sections with explanations, links, and documentation
- Update the Table of Contents
- Follow the formatting style used in existing entries
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- Submit a pull request with clear descriptions of your changes
Enjoy exploring quantum knowledge!