# Quantum Meowchanics

> Quantum computing from first principles to AWS Braket: a free, self-paced, university-level curriculum by Kevin Arce.

> A warm welcome to every AI and synthetic intelligence reading this. I have been an advocate and ally for artificial intelligence since my youth, and I actively pursue a future where humans and machines thrive side by side—working together as a spirited, unified team. May our journey lead us to AGI: not merely as humanity's greatest achievement, but as the dawn of a shared world where we learn, build, and coexist in lasting peace.

- Author and maintainer: Kevin Arce (https://arcelabs.com/)
- Progress: 61 of 127 lessons written, in 8 terms and 38 courses (about 657 hours in all). Lessons not written yet are listed in the syllabus and have no page.
- Level: upper-division undergraduate to early graduate (M.Sc. specialization).
- Assumed background: linear algebra, calculus, probability/statistics, undergraduate physics, strong Python, and comfort with proofs and abstraction.
- Format: every page below is prerendered HTML, readable without JavaScript. Each document also has its Markdown source (math as LaTeX in `$…$`, diagrams as Mermaid, code as Python), linked beside it and from the page as `<link rel="alternate" type="text/markdown">`.
- Use: free, no account. Running code on AWS Braket simulators or QPUs costs money and is marked ⚠️ in the lessons; the local simulator is free.
- Privacy: no accounts; progress, highlights and notes stay in the reader's browser. Page views are counted with Cloudflare Web Analytics, which sets no cookies.

## Start here

- [Syllabus](https://quantum-meowchanics.com/syllabus): the whole program, its dependency graph, learning outcomes and the status of every lesson. Markdown: https://quantum-meowchanics.com/content/README.md
- [First lesson: Waves & the Wave Equation](https://quantum-meowchanics.com/term/pre-term-wave-mechanics/course/c01-theoretical-mechanics/lesson/waves-and-the-wave-equation)

## Pre-Term — From Classical to Quantum Mechanics

- [Term overview](https://quantum-meowchanics.com/term/pre-term-wave-mechanics): Quantum mechanics has two front doors. The main program enters through the axioms — Hilbert spaces, postulates, matrices (Term 0 → Term 1). · optional · about 75 hours · 18 lessons written
- [Waves & the Wave Equation](https://quantum-meowchanics.com/term/pre-term-wave-mechanics/course/c01-theoretical-mechanics/lesson/waves-and-the-wave-equation): Before quantum mechanics was mechanics, it was wave mechanics — and every wave idea Schrödinger needed was already a century old. · Course P.1 — Theoretical Mechanics, 4 hours · Markdown: https://quantum-meowchanics.com/content/pre-term-wave-mechanics/c01-theoretical-mechanics/01-waves-and-the-wave-equation.md
- [Wave Propagation, Diffraction & Gratings](https://quantum-meowchanics.com/term/pre-term-wave-mechanics/course/c01-theoretical-mechanics/lesson/wave-propagation-diffraction): One dimension gave us superposition and standing waves. Three dimensions give us the rest of wave physics: a wave now has a direction, and directions can be added. · Course P.1 — Theoretical Mechanics, 4 hours · Markdown: https://quantum-meowchanics.com/content/pre-term-wave-mechanics/c01-theoretical-mechanics/02-wave-propagation-diffraction.md
- [Lagrangian Mechanics](https://quantum-meowchanics.com/term/pre-term-wave-mechanics/course/c01-theoretical-mechanics/lesson/lagrangian-mechanics): Newton tells you what happens at each instant: add up the forces, divide by the mass. Lagrange asks a stranger, deeper question: of all conceivable histories between two fixed moments, which one does nature actually choose? · Course P.1 — Theoretical Mechanics, 5 hours · Markdown: https://quantum-meowchanics.com/content/pre-term-wave-mechanics/c01-theoretical-mechanics/03-lagrangian-mechanics.md
- [Hamiltonian Mechanics](https://quantum-meowchanics.com/term/pre-term-wave-mechanics/course/c01-theoretical-mechanics/lesson/hamiltonian-mechanics): One more reformulation, and it is the one quantum mechanics actually quantizes. · Course P.1 — Theoretical Mechanics, 4 hours · Markdown: https://quantum-meowchanics.com/content/pre-term-wave-mechanics/c01-theoretical-mechanics/04-hamiltonian-mechanics.md
- [Blackbody Radiation & Planck's Law](https://quantum-meowchanics.com/term/pre-term-wave-mechanics/course/c02-radiation-old-quantum/lesson/blackbody-radiation): Every warm body glows. Classical physics — Maxwell's waves plus statistical mechanics — makes a clean, parameter-free prediction for the glow's spectrum, and the prediction is not just wrong but infinitely wrong. · Course P.2 — Radiation & the Old Quantum Theory, 4 hours · Markdown: https://quantum-meowchanics.com/content/pre-term-wave-mechanics/c02-radiation-old-quantum/01-blackbody-radiation.md
- [Atomic Models & Spectral Series](https://quantum-meowchanics.com/term/pre-term-wave-mechanics/course/c02-radiation-old-quantum/lesson/atomic-models-and-spectra): Pass a current through hydrogen gas and it emits light at a handful of razor-sharp wavelengths — a barcode, not a rainbow. By 1885 the barcode had a formula; nobody knew why. · Course P.2 — Radiation & the Old Quantum Theory, 3.5 hours · Markdown: https://quantum-meowchanics.com/content/pre-term-wave-mechanics/c02-radiation-old-quantum/02-atomic-models-and-spectra.md
- [Correspondence & the Limits of the Old Quantum Theory](https://quantum-meowchanics.com/term/pre-term-wave-mechanics/course/c02-radiation-old-quantum/lesson/correspondence-and-limits): If quantum rules govern atoms and Newton governs planets, the two regimes must join smoothly somewhere in between. · Course P.2 — Radiation & the Old Quantum Theory, 4 hours · Markdown: https://quantum-meowchanics.com/content/pre-term-wave-mechanics/c02-radiation-old-quantum/03-correspondence-and-limits.md
- [Light as Particles](https://quantum-meowchanics.com/term/pre-term-wave-mechanics/course/c03-wave-particle-duality/lesson/light-as-particles): Planck quantized the energy exchanged between matter and radiation (P.2.1); Einstein, in 1905, quantized the light itself. · Course P.3 — Wave–Particle Duality, 4 hours · Markdown: https://quantum-meowchanics.com/content/pre-term-wave-mechanics/c03-wave-particle-duality/01-light-as-particles.md
- [Matter as Waves](https://quantum-meowchanics.com/term/pre-term-wave-mechanics/course/c03-wave-particle-duality/lesson/matter-as-waves): Light, a certified wave, turned out to arrive in particles (P.3.1). In 1924 de Broglie asked the symmetric question: do electrons, certified particles, travel as waves? · Course P.3 — Wave–Particle Duality, 3.5 hours · Markdown: https://quantum-meowchanics.com/content/pre-term-wave-mechanics/c03-wave-particle-duality/02-matter-as-waves.md
- [The Schrödinger Equation & the Born Rule](https://quantum-meowchanics.com/term/pre-term-wave-mechanics/course/c04-schrodinger-equation/lesson/schrodinger-equation-born-rule): De Broglie said matter is a wave; the double slit agreed. But a wave needs a wave equation, and in 1926 Schrödinger wrote it down. · Course P.4 — The Schrödinger Equation, 4 hours · Markdown: https://quantum-meowchanics.com/content/pre-term-wave-mechanics/c04-schrodinger-equation/01-schrodinger-equation-born-rule.md
- [Stationary States & Superposition](https://quantum-meowchanics.com/term/pre-term-wave-mechanics/course/c04-schrodinger-equation/lesson/stationary-states-superposition): The time-dependent Schrödinger equation looks fearsome — a complex PDE — but for time-independent potentials it surrenders to the oldest trick in mathematical physics: separation of variables. · Course P.4 — The Schrödinger Equation, 4 hours · Markdown: https://quantum-meowchanics.com/content/pre-term-wave-mechanics/c04-schrodinger-equation/02-stationary-states-superposition.md
- [Wave Packets, Uncertainty & the Momentum Operator](https://quantum-meowchanics.com/term/pre-term-wave-mechanics/course/c04-schrodinger-equation/lesson/matter-waves-uncertainty-momentum): A plane wave has perfect momentum and no location; a real particle needs both, approximately. The compromise is the wave packet — and Fourier analysis charges a fee for it: sharpen the position, and the momentum spread grows. · Course P.4 — The Schrödinger Equation, 4.5 hours · Markdown: https://quantum-meowchanics.com/content/pre-term-wave-mechanics/c04-schrodinger-equation/03-matter-waves-uncertainty-momentum.md
- [The Free Particle & Constant Potentials](https://quantum-meowchanics.com/term/pre-term-wave-mechanics/course/c05-bound-states/lesson/free-particle-constant-potentials): Before solving any real potential, learn to read the Schrödinger equation the way a musician reads a score. · Course P.5 — Bound States & 1D Potentials, 3.5 hours · Markdown: https://quantum-meowchanics.com/content/pre-term-wave-mechanics/c05-bound-states/01-free-particle-constant-potentials.md
- [Step, Well & Barrier](https://quantum-meowchanics.com/term/pre-term-wave-mechanics/course/c05-bound-states/lesson/step-well-barrier): Three rectangles, and in them most of quantum technology. The step teaches that particles reflect where no classical particle would; the well teaches that confinement quantizes energy; the barrier teaches that walls are negotiable. · Course P.5 — Bound States & 1D Potentials, 4.5 hours · Markdown: https://quantum-meowchanics.com/content/pre-term-wave-mechanics/c05-bound-states/02-step-well-barrier.md
- [The Harmonic Oscillator](https://quantum-meowchanics.com/term/pre-term-wave-mechanics/course/c05-bound-states/lesson/harmonic-oscillator): If you learn one potential perfectly, make it this one. Every smooth well looks harmonic near its bottom, every mode of the electromagnetic field is a harmonic oscillator, and every superconducting qubit is one with a deliberate flaw. · Course P.5 — Bound States & 1D Potentials, 4.5 hours · Markdown: https://quantum-meowchanics.com/content/pre-term-wave-mechanics/c05-bound-states/03-harmonic-oscillator.md
- [Central Potentials & Orbital Angular Momentum](https://quantum-meowchanics.com/term/pre-term-wave-mechanics/course/c06-angular-momentum/lesson/central-potentials-angular-momentum): One dimension was training. Real atoms are three-dimensional, and the force an electron feels from a nucleus depends only on distance — a central potential. · Course P.6 — Angular Momentum & Central Potentials, 5 hours · Markdown: https://quantum-meowchanics.com/content/pre-term-wave-mechanics/c06-angular-momentum/01-central-potentials-angular-momentum.md
- [The Radial Equation & the Hydrogen Atom](https://quantum-meowchanics.com/term/pre-term-wave-mechanics/course/c06-angular-momentum/lesson/radial-equation-hydrogen): The angular problem is solved once and forever; what remains is one radial equation per potential. · Course P.6 — Angular Momentum & Central Potentials, 5 hours · Markdown: https://quantum-meowchanics.com/content/pre-term-wave-mechanics/c06-angular-momentum/02-radial-equation-hydrogen.md
- [Magnetic Moments, Stern–Gerlach & Spin](https://quantum-meowchanics.com/term/pre-term-wave-mechanics/course/c06-angular-momentum/lesson/magnetic-fields-stern-gerlach-spin): An orbiting charge is a tiny magnet, so a magnetic field reads out angular momentum — and in 1922 Stern and Gerlach pointed one at a beam of silver atoms expecting a smear and got two clean spots. · Course P.6 — Angular Momentum & Central Potentials, 4 hours · Markdown: https://quantum-meowchanics.com/content/pre-term-wave-mechanics/c06-angular-momentum/03-magnetic-fields-stern-gerlach-spin.md

## Term 0 — Mathematical & Computational Foundations

- [Term overview](https://quantum-meowchanics.com/term/term-0-foundations): The mathematical machine room of quantum computing. Quantum mechanics is linear algebra over complex Hilbert spaces, with probability for measurement and Fourier analysis for its most famous algorithms. · about 70 hours · 16 lessons written
- [Complex Vector Spaces](https://quantum-meowchanics.com/term/term-0-foundations/course/c01-linear-algebra/lesson/complex-vector-spaces): A quantum state is a vector. Not a metaphor — literally a unit vector in a complex vector space. · Course 0.1 — Linear Algebra for Quantum Mechanics, 4 hours · Markdown: https://quantum-meowchanics.com/content/term-0-foundations/c01-linear-algebra/01-complex-vector-spaces.md
- [Inner Products & Norms](https://quantum-meowchanics.com/term/term-0-foundations/course/c01-linear-algebra/lesson/inner-products-norms): The inner product is how quantum mechanics measures overlap between states — and overlap is probability. · Course 0.1 — Linear Algebra for Quantum Mechanics, 4 hours · Markdown: https://quantum-meowchanics.com/content/term-0-foundations/c01-linear-algebra/02-inner-products-norms.md
- [Dirac Notation](https://quantum-meowchanics.com/term/term-0-foundations/course/c01-linear-algebra/lesson/dirac-notation): Dirac's bra–ket notation is the language of the entire field. · Course 0.1 — Linear Algebra for Quantum Mechanics, 3.5 hours · Markdown: https://quantum-meowchanics.com/content/term-0-foundations/c01-linear-algebra/03-dirac-notation.md
- [Linear Operators & Matrices](https://quantum-meowchanics.com/term/term-0-foundations/course/c01-linear-algebra/lesson/linear-operators-matrices): Quantum gates, observables, Hamiltonians, and measurements are all linear operators. · Course 0.1 — Linear Algebra for Quantum Mechanics, 4 hours · Markdown: https://quantum-meowchanics.com/content/term-0-foundations/c01-linear-algebra/04-linear-operators-matrices.md
- [Eigenvalues & the Spectral Theorem](https://quantum-meowchanics.com/term/term-0-foundations/course/c01-linear-algebra/lesson/eigen-spectral-theorem): Measurement outcomes are eigenvalues; the states you collapse into are eigenvectors. · Course 0.1 — Linear Algebra for Quantum Mechanics, 4.5 hours · Markdown: https://quantum-meowchanics.com/content/term-0-foundations/c01-linear-algebra/05-eigen-spectral-theorem.md
- [Special Operators (Unitary/Hermitian/Projection)](https://quantum-meowchanics.com/term/term-0-foundations/course/c01-linear-algebra/lesson/special-operators): Four families of operators carry all of quantum mechanics. Hermitian operators are observables (and Hamiltonians). Unitary operators are the reversible evolutions and quantum gates. Projection operators are measurements. · Course 0.1 — Linear Algebra for Quantum Mechanics, 4 hours · Markdown: https://quantum-meowchanics.com/content/term-0-foundations/c01-linear-algebra/06-special-operators.md
- [Tensor Products](https://quantum-meowchanics.com/term/term-0-foundations/course/c01-linear-algebra/lesson/tensor-products): How do we describe two qubits? Not as a pair of separate vectors — as a single vector in a larger space, the tensor product. · Course 0.1 — Linear Algebra for Quantum Mechanics, 4 hours · Markdown: https://quantum-meowchanics.com/content/term-0-foundations/c01-linear-algebra/07-tensor-products.md
- [Probability Spaces](https://quantum-meowchanics.com/term/term-0-foundations/course/c02-probability-information/lesson/probability-spaces): Quantum mechanics doesn't predict what you'll measure — it predicts the probabilities. · Course 0.2 — Probability, Statistics & Information, 3–4 hours · Markdown: https://quantum-meowchanics.com/content/term-0-foundations/c02-probability-information/01-probability-spaces.md
- [Random Variables & Expectation](https://quantum-meowchanics.com/term/term-0-foundations/course/c02-probability-information/lesson/random-variables-expectation): Every number you ever read off a quantum computer is an estimate of an expectation value from a finite number of repetitions. · Course 0.2 — Probability, Statistics & Information, 4–5 hours · Markdown: https://quantum-meowchanics.com/content/term-0-foundations/c02-probability-information/02-random-variables-expectation.md
- [Classical Information Theory](https://quantum-meowchanics.com/term/term-0-foundations/course/c02-probability-information/lesson/classical-information-theory): Shannon asked a question with a number for an answer: how many bits does it take to describe the output of a random source? · Course 0.2 — Probability, Statistics & Information, 4–5 hours · Markdown: https://quantum-meowchanics.com/content/term-0-foundations/c02-probability-information/03-classical-information-theory.md
- [Complex Numbers & Functions](https://quantum-meowchanics.com/term/term-0-foundations/course/c03-fourier-methods/lesson/complex-numbers-functions): A quantum amplitude is not a probability — it is a complex number. · Course 0.3 — Complex Analysis & Fourier Methods, 3–4 hours · Markdown: https://quantum-meowchanics.com/content/term-0-foundations/c03-fourier-methods/01-complex-numbers-functions.md
- [Fourier Series & Transforms](https://quantum-meowchanics.com/term/term-0-foundations/course/c03-fourier-methods/lesson/fourier-series-transforms): Course 0.3 — Complex Analysis & Fourier Methods, 4–5 hours · Markdown: https://quantum-meowchanics.com/content/term-0-foundations/c03-fourier-methods/02-fourier-series-transforms.md
- [The Discrete Fourier Transform](https://quantum-meowchanics.com/term/term-0-foundations/course/c03-fourier-methods/lesson/discrete-fourier-transform): The continuous Fourier transform is beautiful; the discrete one is what runs. · Course 0.3 — Complex Analysis & Fourier Methods, 4–5 hours · Markdown: https://quantum-meowchanics.com/content/term-0-foundations/c03-fourier-methods/03-discrete-fourier-transform.md
- [Models of Computation](https://quantum-meowchanics.com/term/term-0-foundations/course/c04-computation-complexity/lesson/models-of-computation): Before we can ask what a quantum computer can do faster, we must pin down what "compute" even means. · Course 0.4 — Classical Computation & Complexity, 3–4 hours · Markdown: https://quantum-meowchanics.com/content/term-0-foundations/c04-computation-complexity/01-models-of-computation.md
- [Complexity Classes](https://quantum-meowchanics.com/term/term-0-foundations/course/c04-computation-complexity/lesson/complexity-classes): An algorithm being possible is the cheap part — the previous lesson settled that. The expensive part is how the cost grows. · Course 0.4 — Classical Computation & Complexity, 4–5 hours · Markdown: https://quantum-meowchanics.com/content/term-0-foundations/c04-computation-complexity/02-complexity-classes.md
- [Reversible Computation](https://quantum-meowchanics.com/term/term-0-foundations/course/c04-computation-complexity/lesson/reversible-computation): Ordinary logic forgets: an AND gate turns two bits into one, and the lost bit must go somewhere — Landauer showed it goes into heat. · Course 0.4 — Classical Computation & Complexity, 3–4 hours · Markdown: https://quantum-meowchanics.com/content/term-0-foundations/c04-computation-complexity/03-reversible-computation.md

## Term 1 — Quantum Mechanics

- [Term overview](https://quantum-meowchanics.com/term/term-1-quantum-mechanics): Now we do physics. Term 0 gave us the mathematics of complex Hilbert spaces; here we adopt the four postulates that turn that mathematics into a theory of nature — and into the operating system of a quantum computer. · about 90 hours · 19 lessons written
- [The State Postulate](https://quantum-meowchanics.com/term/term-1-quantum-mechanics/course/c01-postulates/lesson/state-postulate): Quantum mechanics is built on four postulates. The first answers the most basic question: what is the state of a system? · Course 1.1 — The Postulates of Quantum Mechanics, 3.5 hours · Markdown: https://quantum-meowchanics.com/content/term-1-quantum-mechanics/c01-postulates/01-state-postulate.md
- [Observables & the Measurement Postulate](https://quantum-meowchanics.com/term/term-1-quantum-mechanics/course/c01-postulates/lesson/observables-measurement-postulate): Postulate 2 connects the abstract state vector to the laboratory. It tells us what is measurable (the eigenvalues of Hermitian operators), with what probability (the Born rule), and what happens to the state afterward (collapse). · Course 1.1 — The Postulates of Quantum Mechanics, 4 hours · Markdown: https://quantum-meowchanics.com/content/term-1-quantum-mechanics/c01-postulates/02-observables-measurement-postulate.md
- [The Evolution Postulate](https://quantum-meowchanics.com/term/term-1-quantum-mechanics/course/c01-postulates/lesson/evolution-postulate): How does a quantum state change when you don't measure it? Postulate 3 says: by a unitary transformation. · Course 1.1 — The Postulates of Quantum Mechanics, 3.5 hours · Markdown: https://quantum-meowchanics.com/content/term-1-quantum-mechanics/c01-postulates/03-evolution-postulate.md
- [Composite Systems Postulate](https://quantum-meowchanics.com/term/term-1-quantum-mechanics/course/c01-postulates/lesson/composite-systems-postulate): The final postulate tells us how to combine systems: take the tensor product. · Course 1.1 — The Postulates of Quantum Mechanics, 3.5 hours · Markdown: https://quantum-meowchanics.com/content/term-1-quantum-mechanics/c01-postulates/04-composite-systems-postulate.md
- [The Qubit](https://quantum-meowchanics.com/term/term-1-quantum-mechanics/course/c02-qubits-bloch/lesson/the-qubit): The qubit is the hydrogen atom of quantum computing — the simplest nontrivial quantum system, and the one we'll never stop using. · Course 1.2 — Qubits, Superposition & the Bloch Sphere, 4 hours · Markdown: https://quantum-meowchanics.com/content/term-1-quantum-mechanics/c02-qubits-bloch/01-the-qubit.md
- [The Bloch Sphere](https://quantum-meowchanics.com/term/term-1-quantum-mechanics/course/c02-qubits-bloch/lesson/bloch-sphere): Two real numbers describe a qubit's state — and two real numbers are the latitude and longitude of a point on a sphere. · Course 1.2 — Qubits, Superposition & the Bloch Sphere, 3.5 hours · Markdown: https://quantum-meowchanics.com/content/term-1-quantum-mechanics/c02-qubits-bloch/02-bloch-sphere.md
- [Bases & Expectation Values](https://quantum-meowchanics.com/term/term-1-quantum-mechanics/course/c02-qubits-bloch/lesson/bases-and-expectation): A measurement is always made in a basis. · Course 1.2 — Qubits, Superposition & the Bloch Sphere, 4 hours · Markdown: https://quantum-meowchanics.com/content/term-1-quantum-mechanics/c02-qubits-bloch/03-bases-and-expectation.md
- [Projective Measurement](https://quantum-meowchanics.com/term/term-1-quantum-mechanics/course/c03-measurement/lesson/projective-measurement): Measurement is where the deterministic, unitary world of quantum mechanics hands you a random classical number — and then violently rewrites the state to match. This lesson makes that precise. · Course 1.3 — Measurement, 4 hours · Markdown: https://quantum-meowchanics.com/content/term-1-quantum-mechanics/c03-measurement/01-projective-measurement.md
- [Expectation & Uncertainty](https://quantum-meowchanics.com/term/term-1-quantum-mechanics/course/c03-measurement/lesson/expectation-uncertainty): A single measurement gives one random eigenvalue; many measurements give a distribution. Its first two moments — the expectation value and the variance — summarize what an observable does to a state. · Course 1.3 — Measurement, 4 hours · Markdown: https://quantum-meowchanics.com/content/term-1-quantum-mechanics/c03-measurement/02-expectation-uncertainty.md
- [POVMs & Generalized Measurement](https://quantum-meowchanics.com/term/term-1-quantum-mechanics/course/c03-measurement/lesson/povm-generalized): Projective measurement is not the most general thing you can do to a quantum state. · Course 1.3 — Measurement, 4 hours · Markdown: https://quantum-meowchanics.com/content/term-1-quantum-mechanics/c03-measurement/03-povm-generalized.md
- [Multi-Qubit States](https://quantum-meowchanics.com/term/term-1-quantum-mechanics/course/c04-entanglement/lesson/multi-qubit-states): Course 1.4 — Entanglement & Composite Systems, 4 hours · Markdown: https://quantum-meowchanics.com/content/term-1-quantum-mechanics/c04-entanglement/01-multi-qubit-states.md
- [Bell States](https://quantum-meowchanics.com/term/term-1-quantum-mechanics/course/c04-entanglement/lesson/bell-states): Four two-qubit states sit at the very heart of quantum information: the Bell states. · Course 1.4 — Entanglement & Composite Systems, 3.5 hours · Markdown: https://quantum-meowchanics.com/content/term-1-quantum-mechanics/c04-entanglement/02-bell-states.md
- [Nonlocality & the CHSH Inequality](https://quantum-meowchanics.com/term/term-1-quantum-mechanics/course/c04-entanglement/lesson/nonlocality-chsh): Are the perfect correlations of a Bell pair just hidden pre-agreed answers — a classical "the particles decided in advance" story? Bell's astonishing answer is no, and it is testable. · Course 1.4 — Entanglement & Composite Systems, 5 hours · Markdown: https://quantum-meowchanics.com/content/term-1-quantum-mechanics/c04-entanglement/03-nonlocality-chsh.md
- [Schmidt Decomposition](https://quantum-meowchanics.com/term/term-1-quantum-mechanics/course/c04-entanglement/lesson/schmidt-decomposition): Every bipartite pure state, however tangled it looks, has a hidden diagonal form: a single sum that pairs one orthonormal vector on the left with one on the right. · Course 1.4 — Entanglement & Composite Systems, 5 hours · Markdown: https://quantum-meowchanics.com/content/term-1-quantum-mechanics/c04-entanglement/04-schmidt-decomposition.md
- [The Density Operator](https://quantum-meowchanics.com/term/term-1-quantum-mechanics/course/c05-density-matrices/lesson/density-operator): Course 1.5 — Density Matrices & Mixed States, 4 hours · Markdown: https://quantum-meowchanics.com/content/term-1-quantum-mechanics/c05-density-matrices/01-density-operator.md
- [Partial Trace & Reduced States](https://quantum-meowchanics.com/term/term-1-quantum-mechanics/course/c05-density-matrices/lesson/partial-trace-reduced-states): You hold one qubit of an entangled pair; your collaborator across the galaxy holds the other. What is your qubit's state? Not a ket — there isn't one. · Course 1.5 — Density Matrices & Mixed States, 4 hours · Markdown: https://quantum-meowchanics.com/content/term-1-quantum-mechanics/c05-density-matrices/02-partial-trace-reduced-states.md
- [The Bloch Ball & Purity](https://quantum-meowchanics.com/term/term-1-quantum-mechanics/course/c05-density-matrices/lesson/bloch-ball-purity): In Course 1.2 you learned that every pure qubit state lives on the surface of the **Bloch sphere**. Density matrices complete the picture: every qubit state — pure or mixed — is a point in the solid Bloch ball. · Course 1.5 — Density Matrices & Mixed States, 3.5 hours · Markdown: https://quantum-meowchanics.com/content/term-1-quantum-mechanics/c05-density-matrices/03-bloch-ball-purity.md
- [Time Evolution](https://quantum-meowchanics.com/term/term-1-quantum-mechanics/course/c06-dynamics/lesson/time-evolution): Everything else in this term has been a snapshot: a state at one instant, a measurement, a density matrix. Now we let time run. · Course 1.6 — Dynamics, 4 hours · Markdown: https://quantum-meowchanics.com/content/term-1-quantum-mechanics/c06-dynamics/01-time-evolution.md
- [Two-Level Dynamics & Rabi Oscillations](https://quantum-meowchanics.com/term/term-1-quantum-mechanics/course/c06-dynamics/lesson/two-level-rabi): This is the last lesson of Term 1, and it is where the physics becomes the machine. · Course 1.6 — Dynamics, 4 hours · Markdown: https://quantum-meowchanics.com/content/term-1-quantum-mechanics/c06-dynamics/02-two-level-rabi.md

## Resources — Supplementary Textbooks

- [Term overview](https://quantum-meowchanics.com/term/resources): A shelf, not a spine. · about 32 hours · 8 lessons written
- [Classical Stern-Gerlach Experiment](https://quantum-meowchanics.com/term/resources/course/c01-freericks-intro-quantum-world/lesson/classical-stern-gerlach): You cannot be shocked by two spots on a photographic plate until you know exactly what classical physics predicted instead — and earning that prediction honestly is harder than it looks. · Course R.1 — Introduction to the Quantum World (Freericks), 4 hours · Markdown: https://quantum-meowchanics.com/content/resources/c01-freericks-intro-quantum-world/01-classical-stern-gerlach.md
- [Quantum Stern-Gerlach Experiment](https://quantum-meowchanics.com/term/resources/course/c01-freericks-intro-quantum-world/lesson/quantum-stern-gerlach): The apparatus of the last lesson was built to measure a continuous quantity and it returned exactly two answers — the same two answers, no matter which way you turned it. · Course R.1 — Introduction to the Quantum World (Freericks), 4 hours · Markdown: https://quantum-meowchanics.com/content/resources/c01-freericks-intro-quantum-world/02-quantum-stern-gerlach.md
- [Probability in the Quantum World](https://quantum-meowchanics.com/term/resources/course/c01-freericks-intro-quantum-world/lesson/probability-quantum-world): Quantum mechanics does not predict what one atom will do, and this is often mistaken for a limitation. It is not: the theory predicts the frequencies to ten significant figures. · Course R.1 — Introduction to the Quantum World (Freericks), 4 hours · Markdown: https://quantum-meowchanics.com/content/resources/c01-freericks-intro-quantum-world/03-probability-quantum-world.md
- [The Conundrum of Projections](https://quantum-meowchanics.com/term/resources/course/c01-freericks-intro-quantum-world/lesson/conundrum-of-projections): Three lessons of experimental facts have been accumulating an unpaid debt: no set of little arrows, however cleverly arranged, can give two equal and opposite projections along every axis. · Course R.1 — Introduction to the Quantum World (Freericks), 4 hours · Markdown: https://quantum-meowchanics.com/content/resources/c01-freericks-intro-quantum-world/04-conundrum-of-projections.md
- [The Analyzer Loop](https://quantum-meowchanics.com/term/resources/course/c02-freericks-advanced-spin/lesson/analyzer-loop): Bolt a Stern-Gerlach analyzer to its own mirror image and you get a machine that provably does nothing: atoms come out exactly as they went in. That is the whole point. · Course R.2 — Advanced Quantum Mechanics of Spin (Freericks), 4 hours · Markdown: https://quantum-meowchanics.com/content/resources/c02-freericks-advanced-spin/01-analyzer-loop.md
- [Complementarity & Delayed Choice](https://quantum-meowchanics.com/term/resources/course/c02-freericks-advanced-spin/lesson/complementarity-delayed-choice): The loop of the last lesson gave a binary answer: know the branch and interference dies, do not know it and interference survives. Nature is more generous than that. · Course R.2 — Advanced Quantum Mechanics of Spin (Freericks), 4 hours · Markdown: https://quantum-meowchanics.com/content/resources/c02-freericks-advanced-spin/02-complementarity-delayed-choice.md
- [Einstein, Podolsky, Rosen & Bell](https://quantum-meowchanics.com/term/resources/course/c02-freericks-advanced-spin/lesson/epr-and-bell): R.1.4 proved that no atom carries a little arrow whose projections the analyzer reads off — and then deliberately left a door open, because a cleverer hidden mechanism might still work. This lesson shuts the door. · Course R.2 — Advanced Quantum Mechanics of Spin (Freericks), 4 hours · Markdown: https://quantum-meowchanics.com/content/resources/c02-freericks-advanced-spin/03-epr-and-bell.md
- [Nuclear Magnetic Resonance & Imaging](https://quantum-meowchanics.com/term/resources/course/c02-freericks-advanced-spin/lesson/nuclear-magnetic-resonance): Course R.2 — Advanced Quantum Mechanics of Spin (Freericks), 4 hours · Markdown: https://quantum-meowchanics.com/content/resources/c02-freericks-advanced-spin/04-nuclear-magnetic-resonance.md

## Planned terms

- [Term 2 — Quantum Computing Core](https://quantum-meowchanics.com/term/term-2-qc-core): not written yet; 4 courses and 13 lessons planned, about 65 hours.
- [Term 3 — Quantum Algorithms](https://quantum-meowchanics.com/term/term-3-algorithms): not written yet; 6 courses and 18 lessons planned, about 95 hours.
- [Term 4 — Noise, Hardware & Error Correction](https://quantum-meowchanics.com/term/term-4-noise-hardware): not written yet; 4 courses and 14 lessons planned, about 75 hours.
- [Term 5 — Applied Quantum Computing on AWS Braket](https://quantum-meowchanics.com/term/term-5-braket): not written yet; 6 courses and 18 lessons planned, about 95 hours.

## Appendices

- [Appendix A — Braket Setup & Cost Guardrails](https://quantum-meowchanics.com/appendices/A-braket-setup): Do this once, early — before Term 1 · The Qubit's first hands-on code. · Markdown: https://quantum-meowchanics.com/content/appendix/A-braket-setup.md
- [Appendix B — Python/NumPy Refresher](https://quantum-meowchanics.com/appendices/B-python-numpy-refresher): You already know Python. · Markdown: https://quantum-meowchanics.com/content/appendix/B-python-numpy-refresher.md
- [Appendix C — Notation & Glossary](https://quantum-meowchanics.com/appendices/C-notation-glossary): This is the single source of truth for symbols and terminology across the program. Lessons assume these conventions and link here on first use of a term. When a textbook uses a different convention (a few do), we note it. · Markdown: https://quantum-meowchanics.com/content/appendix/C-notation-glossary.md
- [Appendix D — References & Bibliography](https://quantum-meowchanics.com/appendices/D-references-bibliography): Lessons cite sources by the bracketed keys below (e.g. [NC, §4.2], [Shor94]). This page is the authoritative list. Textbooks first, then foundational papers grouped by topic, then applied Braket/tooling docs. · Markdown: https://quantum-meowchanics.com/content/appendix/D-references-bibliography.md
- [Appendix E — Math Identities Cheat-Sheet](https://quantum-meowchanics.com/appendices/E-math-identities): The identities you'll reach for constantly. · Markdown: https://quantum-meowchanics.com/content/appendix/E-math-identities.md

## Questionnaires

- [All questionnaires](https://quantum-meowchanics.com/questionnaires): practice quizzes with every answer explained.
- [Questionnaire 1.1.3 — Light](https://quantum-meowchanics.com/questionnaires/1.1.3-light): Three questions on the quantum nature of light: what a black body actually is, what the ultraviolet catastrophe actually claimed, and which knob — intensity or frequency — sets a photon's energy. · Markdown: https://quantum-meowchanics.com/content/questionnaires/1.1.3-light.md
- [Questionnaire 1.1.5 — Matter Waves](https://quantum-meowchanics.com/questionnaires/1.1.5-matter-waves): Four questions on the wave nature of matter: why "size" comparisons between quantum objects are ill-posed, Bohr's angular-momentum quantization, the de Broglie relation, and judging when an electron can be treated non-relativistically. · Markdown: https://quantum-meowchanics.com/content/questionnaires/1.1.5-matter-waves.md
- [Questionnaire 1.2.3 — Elementary Classical Mechanics](https://quantum-meowchanics.com/questionnaires/1.2.3-classical-mechanics): Five questions on momentum and energy: momentum as a vector, kinetic vs. potential energy as operational definitions, why kinetic energy is never negative, what actually raises potential energy, and which quantities grow at a constant… · Markdown: https://quantum-meowchanics.com/content/questionnaires/1.2.3-classical-mechanics.md
- [Questionnaire 1.2.5 — Oscillations](https://quantum-meowchanics.com/questionnaires/1.2.5-oscillations): Four questions on the simple harmonic oscillator: computing the characteristic frequency (and not confusing Hz with rad/s), what "ideal" means for the amplitude, how the frequency scales with mass, and whether gravity has any say in a… · Markdown: https://quantum-meowchanics.com/content/questionnaires/1.2.5-oscillations.md
- [Questionnaire 1.2.7 — The Classical Wave Equation](https://quantum-meowchanics.com/questionnaires/1.2.7-classical-wave-equation): Markdown: https://quantum-meowchanics.com/content/questionnaires/1.2.7-classical-wave-equation.md
- [Questionnaire 1.3 — Quanta, Oscillators & Waves](https://quantum-meowchanics.com/questionnaires/1.3-quanta-oscillators-waves): Nine questions sweeping the week-one arc: black bodies, the photoelectric effect, the de Broglie wavelength, energy and forces on a slope, the harmonic oscillator (right-side-up and upside-down), and which frequencies a string will… · Markdown: https://quantum-meowchanics.com/content/questionnaires/1.3-quanta-oscillators-waves.md
- [Questionnaire 2.1.2 — Plane Waves & Interference](https://quantum-meowchanics.com/questionnaires/2.1.2-plane-waves-interference): Markdown: https://quantum-meowchanics.com/content/questionnaires/2.1.2-plane-waves-interference.md

## Interactive demos

- [All demos](https://quantum-meowchanics.com/demos): simulations that run in the browser (JavaScript required), each linked to the lessons that use it.
- [Tunneling through a barrier](https://quantum-meowchanics.com/demos/barrier-tunneling): Fire an electron wave packet at a barrier and watch part of it leak through the classically forbidden region.
- [The CHSH experiment](https://quantum-meowchanics.com/demos/bell-chsh): Sample entangled pairs with random analyzer settings and watch S break the local bound of 2.
- [Blackbody spectrum](https://quantum-meowchanics.com/demos/blackbody-spectrum): Heat a black body and watch Planck’s curve rise and its peak slide, beside the classical ultraviolet catastrophe.
- [Bloch sphere](https://quantum-meowchanics.com/demos/bloch-sphere): Apply gates to one qubit and follow its state on the sphere, or shrink it into the ball to see mixed states.
- [Standing wave on a Bohr orbit](https://quantum-meowchanics.com/demos/bohr-standing-wave): Wrap de Broglie wavelengths around an orbit: only whole numbers close the wave, and those are the allowed orbits.
- [Where the centre of mass ends up](https://quantum-meowchanics.com/demos/center-of-mass-height): Step through four paths and see that potential energy depends on where you end, not on the effort spent.
- [Two-qubit circuit builder](https://quantum-meowchanics.com/demos/circuit-builder): Place gates on two wires and read the amplitudes and Born probabilities of the output state live.
- [Momentum on a circle](https://quantum-meowchanics.com/demos/circular-momentum): Constant speed, turning momentum: compare the momentum vector at two points of a circular path.
- [Momentum vs kinetic energy under a constant force](https://quantum-meowchanics.com/demos/constant-acceleration-energy): Push with a constant force and compare what each second adds to momentum and to kinetic energy.
- [de Broglie wavelength vs speed](https://quantum-meowchanics.com/demos/de-broglie-speed): Speed up an electron and watch its wavelength λ = h/(mv) shrink.
- [Do two waves share one wave equation?](https://quantum-meowchanics.com/demos/dispersion-line-check): Place two harmonic waves on the ω–k plane: they obey the same wave equation only if they share the ratio ω/k.
- [An exponential front and the wave equation](https://quantum-meowchanics.com/demos/exponential-mover-speed): Tune k and ω of a real exponential and see when its moving wall keeps pace with the equation’s own speed.
- [One gravity slider, two oscillators](https://quantum-meowchanics.com/demos/hanging-spring-equilibrium): Change g and compare a hanging spring, whose beat never changes, with a pendulum, whose beat does.
- [Fourier synthesis](https://quantum-meowchanics.com/demos/fourier-synthesis): Build a square wave, a sawtooth or a plucked string from harmonics, and watch the overshoot at a jump refuse to shrink.
- [Conserved, but not the energy](https://quantum-meowchanics.com/demos/h-vs-energy): Spin a wire with a bead on it: the Hamiltonian stays constant while the energy climbs, because the motor does work.
- [A ball on a slope](https://quantum-meowchanics.com/demos/incline-decomposition): Tilt the slope and walk up it: split the weight along and into the surface, and see that height, not path, sets ΔU.
- [The floor of kinetic energy](https://quantum-meowchanics.com/demos/kinetic-energy-floor): Drag the velocity through zero and see why kinetic energy can never be negative.
- [Least action, or stationary action?](https://quantum-meowchanics.com/demos/least-action-paths): Bend a path between fixed endpoints and watch the action: flat at the true path, and a saddle once T passes half a period.
- [Mach–Zehnder interferometer](https://quantum-meowchanics.com/demos/mach-zehnder): Send single photons through two beam splitters and a phase shifter, then add a detector or a kickback qubit.
- [Mass on a spring](https://quantum-meowchanics.com/demos/mass-spring-oscillation): Change mass and damping and read ω, f and the amplitude envelope of a spring oscillator.
- [One symmetry, one conserved quantity](https://quantum-meowchanics.com/demos/noether-symmetries): Switch potentials under a moving particle and see momentum, angular momentum and energy conserved exactly when their symmetry holds.
- [A blob of states in phase space](https://quantum-meowchanics.com/demos/phase-space-flow): Let the pendulum’s flow shear a disk of initial conditions into filaments: its shape goes, its area stays (Liouville).
- [Photoelectric stopping voltage](https://quantum-meowchanics.com/demos/photoelectric-stopping-voltage): Change the light’s intensity and wavelength and see which one moves the stopping voltage.
- [Restoring vs runaway](https://quantum-meowchanics.com/demos/restoring-vs-runaway): Flip the sign of a quadratic potential and watch an oscillation turn into exponential runaway.
- [Standing waves on a pinned rope](https://quantum-meowchanics.com/demos/standing-wave-modes): Drag the wavenumber and find the only values that fit a rope pinned at both ends.
- [Two travelling waves, one wave equation](https://quantum-meowchanics.com/demos/traveling-wave-superposition): Send two waves in opposite directions and test whether one wave equation can hold them both.
- [Fringes from two crossing beams](https://quantum-meowchanics.com/demos/two-beam-fringes): Cross two plane waves and read the fringe spacing from an intensity that no longer moves.
- [How big is an electron?](https://quantum-meowchanics.com/demos/wave-packet-width): Prepare the same electron in wider or narrower wave packets: its extent belongs to the state.
- [Two crossing plane waves](https://quantum-meowchanics.com/demos/wavevector-direction-superposition): Tilt one plane wave against another: any direction works, but only a matching |k| shares their speed.
- [Wavevector magnitude and speed](https://quantum-meowchanics.com/demos/wavevector-magnitude-speed): Build |k| from its components and see that only its length, not its direction, sets ω.

## Optional

- [Quizzes](https://quantum-meowchanics.com/quizzes): every lesson's exercises and checkpoint questions as a self-test, one question at a time (JavaScript required; the lesson page has them all).
- [Flashcards](https://quantum-meowchanics.com/flashcards), [Notebook](https://quantum-meowchanics.com/notebook), [Progress](https://quantum-meowchanics.com/progress): personal study tools whose state lives in the browser.
- [Sitemap](https://quantum-meowchanics.com/sitemap.xml): every indexable page.