Term

Term 1 — Quantum Mechanics

~90 h19/19 lessons written0 completed

Course 1.1 — The Postulates of Quantum Mechanics

  • The State Postulate
  • Observables & the Measurement Postulate
  • The Evolution Postulate
  • Composite Systems Postulate

Course 1.2 — Qubits, Superposition & the Bloch Sphere

  • The Qubit
  • The Bloch Sphere
  • Bases & Expectation Values

Course 1.3 — Measurement

  • Projective Measurement
  • Expectation & Uncertainty
  • POVMs & Generalized Measurement

Course 1.4 — Entanglement & Composite Systems

  • Multi-Qubit States
  • Bell States
  • Nonlocality & the CHSH Inequality
  • Schmidt Decomposition

Course 1.5 — Density Matrices & Mixed States

  • The Density Operator
  • Partial Trace & Reduced States
  • The Bloch Ball & Purity

Course 1.6 — Dynamics

  • Time Evolution
  • Two-Level Dynamics & Rabi Oscillations

Term guide

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. By the end you'll know precisely what a quantum state is, how it evolves, what measurement does to it, and how systems combine to produce entanglement. This is also where the curriculum becomes hands-on: your first AWS Braket code appears in Course 1.2.

Estimated time: ~90 hours · Lessons: 19 across 6 courses Prerequisites: Term 0 — Mathematical & Computational Foundations (especially Course 0.1 — Linear Algebra). Lab setup: complete Appendix A — Braket Setup before Course 1.2.

The Four Postulates (the spine of this term)

All of quantum mechanics hangs on four statements. Course 1.1 introduces them; the rest of the term unpacks each one with the full machinery.

# Postulate Mathematical content Developed in
1 State A system's state is a unit vector ∣ψ⟩\lvert\psi\rangle in a Hilbert space. 1.1.1, Course 1.2
2 Observables & Measurement Observables are Hermitian operators; outcomes are eigenvalues; probabilities obey the Born rule; the state collapses. 1.1.2, Course 1.3
3 Evolution Closed-system dynamics is unitary: ∣ψ(t)⟩=e−iHt∣ψ(0)⟩\lvert\psi(t)\rangle = e^{-iHt}\lvert\psi(0)\rangle. 1.1.3, Course 1.6
4 Composite systems Joint systems combine via the tensor product — the origin of entanglement. 1.1.4, Courses 1.4–1.5

Course Map

flowchart TD
    C1["1.1 Postulates of QM\n(4 lessons)"] --> C2["1.2 Qubits & Bloch Sphere\n(3 lessons)"]
    C2 --> C3["1.3 Measurement\n(3 lessons)"]
    C2 --> C4["1.4 Entanglement\n(4 lessons)"]
    C3 --> C4
    C4 --> C5["1.5 Density Matrices\n(3 lessons)"]
    C2 --> C6["1.6 Dynamics\n(2 lessons)"]
    C1 --> C6
    C5 --> T2["→ Term 2: QC Core"]
    C6 --> T2
    LAB["Braket setup (App. A)"] -.-> C2

Courses & Lessons

Course 1.1 — The Postulates of Quantum Mechanics c01-postulates/

The axioms, stated once, cleanly, with their immediate consequences.

  1. The State Postulate — states as rays; normalization; global vs relative phase.
  2. Observables & the Measurement Postulate — Hermitian observables, the Born rule, collapse.
  3. The Evolution Postulate — unitarity and the Schrödinger equation.
  4. The Composite Systems Postulate — tensor products and the seed of entanglement.

Course 1.2 — Qubits, Superposition & the Bloch Sphere c02-qubits-bloch/

The qubit, made concrete — and your first runnable Braket code.

  1. The Qubit — two-level systems, superposition; first Braket circuit.
  2. The Bloch Sphere — the geometry of one qubit.
  3. Bases & Expectation Values — X/Y/Z bases; measuring on Braket.

Course 1.3 — Measurement c03-measurement/

What measurement really is, from projectors to POVMs.

  1. Projective Measurement — Born rule, collapse, measuring in any basis.
  2. Expectation & Uncertainty — variance and the Robertson uncertainty relation.
  3. POVMs & Generalized Measurement — the most general measurements.

Course 1.4 — Entanglement & Composite Systems c04-entanglement/

The defining quantum resource.

  1. Multi-Qubit States — product vs entangled.
  2. Bell States — maximal entanglement.
  3. Nonlocality & the CHSH Inequality — Bell's theorem, 222\sqrt2.
  4. Schmidt Decomposition — quantifying entanglement.

Course 1.5 — Density Matrices & Mixed States c05-density-matrices/

The formalism for noise, ensembles, and subsystems.

  1. The Density Operator — pure vs mixed states.
  2. Partial Trace & Reduced States — the state of a subsystem.
  3. The Bloch Ball & Purity — mixed states geometrically.

Course 1.6 — Dynamics c06-dynamics/

How states change in time — and where gates come from.

  1. Time Evolution — the Schrödinger equation and the propagator.
  2. Two-Level Dynamics & Rabi Oscillations — the physical origin of single-qubit gates.

Term Learning Outcomes

By the end of Term 1 you will be able to:

  1. State and apply the four postulates of quantum mechanics in Dirac notation.
  2. Represent a qubit as a state vector and a Bloch-sphere point, and compute measurement probabilities and expectation values.
  3. Analyze projective and POVM measurements and derive the uncertainty relation.
  4. Identify and quantify entanglement, and prove the CHSH violation of local realism.
  5. Use the density-matrix formalism for mixed states, partial traces, and reduced subsystems.
  6. Solve time evolution under a Hamiltonian and explain how Rabi oscillations become gates.
  7. Run and interpret your first AWS Braket circuits on the local simulator.

← Back to Program Index · Prev term: Term 0 · Begin: 1.1.1 The State Postulate →