Below is a teaching plan for which topics will be covered in which lectures, and some details about the lecture content. Changes in the teaching plan may occur during the semester.?
The chapter numbers refer to which chapters in Mike & Ike that cover the lecture content. It does not mean that a given week's lectures will necessarily cover all of the material in the stated chapters. E.g., chapter 2.2 is large, and we will cover various parts of it during different weeks.?
| Week | Notes | Topic | Chs. | Details |
|---|---|---|---|---|
| 4 | ? | Math fundamentals | 2.1 | Course goals, brief history, vector space, bases, operators, matrices, eigenvalues, spectral decomposition, operator functions, types of operators (normal, unitary, Hermitian, positive, projectors).? |
| 5 | ? | States, qubits, entanglement + classical gates | 1, 2.1, 3.1 | Polar decomposition, trace, commutators, postulates about states and evolution, qubits, global vs. relative phase, Bloch sphere, several qubits, computational basis, Bell states, entanglement, relation between wave functions and vectors, classical gates, reversible classical computation |
| 6 | No lecture Monday | Simple quantum gates + measurement postulates | 1, 2.2 | Single-qubit gates, projective measurements, Born rule, state update, expectation values, observables |
| 7 | ? | Circuit basics + teleportation, superdense coding | 1, 2.3 | Quantum circuit model, wires, gates, controlled gates, no-cloning theorem, teleportation, superdense coding, no signaling, resource accounting |
| 8 | ? | Density matrices | 2.4, 2.5 | Mixtures, density operators, Bloch sphere, non-uniqueness of ensemble decomposition, reduced density operators, partial trace, Schmidt decomposition, purification, postulates for density operators |
| 9 | ? | Generalized measurements + circuits | 2.2, 4.1-4.4 | General measurement operators, POVMs, Naimark dilation, ancillas, state discrimination, circuit principles |
| 10 | ? | Computing, algorithms, Grover | 3, 5.1, 6.1 | Universality, oracle model, Deutsch-Jozsa, overview of algorithms, Grover's algorithm |
| 11 | Midterm | Channels 1: Kraus operators, environment | 8.1, 8.2 | CPTP maps, Kraus operator representation, non-uniqueness of Kraus representation, environment, Stinespring dilation |
| 12 | ? | Channels 2: Noise examples | 8.3 | Examples of standard noise channels, erasure channel, effect on Bloch vectors |
| 13 | ? | Distance measures | 9 | Trace distance, fidelity, monotonicity/contractivity, relation to measurements, relationship between measures, Uhlmann's theorem |
| 14 | Easter (no teaching) | ? | ? | ? |
| 15 | Easter (no teaching) | ? | ? | ? |
| 16 | ? | Noise, error correction, hardware | 7.1-7.2, 10.1-10.2 | Noise, bit-flip, phase-flip, Shor code, syndromes, hardware principles, DiVincenzo's criteria |
| 17 | ? | Entropy and information 1: Classical, von Neumann | 11.1, 11.2, 11.3 | Classical entropy, joint-system classical entropy, classical mutual information, von Neumann entropy |
| 18 | ? | Entropy and information 2: Joint-system quantum, Holevo | 11.2, 11.3, 12.1 | Joint-system quantum entropy, Holevo information, Holevo bound |
| 19 | ? | Bell's inequality and nonlocality | 2.6 | CHSH inequality, nonlocality, Tsirelson bound |
| 20 | ? | Quantum cryptography | 12.6 | QKD, third-party entanglement, BB84, device-independent cryptography |
| 21 | ? | Review | ? | ? |
| 22 | Exam | ? | ? | ? |