Below is a teaching plan for which topics will be covered in which lectures, and some details about the lecture content. Changes will occur as we progress through the semester, and the teaching plan below will be updated continuously.
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, linear algebra | 1.1, 2.1 | Course goals, brief history, vector space, bases, linear operators, matrices, eigenvalues, spectral decomposition, operator functions, types of operators (normal, unitary, Hermitian, positive, projectors). | |
| 5 | Classical computing + state space postulates, qubits, one-qubit gates | 1.2, 2.1, 2.2, 3.1 | Non-normal matrices, polar decomposition, trace, commutators, classical computing (Boolean functions, circuits, ancillas, reversibility, universality), classical gates, postulates about quantum states and time-evolution, qubits, global phase, Bloch sphere, one-qubit gates. | |
| 6 | No lecture Monday | Tensor products, several qubits, multi-qubit gates, quantum circuit model | 1.3, 2.2, 4.1, 4.2, 4.3 | Examples of one-qubit gates, tensor products, several qubits, computational basis, multi-qubit gates, controlled gates, quantum circuit model, wires, gates. |
| 7 | No-cloning, simple measurement, entanglement, teleportation | 1.3, 2.2 | Examples of multi-qubit gates, no-cloning theorem, measurement, projective measurements, Born rule, state update, expectation values, observables, classical control, entanglement, Bell states, teleportation protocol. | |
| 8 | Superdense coding, general measurements + density operators | 2.2, 2.3, 2.4 | Superdense coding, general measurement operators, POVMs, minimum-error state discrimination, unambiguous state discrimination, ensemble mixtures, density operators, non-uniqueness of ensemble decomposition. | |
| 9 | Density operators and partial trace | 2.4, 2.5 | Postulates of quantum mechanics for mixed states, measurement for mixed states, Bloch sphere for mixed states, partial trace, reduced density operators, Schmidt decomposition, purification. | |
| 10 | Circuit design, universality | 3, 4.4 | Circuit identities and controlled-gate decompositions, exact and approximate universality, measurement principles for quantum circuits (basis-change measurements, principles of deferred and implicit measurement). | |
| 11 | Midterm | Deutsch–Jozsa & Grover's algorithms + quantum channels | 1.4, 6.1, 8.1 | Classical computation inside quantum circuits, oracle model, phase kickback, Deutsch–Jozsa algorithm, Grover search, quantum channels, system-environment interactions, Kraus representation. |
| 12 | Quantum channels, Kraus operators, channel examples | 8.2, 8.3 | Non-uniqueness of Kraus representation, Stinespring dilation, Naimark dilation, effect of channels on Bloch vectors, examples of noise channels: replacement channel, (completely) depolarizing channel, bit & phase flip channels, amplitude damping channel. | |
| 13 | No lecture Monday | Distance measures | 9 | Phase damping channel, Schrödinger's cat and decoherence, trace distance, connection to maximum difference in measurement probability. |
| 14 | Easter (no teaching) | |||
| 15 | Easter (no teaching) | |||
| 16 | Distance measures + error correction | 9, 10.1 | Fidelity, Uhlmanns' theorem, properties of trace distance and fidelity, contractivity/monotonicity, relationship between measures, classical repetition codes, why quantum error correction seems impossible, three-qubit bit-flip code, syndrome measurements, phase-flip code. | |
| 17 | Error correction + hardware | 7.1, 7.2, 10.2 | Shor code, noise handling in practical systems, hardware principles, implementing qubits. | |
| 18 | Entropy and information | 11.1, 11.2, 11.3 | Implementing gates and measurement, classical entropy (Shannon entropy, relative entropy, joint-system entropy, conditional entropy, mutual information), quantum entropy (von Neumann entropy, joint-system entropy). | |
| 19 | Holevo + Bell's inequality and nonlocality | 12.1, 2.6 | Quantum entropy (relative entropy, conditional entropy, mutual information), Holevo information, Holevo bound, Bell experiments, nonlocality, hidden-variable models, CHSH inequality. | |
| 20 | Last lecture | Quantum cryptography | 12.6 | QKD, BB84, classical post-processing, asymptotic key gain, basic idea of device-independent quantum cryptography. |
| 21 | Q&A session | |||
| 22 | Exam |