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, 4.1-4.3 | 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, 2.3 | 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, Bloch sphere for mixed states, partial trace, reduced density operators, Schmidt decomposition, purification, designing quantum circuits, circuit measurement principles. |
| 10 | ? | Computing, algorithms, Grover | 3, 5.1, 6.1 | Classical computing on quantum computers, 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, Naimark dilation, relation between wave functions and vectors.? |
| 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 | ? | ? | ? |