Consult the COURSE SYLLABUS for basic information about the course: time, place, overview, grading, prerequisites, policies, etc.
This page contains resources for the course and will be updated as the course progresses.
All hand-written notes linked to below are from the current semester, Fall 2023, and Fall 2024.
| Date | Lecture # | Topic | Fall 2023 notes | Fall 2024 notes | Current notes |
| 2025-08-20 | Lecture 01 | Introduction to the course | |||
| 2024-08-25 | Lecture 02 | Math prelims: complex numbers, vectors, matrices, inner product | |||
| 2025-08-27 | Lecture 03 | Orthonormal bases, adjoints, probability distributions; electron spin: Stern-Gerlach experiment, Bloch sphere | |||
| 2025-09-03 | Lecture 04 | Matrices and operators, Hermitian and unitary matrices/operators, projectors, ker and img; Dirac notation; electron spin states | |||
| 2025-09-08 | Lecture 05 | Csop's and projective measurements; parameterizing electron spin states: Pauli operators, spherical vs cartesian coordinates | |||
| 2025-09-10 | Lecture 06 | Isolated systems and unitary evolution; change of basis and unitary conjugation; cyclic trace property; Schroedinger's equation and exp function on operators; combined systems and the tensor product | |||
| 2025-09-15 | Lecture 07 | Combined systems and tensor products; Bell states and entanglement; quantum circuit model (intro.) | |||
| 2025-09-17 | Lecture 08 | Quantum circuits (cont.); 1-qubit gates vs Bloch sphere rotations, Euler angle decomp.; H, S, T gates, controlled gates | |||
| 2025-09-22 | Lecture 09 | Controlled gates; complete sets of gates; L(H,J) is a C-space; Pauli basis; Bloch sphere rotations about an arbitrary axis; S3 parameterization; SWAP operator | |||
| 2025-09-24 | Lecture 10 | Measurement gates; spectral theorem (eigenvectors, eigenvalues, characteristic polynomial, diagonal matrices, normal operators) | |||
| 2025-09-29 | Lecture 11 | Spectral theorem (cont.): spectra of Hermitian, unitary operators, projectors; commuting normal operators; Bell state circuit; Deutsch's problem and black-box queries (intro) | |||
| 2025-10-01 | Lecture 12 | Deutsch's problem (cont.); classical states, gates, and circuits; Toffoli gates; cleanly simulating a classical computation | |||
| 2025-10-06 | Lecture 13 | Deutsch-Jozsa problem; some circuit transformations; some measurement techniques: Hadamard test | |||
| 2025-10-08 | Lecture 14 | Quantum teleportation, entanglement swapping; starting Simon's problem | |||
| 2025-10-13 | Lecture 15 | Clifford (H, S, C-NOT) + T gates, implementing C-C-Z with T gates on one layer | |||
| 2025-10-15 | Lecture 16 | Simon's problem; intro to quantum Fourier transform (QFT) | |||
| 2025-10-20 | Lecture 17 | QFT (cont.), quantum phase estimation; Shor's algorithm for factoring (intro.) | |||
| 2025-10-22 | Lecture 18 | Shor's algo (cont.): factoring reduces to order-finding, quantum circuit for order-finding using QFT, rational approximations; intro. to QFT implementation | |||
| 2025-10-27 | Lecture 19 | Implementing QFT (cont.), asymptotic circuit depth for QFT | |||
| 2025-10-29 | Lecture 20 | Grover's algorithm for quantum search with quadratic speed-up | |||
| 2025-11-03 | Lecture 21 | Quantum cryptographic key distribution: the BB84 protocol | |||
| 2025-11-05 | Lecture 22 | Basic quantum info: spectral decomposition, functions of operators, positive operators and square roots, operator norms, states as density operators (pure and mixed), redoing QM axioms | |||
| 2025-11-10 | Lecture 23 | POVMs, 1-qubit state geometry; quantum channels: superoperators, conditions for a channel, (Kraus) operator-sum representation; partial trace, unitary channels, information-free projective measurement channels | |||
| 2025-11-12 | Lecture 24 | Alice's two plans; completely depolarizing channel, completely dephasing channel, classical states, general measurement channels and their operator-sum reps; error channels: bit-flip, phase-flip; classical error correction (maj-of-3 code) | |||
| 2025-11-17 | Lecture 25 | quantum maj-of-3 code for bit-flip channel: error syndrome measurement, recovery; alterations for the phase-flip channel; partially depolarizing channel, 9-qubit Shor code; discretization of errors | |||
| 2025-11-19 | Lecture 26 | Shor code details; fault-tolerant logical gates: transversal gates, C-NOT gate in the Shor code; Eastin-Knill theorem; general conditions for correctable error channels; beginning stabilizer formalism: n-qubit Pauli group, stabilizing subgroups | |||
| 2025-12-01 | Lecture 27 | The Shor code (9-qubit code); 1-qubit error channels | |||
| 2025-12-03 | Lecture 28 | Stabilizer codes; fault-tolerant logical gates; review | |||
| 2023-12-07 | Lecture 29 | Fall 2023: Quantifying bipartite pure state entanglement; Review |
These will be visible as they become available. The number of homeworks is subject to change.
I will post announcements to the class here from time to time.
My COURSE NOTES (revised Thursday August 21, 2025) for the current semester are available in PDF format on Blackboard. These will be updated regularly through the semester. Here is a link to the course notes from Fall 2021.
There are a number of sources on the web relating to quantum computation and information, from basic tutorials to current research. By far the most comprehensive online repository for current research is the
For a dated but fuller list of resources, look at my
This course material is based upon work supported by the National Science Foundation under Grant Nos. CCF-0515269 and CCF-0915948. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation (NSF).