CSCE 785/MATH 763/PHYS 743
Quantum Computer Science
Fall 2024
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Please note: my.sc.edu still lists this course as "Quantum Computing and Information." The name-change has been approved by the Graduate School.

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 Fall 2023 and Fall 2024.

Date Lecture # Topic Fall 2023 notes Fall 2024 notes
2024-08-21 Lecture 01 Introduction to the course pdf pdf
2024-08-26 Lecture 02 Math prelims: complex numbers, vectors, matrices, inner product pdf pdf
2024-08-28 Lecture 03 Orthonormal bases, adjoints, probability distributions; electron spin: Stern-Gerlach experiment, Bloch sphere pdf pdf
2024-09-04 Lecture 04 Matrices and operators, Hermitian and unitary matrices/operators, projectors, ker and img; Dirac notation; electron spin states pdf pdf
2024-09-09 Lecture 05 Csop's and projective measurements; parameterizing electron spin states: Pauli operators, spherical vs cartesian coordinates pdf pdf
2024-09-11 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 pdf pdf
2024-09-16 Lecture 07 Combined systems and tensor products; Bell states and entanglement; quantum circuit model (intro.) pdf pdf
2024-09-18 Lecture 08 Quantum circuits (cont.); 1-qubit gates vs Bloch sphere rotations, Euler angle decomp.; H, S, T gates, controlled gates pdf pdf
2024-09-23 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 pdf pdf
2024-09-25 Lecture 10 Measurement gates; spectral theorem (eigenvectors, eigenvalues, characteristic polynomial, diagonal matrices, normal operators) pdf pdf
2024-09-30 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) pdf pdf
2024-10-02 Lecture 12 Deutsch's problem (cont.); classical states, gates, and circuits; Toffoli gates; cleanly simulating a classical computation pdf pdf
2024-10-07 Lecture 13 Deutsch-Jozsa problem; some circuit transformations; some measurement techniques: Hadamard test pdf pdf
2024-10-09 Lecture 14 Quantum teleportation, entanglement swapping; starting Simon's problem pdf pdf
2024-10-14 Lecture 15 Clifford (H, S, C-NOT) + T gates, implementing C-C-Z with T gates on one layer (guest lecture by Dr. Peng (Frank) Fu) pdf pdf
2024-10-16 Lecture 16 Simon's problem; intro to quantum Fourier transform (QFT) pdf pdf
2024-10-21 Lecture 17 QFT (cont.), quantum phase estimation; Shor's algorithm for factoring (intro.) pdf pdf
2024-10-23 Lecture 18 Shor's algo (cont.): factoring reduces to order-finding, quantum circuit for order-finding using QFT, rational approximations; intro. to QFT implementation pdf pdf
2024-10-28 Lecture 19 Implementing QFT (cont.), asymptotic circuit depth for QFT pdf pdf
2024-10-30 Lecture 20 Grover's algorithm for quantum search with quadratic speed-up pdf pdf
2024-11-04 Lecture 21 Quantum cryptographic key distribution: the BB84 protocol pdf pdf
2024-11-06 Lecture 22 Fall 2023: Beginning quantum info: functions and norms of operators, positive operators and the square root, states (pure and mixed), revised QM axioms pdf pdf
2024-11-11 Lecture 23 Fall 2023: Quantum cryptography: the BB84 protocol pdf pdf
2024-11-13 Lecture 24 Fall 2023: Basic quantum info: norms of operators, POVMs, mixed states pdf pdf
2024-11-18 Lecture 25 Fall 2023: Quantum channels: Kraus operator representation, 1-qubit bit/phase flip channels pdf pdf
2024-11-20 Lecture 26 Fall 2023: Classical error correction: binary linear codes, quantum codes for bit-flip and phase-flip channels pdf pdf
2024-12-02 Lecture 27 Fall 2023: The Shor code (9-qubit code); 1-qubit error channels pdf pdf
2024-12-04 Lecture 28 Fall 2023: Stabilizer codes; fault-tolerant logical gates pdf pdf
2023-12-07 Lecture 29 Fall 2023: Quantifying bipartite pure state entanglement; Review pdf

Announcements

I will post announcements to the class here from time to time.

(November 8, 2024) Homework 4 is due November 15.

(September 25, 2024) Homework 3 is due October 9.

(September 14, 2024) Homework 2 is due September 23.

(September 1, 2024) Homework 1 is due September 6.

Course Notes

My COURSE NOTES (revised Friday November 8, 2024) 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.

Outside Resources

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

Click on any of the links related to Quantum Physics (quant-ph). A site that includes tutorials is The Institute for Quantum Computing at the University of Waterloo (Ontario, Canada) is this field's formost research center in the Western hemisphere.

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).