Quantum Computer Science

Fall 2024

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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 | ||

2024-08-26 | Lecture 02 | Math prelims: complex numbers, vectors, matrices, inner product | ||

2024-08-28 | Lecture 03 | Orthonormal bases, adjoints, probability distributions; electron spin: Stern-Gerlach experiment, Bloch sphere | ||

2024-09-04 | Lecture 04 | Matrices and operators, Hermitian and unitary matrices/operators, projectors, ker and img; Dirac notation; electron spin states | ||

2024-09-09 | Lecture 05 | Csop's and projective measurements; parameterizing electron spin states: Pauli operators, spherical vs cartesian coordinates | ||

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 | ||

2024-09-16 | Lecture 07 | Combined systems and tensor products; Bell states and entanglement; quantum circuit model (intro.) | ||

2024-09-18 | Lecture 08 | Quantum circuits (cont.); 1-qubit gates vs Bloch sphere rotations, Euler angle decomp.; H, S, T gates, controlled gates | ||

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; S^{3} parameterization; SWAP operator |
||

2024-09-25 | Lecture 10 | Measurement gates; spectral theorem (eigenvectors, eigenvalues, characteristic polynomial, diagonal matrices, normal operators) | ||

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) | ||

2024-10-02 | Lecture 12 | Deutsch's problem (cont.); classical states, gates, and circuits; Toffoli gates; cleanly simulating a classical computation | ||

2024-10-07 | Lecture 13 | Deutsch-Jozsa problem; some circuit transformations; some measurement techniques: Hadamard test | ||

2024-10-09 | Lecture 14 | Quantum teleportation, entanglement swapping; starting Simon's problem | ||

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) | ||

2024-10-16 | Lecture 16 | Simon's problem; intro to quantum Fourier transform (QFT) | ||

2024-10-21 | Lecture 17 | QFT (cont.), quantum phase estimation; Shor's algorithm for factoring (intro.) | ||

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 | ||

2024-10-28 | Lecture 19 | Implementing QFT (cont.), asymptotic circuit depth for QFT | ||

2024-10-30 | Lecture 20 | Grover's algorithm for quantum search with quadratic speed-up | ||

2024-11-04 | Lecture 21 | Quantum cryptographic key distribution: the BB84 protocol | ||

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 | ||

2024-11-11 | Lecture 23 | Fall 2023: Quantum cryptography: the BB84 protocol | ||

2024-11-13 | Lecture 24 | Fall 2023: Basic quantum info: norms of operators, POVMs, mixed states | ||

2024-11-18 | Lecture 25 | Fall 2023: Quantum channels: Kraus operator representation, 1-qubit bit/phase flip channels | ||

2024-11-20 | Lecture 26 | Fall 2023: Classical error correction: binary linear codes, quantum codes for bit-flip and phase-flip channels | ||

2024-12-02 | Lecture 27 | Fall 2023: The Shor code (9-qubit code); 1-qubit error channels | ||

2024-12-04 | Lecture 28 | Fall 2023: Stabilizer codes; fault-tolerant logical gates | ||

2023-12-07 | Lecture 29 | Fall 2023: Quantifying bipartite pure state entanglement; Review |

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.

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.

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

- E-print Archive (http://arxiv.org).

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).