Lecture plan

Welcome to the 2026 edition of Quantum Computing course! Our lecture plan is as follows.

• Lecture 1: Overview of the course, history of quantum computing (NC, Section 1.1)
• Lecture 2: Basics in linear algebra, classes of operators, functions of operators (NC, Section 2 and in particular 2.1.8)
• Lecture 3: The Pauli matrices and some hands-on exercises, tensor products, the Bloch sphere (NC, Section 2.1.7)
• Lecture 4: Postulates of quantum mechanics (NC, Section 2.2)
• Lecture 5: Measurement formalism (NC, Section 2.2), discussion of global phases (NC, Section 2.2.7), distinguishing quantum states (NC, Section 2.2.4)
• Lecture 6: Quantum gates and circuits, quantum Zeno effect and the Elitzur¨CVaidman bomb (A, Section 4)
• Lecture 7: The coin problem, distinguishability, multi-qubit states and entanglement (A, Section 5)
• Lecture 8: No-cloning theorem and Wiesner¡¯s quantum money scheme (A, Section 7)
• Lecture 9: Superdense coding, qubit teleportation and entanglement swapping (A, Sections 9, 10.1)
• Lecture 10: The Greenberger¨CHorne¨CZeilinger state and monogamy of entanglement, quantifying entanglement (A, Sections 10.1.2, 11)
• Lecture 11: Hidden variables and Bell¡¯s inequality (A, Section 13)
• Lecture 12: The Clauser¨CHorne¨CShimony¨CHolt game, nonlocal games (A, Sections 13.2, 14)
• Lecture 13: Einstein-certified randomness, quantum query complexity and the Deutsch¨CJosza problem (A, Sections 15, 17)
• Lecture 14: Bernstein¨CVazirani and Simon¡¯s algorithms (A, Section 18)
• Lecture 15: RSA and Shor¡¯s algorithm (A, Sections 19.1, 19.2.1)
• Lecture 16: Quantum algorithm for period-finding, Quantum Fourier Transform (A, Sections 19.2.2, 20.1)
• Lecture 17: Implementing Shor¡¯s algorithm
• Lecture 18: Quantum computing and universal gate sets (A, Section 16)
• Lecture 19: Universality for quantum gates (A, Section 16, NC, Section 4.5)
• Lecture 20: Universality of single qubit gates and CNOT (NC, Section 4.5)
• Lecture 21: The Solovay¨CKitaev theorem
• Lecture 22: Grover¡¯s algorithm (A, Section 22)
• Lecture 23: The Bennett¨CBernstein¨CBrassard¨CVazirani theorem (A, Section 23.1)
• Lecture 24: Applications of Grover¡¯s algorithm
• Lecture 25: Nesting quantum search, complexity theory
• Lecture 26: Quantum error correction (A, Section 27)
• Lecture 27: Hamiltonians (A, Section 25)
• Lecture 28: The adiabatic algorithm (A, Section 26)

NC stands for the Nielsen¨CChuang book, and A stands for Scott Aaronson's lecture note "Introduction to Quantum Information Science". However, we will develop a detailed note along the course, expanding on the previous years' notes (available from Course Schedule pages), in particular from 2022 and 2025.