北京雁栖湖应用数学研究院

2026年03月24日 至 06月11日

calculus, linear algebra, probability

Module 1: Foundations (Lectures 1-6)
Lecture 1: Course Introduction & The Promise of Quantum Computing
Topic: Limits of classical computing (Moore's Law, heat). Introduction to the Qubit. The concepts of superposition, entanglement, and measurement (high-level overview). Quantum Supremacy/Advantage examples.
Reading: QC4QC Ch. 1.

Lecture 2: Math Primer I: Linear Algebra for Qubits
Topic: Vector spaces, Dirac notation (Ket, Bra), inner products, outer products. Unitary matrices and Hermitian matrices. Eigenvalues and eigenvectors.
Reading: N&C Ch. 2.1.

Lecture 3: Math Primer II: Complex Numbers & The Single Qubit
Topic: Complex number review (modulus, phase). The quantum state postulate. Probability amplitudes. Normalization.
Reading: QC4QC Appendix, Ch. 2.

Lecture 4: Single-Qubit Gates & The Bloch Sphere
Topic: The Pauli gates (X, Y, Z), Hadamard (H), Phase (S, T). Visualizing rotations on the Bloch Sphere. The measurement postulate.
Reading: QC4QC Ch. 3 & 4.

Lecture 5: Multi-Qubit Systems & Entanglement
Topic: The tensor product. Representing multi-qubit states. Introduction to the Bell states. The mathematical definition of entanglement.
Reading: QC4QC Ch. 5.

Lecture 6: Multi-Qubit Gates & Quantum Circuits
Topic: The Controlled-NOT (CNOT) gate. The SWAP gate. Building quantum circuits. The No-Cloning Theorem
Reading: QC4QC Ch. 6 & 7.

Module 2: Protocols & Simulation Concepts (Lectures 7-12)
Lecture 7: Quantum Protocols I: Superdense Coding
Topic: Using one qubit to transmit two classical bits. Step-by-step circuit analysis.
Reading: QC4QC Ch. 8.

Lecture 8: Quantum Protocols II: Quantum Teleportation
Topic: Transferring a quantum state without moving the particle. Circuit breakdown and classical communication requirements.
Reading: QC4QC Ch. 9.

Lecture 9: Simulation Theory I: How Simulators Work
Topic: Transition from Coding to Simulation Concepts.
What is a statevector simulator? Memory requirements for n qubits (2^n complex numbers).
How gates are applied (matrix multiplication on the statevector).
Demonstration using Quirk to visualize the statevector changes for simple gates.
Reading: N&C Ch. 4 (Circuit Model).

Lecture 10: Simulation Theory II: Stabilizer Simulation & Gottesman-Knill
Topic: The limits of simulation. The Gottesman-Knill theorem: circuits with only Clifford gates (H, S, CNOT) can be simulated efficiently on a classical computer. Introduction to the Heisenberg representation.
Reading: N&C Ch. 10 (Brief mention) / Online resources on Clifford simulation.

Lecture 11: Deutsch-Jozsa Algorithm
Topic: The first proof of quantum advantage (over deterministic classical computers). The concept of quantum parallelism. Oracles.
Reading: N&C Ch. 1.4.

Lecture 12: Grover's Search Algorithm
Topic: Unstructured search and quadratic speedup. Geometric visualization (amplitude amplification). Circuit structure.
Reading: N&C Ch. 6.

Module 3: Advanced Algorithms (Lectures 13-18)
Lecture 13: Quantum Fourier Transform (QFT)
Topic: From Discrete Fourier Transform to QFT. The circuit structure (phase rotations and swap gates). Why it is efficient.
Reading: N&C Ch. 5.1.

Lecture 14: Quantum Phase Estimation (QPE)
Topic: The core subroutine of many algorithms. How to estimate the eigenvalue of a unitary operator using QFT and controlled gates.
Reading: N&C Ch. 5.2.

Lecture 15: Shor's Algorithm I: The Math
Topic: Reducing factoring to order finding. Modular arithmetic. The role of the Quantum Phase Estimation in Shor's algorithm.
Reading: N&C Ch. 5.3.

Lecture 16: Shor's Algorithm II: The Circuit & Impact
Topic: Putting it all together. The implications for cryptography (RSA). Post-quantum cryptography introduction.
Reading: N&C Ch. 5.3.

Lecture 17: Simulation Theory III: Noise Simulation
Topic: Moving beyond ideal simulation.
What is decoherence? Depolarizing, amplitude damping, phase damping.
Density matrices (conceptual level).
How simulators model noise (probabilistic gate application).
Demonstration: Using IBM Quantum Composer to add noise models to a simulation.
Reading: N&C Ch. 8.

Lecture 18: Variational Quantum Eigensolver (VQE)
Topic: Introduction to hybrid quantum-classical algorithms. The NISQ (Noisy Intermediate-Scale Quantum) era. How VQE finds ground state energies.
Reading: Review Articles (e.g., from arXiv).

Module 4: Robustness & Future (Lectures 19-24)
Lecture 19: Quantum Error Correction (QECC) - Basics
Topic: The problem of noise. Classical repetition codes vs. Quantum challenges (no-cloning, measurement destroying state). The 3-qubit bit flip code.
Reading: N&C Ch. 10.1.

Lecture 20: Quantum Error Correction - The Shor Code
Topic: Combining bit flip and phase flip codes. Introduction to the 9-qubit Shor code (conceptual). The threshold theorem.
Reading: N&C Ch. 10.2.

Lecture 21: Simulation Theory IV: Tensor Networks & Advanced Methods
Topic: The limits of full statevector simulation. Introduction to Matrix Product States (MPS) and how they simulate larger systems by focusing on "low entanglement" regions.
Reading: Review articles on Tensor Networks.

Lecture 22: Quantum Machine Learning (QML)
Topic: Quantum Neural Networks. Parameterized Quantum Circuits (PQC). Applications and hype vs. reality.
Reading: Review Articles.

Lecture 23: Physical Realizations of Qubits
Topic: How qubits are made. Superconducting qubits (Transmon), Trapped Ions, Photonics. How the underlying physics affects simulation strategies.
Reading: N&C Ch. 7.

Lecture 24: Course Summary & The Future
Topic: Review of key concepts. The Quantum Internet. Topological Quantum Computing. Careers in Quantum Information Science.
Reading: None.

Primary Textbook:
"Quantum Computing for the Quantum Curious" by Ciaran Hughes, Joshua Isaacson, Anastasia Perry, Ranbel F. Sun, and Jessica Turner.
Availability: Free PDF available on SpringerLink (Open Access).
Use: Perfect for intuitive understanding, visuals, and analogies.

Comprehensive Reference:
"Quantum Computation and Quantum Information" (10th Anniversary Edition) by Michael A. Nielsen & Isaac L. Chuang.
Availability: Known as "Mike & Ike." Not free, but is the definitive resource. Relevant chapters will be cited for deeper dives.

Simulation & Visualization Tools (No-Code):
Quirk Quantum Circuit Simulator: A browser-based, drag-and-drop tool for visualizing quantum states in real-time. (quirk at algassert com)
IBM Quantum Composer: A graphical interface to build circuits and view statevectors and probabilities. (Requires free IBMid login).

Undergraduate , Advanced Undergraduate , Graduate

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