Introduction to Quantum Computing
This course provides a comprehensive introduction to the principles of quantum computing. Starting from the mathematical foundations of qubits and quantum mechanics, we will progress through quantum gates, circuits, and core protocols. A significant portion of the course is dedicated to understanding how classical computers simulate quantum systems, including state-vector simulators, stabilizer simulators, and the challenges of simulating noise. By the end of the course, students will understand the operational principles behind major algorithms (Grover, Shor) and the limitations of current simulation technology.
讲师
日期
2026年03月24日 至 06月16日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周二,周四 | 16:10 - 17:50 | A14-203 | Zoom 17 | 442 374 5045 | BIMSA |
修课要求
calculus, linear algebra, probability
课程大纲
Module 1: Foundations (Lectures 1-6) (Subject to change)
Lecture 1: Qubit, superposition, Bloch sphere.
Lecture 2: Quantum gates, quantum circuits, quantum teleportation.
Lecture 3: Quantum algorithms, Toffoli gate, Deutsch-Josza algorithm.
Lecture 4: Bra-ket notation, vector space, operators. tensor product.
Lecture 5: Operator functions, commutator.
Lecture 6: Simultaneouse diagonalization, polar decomposition.
Lecture 7: Quantum postulates: state space, evolution, measurement.
Lecture 8: Projective measurement, positive operator-valued measurement (POVM)
Lecture 9: Superdense coding, density operator
Lecture 10: Partial trace and Schimidt decomposition and purification.
Lecture 11: EPR and Bell inequality.
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.
Lecture 1: Qubit, superposition, Bloch sphere.
Lecture 2: Quantum gates, quantum circuits, quantum teleportation.
Lecture 3: Quantum algorithms, Toffoli gate, Deutsch-Josza algorithm.
Lecture 4: Bra-ket notation, vector space, operators. tensor product.
Lecture 5: Operator functions, commutator.
Lecture 6: Simultaneouse diagonalization, polar decomposition.
Lecture 7: Quantum postulates: state space, evolution, measurement.
Lecture 8: Projective measurement, positive operator-valued measurement (POVM)
Lecture 9: Superdense coding, density operator
Lecture 10: Partial trace and Schimidt decomposition and purification.
Lecture 11: EPR and Bell inequality.
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.
参考资料
Primary Textbook:
"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.
Easy reading:
"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.
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).
"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.
Easy reading:
"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.
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).
听众
Undergraduate
, Advanced Undergraduate
, Graduate
视频公开
公开
笔记公开
公开
语言
英文
讲师介绍
I am an Associate Professor at BIMSA. I joined BIMSA in the summer of 2025. My Research area is statistical genetics, where I develop statistical and computational methods, mainly from Bayesian perspective, with targeted applications in genomic studies and genetic diagnosis. Currently I am working on studying haplotype variation using deep learning models. I am also interested in studying genetic determinants of autism, and early cancer screening.