Course Overview: This course provides an introduction to quantum computing with an emphasis on applications in quantum chemistry. Over 14 weeks, students will explore fundamental quantum mechanics, quantum algorithms, and practical applications using tools such as Qiskit-Nature.

https://github.com/Qiskit

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Week 1: Introduction to Quantum Computing and Fundamentals of Quantum Mechanics
• Topics:
o Overview of quantum computing
o Importance of quantum computing in chemistry
o Postulates of quantum mechanics
o Quantum states, superposition, and measurement
o Wave-particle duality
• Activities:
o Discuss classical vs. quantum computing
o Explore key challenges in quantum chemistry
o Solve basic quantum mechanics problems using Qiskit tutorials
o Demonstrations of simple quantum systems with Qiskit
Week 2: Basic Linear Algebra for Quantum Computing
• Topics:
o Vectors and matrices
o Eigenvalues and eigenvectors
o Tensor products
• Activities:
o Hands-on exercises with quantum operators and matrices
o Matrix representation of quantum gates using Qiskit
Week 3: Introduction to Bra-Ket Notation
• Topics:
o Bra and ket vectors
o Inner and outer products
o Hermitian and unitary operators
• Activities:
o Practice expressing quantum states in bra-ket notation
o Explore operator algebra with Qiskit examples
Week 4: Basics of Quantum Circuits (Part 1: Single-Qubit Gates)
• Topics:
o Quantum bits (qubits) and single-qubit gates
o Key gates: Hadamard, Pauli-X, Y, Z
o Circuit representation
• Activities:
o Design and simulate circuits using single-qubit gates in Qiskit
o Explore quantum circuit measurement with Qiskit tutorials
Week 5: Basics of Quantum Circuits (Part 2: Multi-Qubit Gates)
• Topics:
o Multi-qubit gates: CNOT, Toffoli, SWAP
o Entanglement and Bell states
o Quantum circuit representation with multiple qubits
• Activities:
o Simulate multi-qubit quantum circuits using Qiskit
o Analyze entanglement and its applications with Qiskit demos
Week 6: The Deutsch-Jozsa Algorithm
• Topics:
o Problem statement
o Algorithm mechanics
o Implementation in quantum circuits
• Activities:
o Hands-on simulation of Deutsch-Jozsa algorithm using Qiskit
o Analyze classical vs. quantum efficiency
Week 7: Grover’s Algorithm
• Topics:
o Problem statement
o Amplitude amplification
o Application in search problems
• Activities:
o Build and simulate Grover’s algorithm with Qiskit tutorials
o Discuss its potential in chemistry
Week 8: Quantum Fourier Transform (QFT)
• Topics:
o Mathematical basis of QFT
o Quantum circuit implementation
o Applications in phase estimation
• Activities:
o Develop QFT circuits using Qiskit
o Understand its role in quantum algorithms through Qiskit examples
Week 9: Shor’s Algorithm (Part 1)
• Topics:
o Introduction to quantum factorization
o Mathematical foundation
o Key steps of Shor’s algorithm
• Activities:
o Simulate initial steps of Shor’s algorithm using Qiskit
o Explore its implications for cryptography
Week 10: Shor’s Algorithm (Part 2)
• Topics:
o Implementation in quantum circuits
o Detailed analysis of performance
o Challenges and future advancements
• Activities:
o Simulate full Shor’s algorithm using Qiskit
o Discuss its scalability and limitations
Week 11: Variational Quantum Eigensolver (VQE)
• Topics:
o Basics of variational principles
o Quantum-classical hybrid algorithms
o Introduction to VQE framework
• Activities:
o Implement VQE for a simple molecular system using Qiskit-Nature
o Discuss convergence challenges with practical examples
Week 12: Applications to Quantum Chemistry (Part 1)
• Topics:
o Molecular Hamiltonians
o Mapping to qubit operators
o Hartree-Fock theory
• Activities:
o Use Qiskit-Nature to model molecular systems
o Explore qubit encodings with provided Qiskit tutorials
Week 13: Applications to Quantum Chemistry (Part 2)
• Topics:
o Solving small molecules using VQE
o Role of quantum computing in chemical reactions
o Advanced quantum chemistry use cases
• Activities:
o Simulate chemical systems in Qiskit-Nature
o Analyze computational results using Qiskit tutorials
Week 14: Current Challenges and Future Directions in Quantum Chemistry
• Topics:
o Noise and error correction in quantum computing
o Scaling quantum chemistry problems
o Advances in hardware and algorithms
• Activities:
o Group discussion on recent papers in the field
o Identify open research problems using Qiskit examples
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Assessment:
• Weekly problem sets and lab assignments (40%)
• Midterm quiz (20%)
• Final project (40%)
Tools:
• Qiskit and Qiskit-Nature
• Python programming
• Quantum circuit simulators

Recorded Online Class