Introduction to Quantum Computing

Graduate Level Course – Semester: Fall 2026

Course Outline
Full Description

Course Outline

  1. Week 1: Introduction to Quantum Mechanics – Hilbert Spaces, Dirac Notation
  2. Week 2: Qubits and State Vectors – Superposition, Bloch Sphere
  3. Week 3: Quantum Gates and Circuits – Pauli, Hadamard, CNOT, Toffoli
  4. Week 4: Measurement Theory – Projective Measurements, POVMs
  5. Week 5: Entanglement and Bell States – EPR paradox, CHSH inequality
  6. Week 6: No-Cloning Theorem and Quantum Teleportation
  7. Week 7: Quantum Error Correction – Shor Code, Steane Code
  8. Week 8: Quantum Algorithms – Deutsch-Jozsa, Simon's Algorithm
  9. Week 9: Quantum Fourier Transform and Phase Estimation
  10. Week 10: Shor’s Factoring Algorithm – Applications to Cryptography
  11. Week 11: Grover’s Search Algorithm – Quadratic Speedup
  12. Week 12: Variational Quantum Algorithms – VQE, QAOA
  13. Week 13: Quantum Simulation – Molecular Hamiltonians, Spin Models
  14. Week 14: Quantum Machine Learning – Quantum Neural Networks
  15. Week 15: Emerging Architectures – Superconducting, Trapped Ions, Topological Qubits
  16. Week 16: Course Review and Final Project Presentations

Course Description

This graduate-level course provides a rigorous introduction to the principles and practice of quantum computing, bridging the gap between foundational quantum mechanics and contemporary algorithmic developments. Students will gain a deep understanding of the mathematical structures that underpin quantum computation, including complex vector spaces, tensor products, and unitary operations, as well as the physical realizations of qubits across various quantum hardware platforms.

Beginning with a review of Hilbert space theory and Dirac notation, the course will progressively introduce qubits, quantum gates, and circuit model formalism. The curriculum emphasizes both conceptual clarity and practical skill, offering hands-on experience with quantum programming frameworks such as Qiskit and Cirq. Throughout the semester, students will explore pivotal quantum algorithms—Deutsch-Jozsa, Simon, Shor, Grover, VQE, and QAOA—demonstrating their computational advantages over classical counterparts.

The course also addresses essential topics in quantum error correction and fault-tolerant computing, presenting the theoretical underpinnings of stabilizer codes and threshold theorems. Students will investigate the challenges of decoherence, leakage, and gate imperfections, and learn strategies for mitigating errors in near-term quantum devices.

By the end of the semester, participants will have designed and simulated a complete quantum algorithm tailored to a real-world problem, showcasing their ability to translate abstract theory into tangible quantum solutions. The final project will be presented to the class, fostering a collaborative learning environment and reinforcing the interdisciplinary nature of quantum technology.