(2024/2025) Quantum Computing

These notes are an unofficial resource and shouldn’t replace the course material or any other book on quantum computing. It is not made for commercial purposes. I’ve made the following notes to help me improve my knowledge and maybe it can be helpful for everyone.

As I have highlighted, a student should choose the teacher’s material or a book on the topic. These notes can only be a helpful material.

(expandable) The notes are taken from the books and other resources required for the course.

• Course slides.

You can view/download the PDF here. In the notes folder, you can also see the source code.

In the CHANGELOG file you can see the changes made to each version of the PDF file. The versioning can be helpful if you want to understand if there are any new features/fixes in the file.

For any issue, use the appropriate section.

Course Syllabus

According to the official course syllabus:

Main lectures topics:

• Quantum information for single qubits
  • Dirac notation
  • Qubit measurement
  • Block sphere
  • Unitary operations (Pauli, Hadamard, Phase) and examples of their application to qubit states
  • No cloning theorem
• Multiple qubit systems
  • Product state (independent systems)
  • Entangled state, bell states
  • Quantify entanglement
  • Measure multiple qubit states
  • Multi qubit operations: Swap, CNOT, Toffoli
  • diVincenzo criteria
  • Clifford gates
• Quantum Circuit representation
  • The oracle model
• Algorithms
  • Phase kickback
  • Deutsch and Deutsch-Jozsa
  • Simon periodicity
  • Shor
  • Grover and applications
  • Quantum walk
  • QFT & Phase estimation
• Variational algorithms
  • NISQ
  • Variational Quantum Eigensolver (VQE)
  • Variational Quantum Approximate Optimization (QAOA)
  • VQLS (least-squares)
• Simulated annealing and quantum annealing
  • Adiabatic QC paradigm
  • Relationship of Ising, Hamiltonian and QUBO
  • Basic concepts on writing problems in QUBO formulation
  • D-Wave QPU and Minor embedding
  • The D-Wave QPU and its architecture
  • Write NP-complete and NP-hard problems in QUBO formulation (max cut, min vertex cover, SAT, quadratic assignment)
  • Annealing Schedule and Reverse Annealing