Introduction to Quantum Computing

Course description

Short Description

Quantum computing introduces a fundamentally different paradigm for information processing, with striking consequences for algorithms, cryptography, and computation. This introductory course combines mathematical foundations with a hands-on laboratory component focused on the implementation and simulation of quantum circuits and basic quantum algorithms using Qiskit or similar tools. The course covers quantum states, measurements, unitary operations, multiple-qubit systems, entanglement, and the quantum circuit model, followed by fundamental quantum algorithms and selected topics in quantum information. It provides a foundation for advanced topics such as quantum cryptography, quantum information theory, and quantum complexity theory.

Full Description

The lecture component will cover the following topics:

  1. Single and multiple quantum systems
    Qubits, quantum states, Dirac notation, measurements, unitary operations, tensor products, product states, and entanglement.
  2. Quantum circuits and entanglement in action
    Quantum gates, circuit model, controlled operations, Bell states, teleportation, superdense coding, and the CHSH game.
  3. Quantum query algorithms and algorithmic foundations
    Query model, Deutsch-Jozsa, Bernstein-Vazirani, Simon’s algorithm, reversible computation, phase kickback, and quantum Fourier transform.
  4. Phase estimation, factoring, and Grover’s algorithm
    Quantum phase estimation, order finding, Shor’s factoring algorithm, unstructured search, and amplitude amplification.
  5. Density matrices
    Mixed states, reduced states, partial trace, ensembles, and the density-matrix formulation of quantum information.
  6. Quantum channels
    Quantum operations, noise, examples of channels, Kraus representations, and basic properties of quantum channels.
  7. General measurements
    Projective measurements, POVMs, measurement implementation, and state discrimination.
  8. Purifications and fidelity
    Purifications, fidelity, trace distance, Uhlmann-type intuition, and selected applications in quantum information.
  9. Quick introduction to quantum cryptography
    Microcrypts and quantum-secure one-way functions.

The tutorials will reinforce the mathematical material through problem-solving sessions.

The laboratory sessions will focus on the implementation and simulation of basic quantum circuits and algorithms using Qiskit or similar tools. Possible lab topics include single- and multi-qubit gates, Bell states, teleportation, Deutsch-Jozsa and Bernstein-Vazirani algorithms, Grover search, quantum Fourier transform, phase estimation, and more.

Learning Outcomes

Knowledge

  1. Has knowledge of the basic mathematical formalism of quantum computation.
  2. Knows the quantum circuit model and the role of gates, measurements, and entanglement.
  3. Knows selected fundamental quantum algorithms and basic notions of quantum information.

Skills

  1. Can analyze simple quantum states, measurements, circuits, and protocols.
  2. Can reason about the correctness and limitations of basic quantum algorithms.
  3. Can implement and simulate simple quantum circuits using Qiskit or similar tools.

Competences

  1. Understands the need for mathematical rigor in quantum computation.
  2. Knows the basic possibilities and limitations of quantum information processing.
  3. Can assess the suitability of basic quantum algorithms for selected computational problems.

Bibliography

Assessment Methods and Criteria

To pass the course, the student must pass both the theoretical part and the practical/tutorial part. The theoretical part will be assessed by a mid-term exam and a final written exam. The practical/tutorial part will be assessed through homework, tutorial activity, and a programming/lab test or assignment involving the implementation and simulation of simple quantum circuits using Qiskit or similar tools.

The final grade will be based on the following components:

  • Mid-term exam: 25%.
  • Final exam: 25%.
  • Programming/lab test or assignment: 20%.
  • Homework, tutorial activity, and participation: 30%.

For PhD students, an additional paper presentation and oral discussion/viva will be required. The presentation should concern an advanced topic related to quantum computing, quantum algorithms, quantum information theory, or quantum cryptography. This component may be used to increase the final grade or may be required for obtaining the highest grade.

Prerequisites

  1. Algorithms and data structures
  2. Discrete mathematics
  3. Foundations of mathematics
  4. Geometry with linear algebra
  5. Languages, automata and computations
  6. Mathematical analysis for computer science I
  7. Probability theory and statistics
  8. Basics of Python programming

Assumed Background

  • Basic algorithms and theory of computation
  • Linear algebra, including vectors, matrices, inner products, and tensor products
  • Complex numbers
  • Elementary probability
  • Basic Python programming