Quantum 201: Quantum Computing & Quantum Internet

Building directly on Quantum 101, this programme consists of two advanced courses providing deeper mathematical and conceptual understanding of quantum computing and quantum communication. Where Quantum 101 builds foundations, Quantum 201 develops professional-level depth - the kind needed to work with real quantum algorithms and quantum communication protocols.

Authored by researchers from the QuTech research centre at Delft University of Technology, where scientists and engineers drive quantum technology research.

What you’ll learn

• Density matrices: the general mathematical formalism for quantum states that captures both pure states and mixed states (classical uncertainty about quantum state)
• POVMs (positive operator-valued measures): the general theory of quantum measurements beyond simple projective measurement
• Quantum channels: completely positive trace-preserving maps as the general model for how quantum systems evolve, including under noise
• Quantum algorithm techniques: amplitude amplification, quantum phase estimation, and the quantum Fourier transform as general reusable subroutines
• The Deutsch-Jozsa and Bernstein-Vazirani algorithms worked through with full mathematical detail and circuit construction
• Simon’s algorithm: the hidden subgroup problem, its quantum solution, and why it inspired Shor’s factoring algorithm
• Quantum key distribution: BB84 and E91 protocols with rigorous security arguments showing why eavesdropping is always detectable in principle
• Quantum communication beyond QKD: entanglement-based protocols and their applications
• Secure quantum channels: information-theoretic security and where the limits of quantum cryptography lie

Course structure

Quantum 201 consists of two courses. They can be taken sequentially or in parallel depending on your background.

Course 1 - Quantum Bits, Operations, and Algorithms Revisits qubits and quantum operations at a significantly higher mathematical level than Quantum 101. Density matrices replace pure state vectors as the primary tool. POVM formalism handles general measurements. Quantum algorithm techniques are then covered: phase estimation (the key subroutine behind Shor’s algorithm) and amplitude amplification in full generality. Worked examples include complete implementations of Deutsch-Jozsa, Bernstein-Vazirani, and Simon’s algorithm.

Course 2 - Quantum Communication Builds the theory of quantum cryptography from first principles, including rigorous information-theoretic security arguments. BB84 and E91 are covered with full protocols and proofs of security against specific attack models. The quantum repeater architecture for long-distance quantum networks closes the course.

Both courses assume Quantum 101 content and linear algebra as prerequisites.

Who is this for?

• Quantum 101 graduates ready to develop depth in algorithms and quantum communication
• Graduate students and researchers wanting formal treatment of advanced quantum topics
• Quantum software engineers who want to understand the mathematical foundations of the algorithms they implement
• Security professionals and cryptographers evaluating or implementing quantum-safe and quantum communication systems
• Anyone who wants to be able to read quantum information research papers with genuine comprehension

Prerequisites

Completion of Quantum 101 (or equivalent) is required. You must be comfortable with quantum circuits, Dirac notation, and entanglement at Quantum 101 level. Linear algebra at the level of eigenvalue decompositions and complex vector spaces is essential. Some familiarity with probability theory and basic classical cryptography helps for the quantum communication course.

Hands-on practice

Problem sets at Quantum 201 level require genuine mathematical work:

• Deriving that quantum operations preserve trace and positivity
• Proving security bounds for BB84 against specific attack strategies
• Stepping through Simon’s algorithm for small problem instances algebraically
• Implementing quantum phase estimation circuits in Python on a simulator
• Computing mutual information measures for quantum channels

The mathematical demands are comparable to a graduate quantum information science course - this is not a passive learning experience.

Why take this course?

Quantum 201 bridges the gap between accessible introductions and research-level material.

After completing it, you will be able to read quantum algorithm research papers and follow the mathematical arguments. You will understand the security arguments for quantum cryptography with the precision needed to evaluate them critically. You will be equipped to contribute meaningfully to quantum software development at the algorithm layer.

QuTech’s researchers bring both mathematical rigor and practical clarity - a combination that is harder to find than it sounds in quantum computing education. This programme is the natural next step after Quantum 101 for anyone serious about the field.

Related tutorials

Practise the concepts from this course with these hands-on tutorials:

• Qiskit Hello World - Your first quantum circuit in Qiskit: Bell state, measurement, and histogram output
• Grover’s Algorithm Explained - Step-by-step implementation of Grover’s search algorithm in Qiskit
• Shor’s Algorithm Explained - How Shor’s factoring algorithm works and why it threatens current encryption