Program · a.y. 2026/2027

Course Program

Everything the course covers, from the first qubit to the architecture of the quantum Internet, is included as an official reference for the academic year.

90 contact hours4 × 2-hour sessions per weekAt least one lab session per weekQiskitQuantumSavory.jl

Motivation

Quantum computing is an emerging computational paradigm that exploits the principles of quantum mechanics to process information in ways that are fundamentally different from those of classical computers. By harnessing phenomena such as superposition, interference, and entanglement, quantum algorithms can provide significant advantages for specific computational tasks, including integer factorization, quantum simulation, optimization, and search.

The rapid progress of quantum hardware has been accompanied by the development of increasingly sophisticated software ecosystems. Today, software development kits such as Qiskit enable programmers to design, simulate, test, and execute quantum programs on both classical simulators and quantum processors. As a result, quantum programming is emerging as a new discipline at the intersection of computer science, software engineering, mathematics, and quantum information science.

At the same time, a second technological frontier is taking shape: the quantum Internet. While the classical Internet enables the exchange of digital information, quantum networks are designed to distribute quantum states and entanglement among geographically separated nodes. Such capabilities open the way to applications that have no classical counterpart, including quantum-secure communication, distributed quantum computing, blind quantum computing, and quantum sensing networks.

The long-term vision is the creation of large-scale quantum networks interconnecting quantum processors, memories, and sensors through a new generation of communication infrastructures. Achieving this vision requires the development of novel architectures, protocols, and technologies, including quantum repeaters, entanglement distribution mechanisms, quantum teleportation, and quantum network control protocols.

As quantum technologies continue to mature, computer engineers and software developers will increasingly need to understand not only how quantum computers operate, but also how quantum applications can be designed, implemented, and deployed across interconnected quantum systems.

Designed for Computer Engineering students, this intermediate-level course develops the knowledge and practical skills required to program quantum computers, implement quantum communication protocols, and understand the architectures underlying future quantum networks.

Course description

This course provides an intermediate-level study of quantum computing and quantum networking from a software engineering perspective. It introduces the fundamental concepts of quantum information processing, the principles underlying quantum communication systems, and the methodologies required to design and implement quantum software and protocols.

The course combines theoretical foundations with practical programming experience. Topics include quantum states and operations, quantum algorithms, quantum communication protocols, quantum noise models, quantum error correction, and the architectural principles of the quantum Internet. Particular emphasis is placed on understanding how quantum information can be processed, transmitted, protected, and exploited in both standalone quantum computers and interconnected quantum systems.

A significant component of the course is devoted to software development. Through lectures, guided exercises, and the hands-on Quantum Software Laboratory, students learn how to implement, test, debug, and analyze quantum algorithms and quantum networking protocols using modern software frameworks.

The Quantum Software Laboratory makes use of Qiskit, IBM's open-source Python SDK for quantum computing, and QuantumSavory.jl, a Julia framework for the simulation and study of quantum systems and quantum networks. Students develop programs that can be executed on simulators and, whenever resources are available, on real quantum processors.

Learning outcomes

Upon successful completion of the course, students will be able to:

model and manipulate quantum information using the mathematical formalism of quantum mechanics
design and implement quantum algorithms using contemporary quantum software frameworks
analyze the effects of noise and imperfections in quantum systems
understand the principles and mechanisms of quantum error correction
implement and evaluate quantum communication protocols
model and simulate quantum networks and quantum Internet architectures
critically assess the opportunities and limitations of current and emerging quantum technologies

Scope and focus

This course adopts a software-oriented perspective on quantum computing and quantum networking. Its primary objective is to provide students with the conceptual and practical tools required to design, implement, and analyze quantum algorithms and quantum communication protocols.

Instead, quantum computers and quantum networks are treated as programmable systems whose behavior can be modeled, analyzed, and exploited through software. The emphasis is therefore placed on quantum information processing, quantum programming, quantum algorithms, quantum communication protocols, quantum error correction, and quantum network architectures.

Prerequisites

Students enrolling in this course are expected to possess:

a solid background in linear algebra, including vector spaces, linear operators, matrices, eigenvalues and eigenvectors, basis transformations, tensor products, and spectral decomposition
proficiency in Python programming
a basic understanding of computational complexity and algorithm analysis, including Big-O notation and the complexity classes P and NP

Quantum Software Laboratory

The laboratory component of the course provides hands-on experience with contemporary quantum software frameworks and development tools. Its primary objective is to bridge the gap between theoretical concepts and practical implementation through the design, execution, and analysis of quantum programs and quantum networking protocols.

Students work with two complementary software environments. Qiskit, IBM's open-source Python SDK, is used to develop, simulate, and execute quantum algorithms on both simulators and, whenever resources are available, real quantum processors. QuantumSavory.jl, a Julia-based framework for quantum system and network simulation, is used to model quantum communication protocols, entanglement distribution mechanisms, and quantum Internet architecture.

QiskitPython · IBM Quantum QuantumSavory.jlJulia · Quantum networks

The Quantum Software Laboratory emphasizes software engineering practices, including program design, debugging, validation, performance analysis, and reproducibility. Particular attention is devoted to understanding how theoretical quantum-information concepts are translated into executable software.

Examination

Assessment is based on an oral examination in two parts — a quantum circuit to analyse, then theoretical questions — and on a project developed with Qiskit and/or QuantumSavory.jl. Rules, sample questions and past projects are on the Exam & Projects page.

Exam details, project rules, sample questions and past projects

Detailed program

Two tracks, developed side by side.

The course is organized as a single, integrated learning path combining theoretical foundations and a Quantum Software Laboratory. The laboratory is neither independent nor supplementary: as theoretical concepts are introduced, they are translated into code, explored through simulation, and, whenever possible, tested on quantum hardware. Although the contents of the two components are presented separately below for clarity, they develop in parallel and continuously complement and reinforce each other.

The program is organized into numbered units identified by the labels T and L: T denotes Theoretical Foundations, while L denotes Quantum Software Laboratory.

Theoretical Foundations18 units

1TFoundations of Quantum Computing and Single-Qubit Systems6 topics

Course Overview and Learning Objectives
From Classical Bits to Quantum Bits
The Qubit as the Fundamental Unit of Quantum Computation
Examples of Physical Qubit Realizations
Postulate I: Quantum States and State Representation
Mathematical Description of a Qubit

2TMathematical Foundations of Quantum Computing17 topics

Complex Vector Spaces
Hilbert Spaces
Dirac (Bra-Ket) Notation
Linear Independence and Basis Representations
Linear Operators and Matrix Representations
Inner Products and Outer Products
The Pauli Operators
The Gram–Schmidt Orthogonalization Procedure
Eigenvalues, Eigenvectors, and Eigenspaces
Adjoint, Hermitian, and Unitary Operators
Spectral Decomposition of Hermitian Operators
Positive and Positive Semidefinite Operators
Tensor Products and Composite Systems
Functions of Operators
Commutators and Anticommutators
Polar Decomposition
Singular Value Decomposition (SVD)

3TBloch Sphere and Single-Qubit Measurement6 topics

Bloch Sphere Representation
Single-Qubit Measurement
Geometric Interpretation
Postulate III: Single-Qubit Measurement
Measurements in Bases Other than the Computational Basis
Single-Qubit Measurement Implications

4TSingle-Qubit Quantum Gates7 topics

Unitarity and Reversibility of Quantum Gates
Identity Gate
Pauli X, Z, and Y Gates
S, T, and H Gates
Global Phase and Relative Phase
Rotation About x-, y-, and z-axes in the Bloch Sphere
Postulate II: The Time Evolution of the State of a Closed Quantum System: the Schrödinger Equation

5TMulti-Qubit Systems and Quantum Entanglement12 topics

Postulate IV: Composite Quantum Systems
Tensor Products and Multi-Qubit State Spaces
Representing Multi-Qubit Quantum States
Hermitian Operators and the Measurement Formalism
Observables and Quantum Measurements
Commuting and Non-Commuting Observables
The Heisenberg Uncertainty Principle
Measurements on Multi-Qubit Systems
Bipartite Entanglement
Multipartite Entanglement
Entanglement as a Computational Resource
Monogamy of Entanglement

6TThe Quantum Circuit Model of Computation9 topics

Quantum Circuits as Computational Processes
Multi-Qubit Quantum Gates
Controlled Quantum Gates
Universal Quantum Gate Sets
Quantum Circuit Decomposition
Quantum Circuit Complexity
The No-Cloning Theorem
Quantum Measurements within the Circuit Model
From Quantum Algorithms to Quantum Circuits

7TQuantum Teleportation and Superdense Coding7 topics

Entanglement as a Resource for Quantum Communication
Bell States and Bell-State Measurements
Quantum Teleportation
Classical Communication and Feed-Forward Corrections
Resource Analysis of the Teleportation Protocol
Superdense Coding
Resource Analysis of the Superdense Coding Protocol

8TFoundations of Quantum Algorithms9 topics

Quantum Parallelism
Quantum Interference
Phase Kickback
Quantum Oracles
The Deutsch Problem
The Deutsch Algorithm
The Deutsch–Jozsa Problem
The Deutsch–Jozsa Algorithm
From Classical to Quantum Algorithm Design

9TQuantum Fourier Transform, Phase Estimation, and Order Finding8 topics

The Quantum Fourier Transform (QFT)
The Inverse Quantum Fourier Transform
Quantum Phase Estimation (QPE)
Eigenvalue Estimation with Quantum Circuits
Period Finding
The Order-Finding Problem
Shor's Order-Finding Algorithm
Applications of Quantum Phase Estimation

10TQuantum Search and Amplitude Amplification8 topics

Unstructured Search Problems
Quantum Oracles for Search
Amplitude Amplification
Grover's Search Algorithm
Geometric Interpretation of Grover's Algorithm
Multiple-Solution Search Problems
Quantum Counting
Applications and Limitations of Quantum Search

11TQuantum Key Distribution7 topics

Security from the Laws of Quantum Mechanics
Principles of Quantum Key Distribution
The BB84 Protocol
The B92 Protocol
Entanglement-Based Quantum Key Distribution
Bell Inequalities and the CHSH Test
The E91 Protocol

12TMixed States and the Density Operator Formalism10 topics

Limitations of the State Vector Formalism
Statistical Ensembles of Quantum States
Pure and Mixed Quantum States
Density Operators
Quantum States in the Density Operator Formalism
Trace and Partial Trace
Reduced Density Operators
Properties of Density Operators
Single-Qubit Mixed States and the Bloch Ball
Applications of the Density Operator Formalism

13TQuantum Operations and Noise Models16 topics

Limitations of Closed-System Evolution
Open Quantum Systems
Quantum Operations
Environments and Quantum Operations
The Operator-Sum Representation
Kraus Operators
Quantum Channels
Single-Qubit Noise Models
- Bit-Flip Channel
- Phase-Flip Channel
- Depolarizing Channel
- Amplitude-Damping Channel
- Phase-Damping Channel
Geometric Interpretation of Quantum Channels
Applications of Quantum Operations
Introduction to Quantum State Tomography

14TDistance Measures and Fidelity in Quantum Information9 topics

Distance Measures for Classical Information
Comparing Quantum States
Trace Distance
Quantum State Fidelity
Fidelity Between Pure and Mixed States
Comparing Quantum Channels
Process Fidelity
Performance Evaluation of Quantum Systems
Applications of Fidelity in Quantum Computing and Quantum Communications

15TQuantum Error Correction9 topics

Why Quantum Error Correction Is Necessary
Challenges of Protecting Quantum Information
The Three-Qubit Bit-Flip Code
The Three-Qubit Phase-Flip Code
The Shor Code
Syndrome Extraction and Error Detection
Principles of Quantum Error Correction
The Knill–Laflamme Conditions
Limitations and Practical Challenges of Quantum Error Correction

16TQuantum Internet Background9 topics

From the Classical Internet to the Quantum Internet
Architecture of a Quantum Network
Quantum Nodes, Memories, and Communication Links
Entanglement Distribution Protocols
Entanglement Swapping
Quantum Repeaters
End-to-End Entanglement Distribution
Event-Driven Protocol Execution
Performance Metrics for Quantum Networks

17TEntanglement Purification Protocols9 topics

Imperfect Entanglement in Quantum Networks
Fidelity of Entangled States
Werner States
Principles of Entanglement Purification
The BBPSSW Protocol
The DEJMPS Protocol
Resource Trade-Offs in Entanglement Purification
Entanglement Purification and Quantum Repeaters
The Role of Entanglement Purification in the Quantum Internet

18TMeasurement-Based and Blind Quantum Computation8 topics

Beyond the Quantum Circuit Model
Graph States as Computational Resources
Principles of Measurement-Based Quantum Computation
Adaptive Measurements and Feed-Forward Operations
Universal Quantum Computation with Graph States
Brickwork States
Blind Quantum Computation
The Broadbent–Fitzsimons–Kashefi (BFK) Protocol

Quantum Software Laboratory8 units

1LQuantum Programming with Qiskit1T–4T10 topics

Translates into code the theoretical concepts developed in Units 1T–4T.

Quantum Programming in the Era of Artificial Intelligence
Developing with Large Language Models and Coding Agents
The IBM Quantum Platform
The Qiskit Open-Source SDK
Installing and Configuring the Qiskit Environment
Building and Visualizing Quantum Circuits
Exporting and Importing OpenQASM 3 Programs
Simulating Quantum Circuits with Qiskit Aer
Implementing Single-Qubit Gates and Measurements
Visualizing Single-Qubit States on the Bloch Sphere

2LMulti-Qubit Circuits and Quantum Entanglement with Qiskit5T–6T9 topics

Translates into code the theoretical concepts developed in Units 5T–6T.

Working with Multi-Qubit Registers and Qubit Ordering
Preparing Multi-Qubit Superposition States
Preparing Bell and GHZ States
Implementing Multi-Qubit and Controlled Quantum Gates
Decomposing Circuits into Universal Gate Sets
Measuring Observables in Different Bases
Demonstrating the No-Cloning Theorem through Quantum Circuits
Computing Reduced States and Entanglement Diagnostics
Profiling Circuit Depth, Width, and Gate Count

3LFrom Quantum Circuits to Quantum Execution6T9 topics

Translates into code the theoretical concepts developed in Unit 6T.

The Qiskit Execution Model: Map, Optimize, Execute, Post-Process
Selecting Backends: Simulators and Quantum Processors
Inspecting Backend Targets and Hardware Constraints
Transpiling Circuits with Preset Optimization Levels
Analyzing Instruction Set Architecture (ISA) Circuits
Running the Sampler and Estimator Primitives
Managing Jobs, Batches, and Sessions on the IBM Quantum Compute Service
Executing Quantum Programs on IBM Quantum Hardware
Ensuring Reproducibility: Shots, Seeds, and Metadata

4LQuantum Algorithms with Qiskit8T–10T9 topics

Translates into code the theoretical concepts developed in Units 8T–10T.

Implementing Quantum Oracles
Observing Quantum Interference and Phase Kickback
Implementing the Deutsch and Deutsch–Jozsa Algorithms
Building the Quantum Fourier Transform Circuit
Running Quantum Phase Estimation
Simulating Period Finding and Order Finding
Implementing Grover's Search and Amplitude Amplification
Exploring Multiple-Solution Search and Quantum Counting
Benchmarking Scalability: Depth, Shots, and Result Quality

5LQuantum Communication and Quantum Key Distribution with Qiskit7T and 11T8 topics

Translates into code the theoretical concepts developed in Units 7T and 11T.

Preparing Bell States and Implementing Bell-State Measurements
Implementing Quantum Teleportation with Dynamic Circuits
Implementing Superdense Coding
Analyzing Protocol Resources: Qubits, Ebits, and Classical Bits
Implementing the BB84 Protocol
Implementing the CHSH Test and the E91 Protocol
Simulating Eavesdropping and Estimating the Quantum Bit Error Rate
Evaluating Key Distribution Performance Under Noise

6LNoise Models, Fidelity, and Quantum Error Correction with Qiskit12T–15T9 topics

Translates into code the theoretical concepts developed in Units 12T–15T.

Computing Density Matrices and Reduced Density Operators
Visualizing Mixed States in the Bloch Ball
Implementing Quantum Channels with Kraus Operators
Building Custom and Hardware-Calibrated Noise Models
Running Quantum State and Process Tomography
Estimating Trace Distance, State Fidelity, and Process Fidelity
Applying Error Suppression and Error Mitigation
Implementing the Three-Qubit Bit-Flip and Phase-Flip Codes
Simulating the Shor Code: Error Injection and Recovery

7LQuantum Network Simulation with QuantumSavory.jl16T9 topics

Translates into code the theoretical concepts developed in Unit 16T.

From Quantum Computing to Quantum Networking
Getting Started with the Julia Programming Language
Setting Up QuantumSavory.jl and Its Simulation Backends
Building Quantum Registers and Register Networks
Implementing Quantum Channels and Classical Message Passing
Configuring Noise and Decoherence Models for Quantum Memories
Running Event-Driven Simulations and Synchronizing Protocols
Modeling Quantum Nodes and Elementary Networks
Visualizing and Evaluating Network Simulations

8LQuantum Internet and Graph States with QuantumSavory.jl16T–18T10 topics

Translates into code the theoretical concepts developed in Units 16T–18T.

Implementing Entanglement Distribution Protocols
Simulating Entanglement Swapping and Entanglement Tracking
Building Quantum Repeater Chains with Cutoff Policies
Evaluating End-to-End Entanglement Distribution
Modeling Quantum Internet Architectures: Chains, Grids, and Switches
Generating Noisy Entangled States and Werner States
Running Entanglement Purification: BBPSSW and DEJMPS
Analyzing Fidelity Gain Versus Resource Cost
Preparing Graph States for Measurement-Based Computation
Simulating Blind Quantum Computation Scenarios

References

Quantum Computing

The books are listed in a progression of difficulty: basic, intermediate, and advanced.

Introduction to Classical and Quantum Computing
Thomas G. Wong · 2022
Basic
An Introduction to Quantum Computing
Phillip Kaye, Raymond Laflamme, Michele Mosca · Oxford University Press · 2007
Intermediate
Quantum Computation and Quantum Information
Michael A. Nielsen, Isaac L. Chuang · Cambridge University Press, Cambridge · 2010
Advanced

Quantum Internet

Quantum Networking
Rodney Van Meter · ISTE Ltd and John Wiley & Sons, Inc. · 2014
The Quantum Internet — The Second Quantum Revolution
Peter P. Rohde · Cambridge University Press · 2021
The Quantum Internet (Technical Version)
Peter P. Rohde, Zixin Huang, Yingkai Ouyang, He-Liang Huang, Zu-En Su, et al. · arXiv:2501.12107 · 2025
arxiv.org