Concise Guide to Quantum Computing: Algorithms, Exercises, and Implementations

Sergei Kurgalin, Sergei Borzunov

Davide Pastorello

Mikhail Pavlov

Abstract This practical guide presents hands-on laboratory exercises on variational quantum algorithms (VQAs) and hybrid quantum-classical workflows, based on the IBM Q learning platform. The work was performed by the author on April 28, 2024, using IBM Q cloud resources. Variational algorithms leverage the variational principle of quantum mechanics to optimize quantum circuits for specific tasks, making them particularly suitable for current noisy intermediate-scale quantum (NISQ) devices and offering a practical route toward achieving quantum advantage. The guide explores the full workflow for designing and implementing variational algorithms, highlighting the trade-offs inherent at each stage, including circuit design, parameter initialization, optimization strategies, and measurement post-processing. It also demonstrates the use of Qiskit Runtime primitives to enhance both the speed and accuracy of computations. Through these exercises, participants gain experience in constructing hybrid quantum-classical algorithms, performing parameter optimization, and interpreting results within the context of near-term quantum devices. While this guide focuses on practical implementation, it also encourages exploration of the underlying theoretical foundations of quantum information and computation, connecting applied algorithmic practice with fundamental principles. The course and exercises provide a structured starting point for researchers, developers, and students aiming to explore the utility of quantum computers for real-world problem solving, particularly in optimization, quantum chemistry, and machine learning applications.

Marcus Stephen Edwards

Mikhail Pavlov

Abstract This methodological guide provides a practical framework for performing laboratory work using quantum computers, adapted and translated from the laboratory exercises developed by the International Quantum Center at CERN, Switzerland. It represents the first set of quantum laboratory exercises fully adapted for Russian-speaking students and researchers. The guide is designed to support hands-on learning during the ongoing second quantum revolution, offering insight into quantum computing technologies with applications in both fundamental research and cybersecurity, particularly in the context of heightened geopolitical and cyber threats exploiting emerging quantum capabilities. The laboratory manual consists of eight exercises covering fundamental and advanced quantum protocols, including qubit manipulation, entanglement, quantum teleportation, Grover and Deutsch–Jozsa algorithms, BB84 quantum key distribution, CHSH game, and statistical sampling from random quantum circuits. Each exercise is structured to provide both theoretical understanding and practical implementation. To perform the laboratory exercises, the following prerequisites are required: Internet access on the student-user side. Creation of an account and registration with a cloud-based quantum computing service, such as IBM Quantum or the Russian Quantum Center platform. The methodology for completing the exercises follows a structured workflow: Preparatory stage – study the content, goals, and theoretical background of the laboratory work. Cloud connection – log in to the quantum computing cloud service using the personal account. Simulation stage – execute the laboratory circuit on a quantum computer simulator in the cloud service. Real hardware execution – run the equivalent circuit on an actual quantum processor. Data analysis – compare simulation and hardware results, analyze measurement outcomes, and identify deviations. Conclusion stage – summarize findings, verify learning objectives, and draw insights from experimental results. This guide provides a comprehensive, hands-on approach for students, researchers, and specialists in information security to gain practical experience with quantum computing, bridging theoretical concepts with experimental implementation.

Stefano Olivares