Abstract This laboratory work presents a practical implementation of the CHSH game using the Qiskit framework and IBM quantum hardware. The material is based on educational resources developed by the International Quantum Center at CERN (Switzerland) and aims to provide an experimental demonstration of quantum nonlocality and Bell inequality violation. In Laboratory Work No. 4, participants implement a simplified version of the Clauser–Horne–Shimony–Holt (CHSH) game to test whether IBM quantum processors exhibit genuinely quantum behavior. The CHSH game is a fundamental protocol in quantum information theory that distinguishes classical correlations from quantum correlations through statistical violation of Bell inequalities. Using Qiskit, a two-qubit entangled state is prepared and measurement settings corresponding to different basis choices are applied. By executing the circuit multiple times on a simulator and real quantum hardware, participants collect measurement statistics and compute the CHSH correlation parameter. If the experimentally obtained value exceeds the classical bound, the results provide empirical evidence of quantum entanglement and nonlocal correlations. This laboratory exercise demonstrates how foundational concepts of quantum mechanics—entanglement, superposition, and measurement basis dependence—can be directly tested using cloud-accessible quantum processors. The experiment not only reinforces theoretical understanding of Bell inequalities but also introduces practical skills in circuit construction, parameterized measurements, statistical analysis, and noise considerations in real quantum devices.
Abstract This laboratory work presents a practical implementation of the CHSH game using the Qiskit framework and IBM quantum hardware. The material is based on educational resources developed by the International Quantum Center at CERN (Switzerland) and aims to provide an experimental demonstration of quantum nonlocality and Bell inequality violation. In Laboratory Work No. 4, participants implement a simplified version of the Clauser–Horne–Shimony–Holt (CHSH) game to test whether IBM quantum processors exhibit genuinely quantum behavior. The CHSH game is a fundamental protocol in quantum information theory that distinguishes classical correlations from quantum correlations through statistical violation of Bell inequalities. Using Qiskit, a two-qubit entangled state is prepared and measurement settings corresponding to different basis choices are applied. By executing the circuit multiple times on a simulator and real quantum hardware, participants collect measurement statistics and compute the CHSH correlation parameter. If the experimentally obtained value exceeds the classical bound, the results provide empirical evidence of quantum entanglement and nonlocal correlations. This laboratory exercise demonstrates how foundational concepts of quantum mechanics—entanglement, superposition, and measurement basis dependence—can be directly tested using cloud-accessible quantum processors. The experiment not only reinforces theoretical understanding of Bell inequalities but also introduces practical skills in circuit construction, parameterized measurements, statistical analysis, and noise considerations in real quantum devices.
Abstract This laboratory work presents a practical introduction to the preparation and analysis of entangled quantum states (Bell pairs) using the Qiskit framework. The material is based on educational resources developed by the International Quantum Center at CERN (Switzerland) and is designed to provide hands-on experience with multi-qubit quantum circuits and entanglement generation. In Laboratory Work No. 3, participants construct and simulate a quantum circuit that prepares an entangled two-qubit state. As a representative example of multi-qubit operations in Qiskit, the circuit generates a Bell state by applying a Hadamard (H) gate to the first qubit q[0]q[0]q[0], followed by a controlled-NOT (CNOT) gate with q[0]q[0]q[0] as the control qubit and q[1]q[1]q[1] as the target qubit. This sequence creates a maximally entangled state, demonstrating the fundamental non-classical correlations characteristic of quantum systems. The laboratory exercise includes measurement operations applied to both qubits, illustrating how entanglement manifests in correlated classical outcomes. When the measurement operator is applied to the first qubit q[0]q[0]q[0], the corresponding classical bit records a definite value, and subsequent measurement of the second qubit q[1]q[1]q[1] yields a correlated result consistent with the structure of the Bell state. The probabilistic yet correlated outcomes provide direct evidence of quantum entanglement. The guide emphasizes the conceptual understanding of entanglement, circuit implementation in Qiskit, and the hybrid quantum-classical workflow underlying quantum computation. By bridging theoretical quantum mechanics with executable quantum circuits, this laboratory work enables students and researchers to experimentally explore one of the central phenomena of quantum information science using cloud-based quantum computing resources.
Abstract This laboratory work presents a practical implementation of the BB84 quantum key distribution protocol using the Qiskit framework. The material is based on educational resources developed by the International Quantum Center at CERN (Switzerland) and is intended to provide hands-on experience with quantum circuit construction, quantum state preparation, and quantum cryptographic principles. In Laboratory Work No. 2, participants model the BB84 protocol within a quantum computing environment, emphasizing both theoretical understanding and executable circuit design. The experiment employs quantum circuits to prepare Bell states and to generate random bits as part of the quantum key distribution process. Visual representations of Bell states in the computational and Hadamard bases are analyzed to illustrate their orthonormal structure and physical interpretation. The quantum system is initialized and transformed into Bell states using the Composer interface by applying the Hadamard (H) gate to the first qubit q[0]q[0]q[0] and subsequently entangling it with the second qubit q[1]q[1]q[1]. This procedure produces orthonormal state vectors that form the basis for secure quantum communication. The laboratory work demonstrates how entanglement, basis selection, and measurement outcomes contribute to the security properties of BB84. The guide highlights the hybrid quantum-classical workflow implemented in Qiskit and provides a step-by-step framework for simulating quantum key distribution protocols on cloud-accessible quantum hardware and simulators. Through this practical exercise, participants gain insight into the physical foundations of quantum cryptography, probabilistic measurement, and the implementation of quantum communication protocols in modern quantum computing ecosystems.
Abstract This laboratory work provides a practical exploration of random quantum circuits and their statistical behavior using the Qiskit framework. The material is based on educational resources developed by the International Quantum Center at CERN (Switzerland) and aims to introduce participants to probabilistic outputs in quantum computation and the comparison between experimental and theoretical distributions. In Laboratory Work No. 8, participants generate samples from randomly constructed quantum circuits, which consist of qubits initialized in superposition and subjected to sequences of randomly chosen quantum gates. Measurement operations are applied to obtain classical outcomes, producing a distribution of bitstrings. The resulting empirical distribution is then compared to the theoretical probability distribution expected from the ideal quantum state. This exercise demonstrates the intrinsic probabilistic nature of quantum measurement, the impact of circuit depth and gate selection on outcome distributions, and the role of randomness in quantum circuits. Participants learn to implement, execute, and analyze random quantum circuits in Qiskit, including statistical validation against theoretical models. The laboratory guide emphasizes hands-on experience with quantum circuit sampling, data collection, histogram visualization, and statistical comparison, bridging the gap between theoretical quantum mechanics and practical quantum computation on simulators and cloud-accessible hardware.
Abstract This laboratory work presents a practical implementation of quantum teleportation and superdense coding using the Qiskit framework. The material is based on educational resources developed by the International Quantum Center at CERN (Switzerland) and is designed to provide hands-on experience with multi-qubit quantum protocols and hybrid quantum-classical workflows. In Laboratory Work No. 5, participants implement the quantum teleportation protocol step by step. The procedure begins with the preparation of a randomly generated qubit by directly assigning complex probability amplitudes. The state vector is normalized to ensure physical validity, defining the amplitudes corresponding to the computational basis states ∣0⟩|0\rangle∣0⟩ and ∣1⟩|1\rangle∣1⟩. Once the qubit is prepared for teleportation, an entangled Bell pair is generated to establish a shared quantum channel between two parties, conventionally referred to as Alice and Bob. The protocol proceeds with joint operations and measurement of two classical bits on Alice’s side. The measurement outcomes determine conditional unitary corrections applied to Bob’s qubit, enabling the reconstruction of the original quantum state without physically transmitting the qubit itself. The laboratory exercise includes the construction of a circuit with separate quantum registers and classical bits, explicit amplitude assignment for Alice’s qubit, and verification of successful state transfer through measurement statistics. In addition to teleportation, the conceptual framework of superdense coding is discussed as a complementary protocol demonstrating how entanglement enhances classical information capacity. Together, these experiments illustrate the operational role of entanglement as a quantum communication resource. The guide emphasizes practical circuit design, normalization of quantum states, entanglement generation, conditional gate operations, and execution on both simulators and real quantum hardware. Through this laboratory work, participants gain experimental insight into two cornerstone protocols of quantum information science.
Abstract This laboratory work provides a practical introduction to the use of a quantum computer, based on educational materials developed by the International Quantum Center at CERN (Switzerland). The objective of the first laboratory session is to familiarize users with the quantum computing environment, fundamental circuit construction, and the interaction between quantum and classical registers. In Laboratory Work No. 1, a basic quantum circuit is configured using the IBM Quantum cloud platform. The system consists of a single quantum bit (qubit), denoted as q0, and a single classical bit, denoted as c4. The experiment demonstrates the initialization of a qubit, the construction of a simple quantum circuit, and the measurement process that maps a quantum state onto a classical bit. Through this hands-on implementation, participants gain an operational understanding of quantum state preparation, measurement postulates, and the hybrid quantum-classical computational workflow. The guide emphasizes practical interaction with real quantum hardware and simulators, allowing users to observe probabilistic measurement outcomes and understand the physical interpretation of quantum superposition and state collapse. By bridging theoretical quantum mechanics and executable quantum circuits, this laboratory work lowers the barrier to entry for students and researchers transitioning from classical programming paradigms to quantum computation.
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.