Practical Guide to Using a Quantum Computer (Based on Materials from the International Quantum Center at CERN, Switzerland) # 8

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.