Practical Guide to Quantum Computing – Variational Algorithms: Instances and Extensions (Based on Materials from IBM Q) # 7

Abstract This practical guide explores several instances and extensions of variational quantum algorithms (VQAs), based on IBM Q learning resources. The exercises were completed by the author on May 9, 2024, using IBM Q cloud resources. This lesson introduces advanced applications of VQAs and demonstrates how different algorithmic designs can be adapted for specific computational tasks. Participants study multiple quantum variational algorithms, including: Variational Quantum Eigensolver (VQE) Subspace-Search VQE (SSVQE) Variational Quantum Deflation (VQD) Quantum Subspace Regression (QSR) These algorithms highlight various design concepts, such as the use of weighted cost functions, penalty terms, resampling strategies, and mitigation of undersampling effects. By exploring these approaches, participants gain insight into customizing variational algorithms for specific problems in quantum chemistry, optimization, and machine learning. The Variational Quantum Eigensolver (VQE) is emphasized as a foundational algorithm that serves as a template for many other variational techniques. Exercises focus on constructing parameterized ansätze, defining appropriate cost functions, and integrating extensions that improve convergence, accuracy, or computational efficiency. Participants are encouraged to experiment with these designs and share results within the quantum computing community. Hands-on exercises in Qiskit provide practical experience in applying these advanced algorithms on noisy intermediate-scale quantum (NISQ) devices, bridging theoretical concepts with real-world quantum computation.