Next-Generation Quantum Algorithms

Computational science is rebuilt by the various quantum foundations such as entanglement, superposition, and interference. This chapter connects the recent advances of real-world applications to quantum algorithms. Quantum computing (QC) is becoming increasingly powerful through hardware developments like International Business Machine's (IBM's) Eagle and Google's Willow. Feedback-Based Quantum Algorithms (FQAs), Variational Quantum Algorithms (VQAs), and Quantum Gibbs Sampling are deliberated. These methodologies are well-suited to noisy intermediate-scale quantum (NISQ) devices. Flow diagrams, case studies, and tables highlight the advantages of algorithms over traditional methods. The specialized algorithms and foundational algorithms, such as Shor's factoring, graph analysis-based quantum walk, are also discussed in this chapter. The chapter reviews various hardware challenges such as gate errors, limited connectivity and qubit decoherence. The chapter delves into the hybrid model and quantum classical optimization for the algorithmic issues such as circuit depth and barren plateaus. QC concepts can be addressed and experimented through various cloud platforms such as PennyLane, Amazon Braket, and IBM Quantum. The interdisciplinary approaches in bridging the gap between theory and practice are emphasized. Overall, the chapter serves as a foundational guide for practitioners in quantum technologies.