Variational quantum computing for quantum simulation: principles, implementations, and challenges

This work presents a comprehensive overview of variational quantum computing and their key role in advancing quantum simulation. This work explores the simulation of quantum systems and sets itself apart from approaches centered on classical data processing, by focusing on the critical role of quantum data in Variational Quantum Algorithms (VQA) and Quantum Machine Learning (QML). We systematically delineate the foundational principles of variational quantum computing, establish their motivational and challenges context within the noisy intermediate-scale quantum (NISQ) era, and critically examine their application across a range of prototypical quantum simulation problems. Operating within a hybrid quantum-classical framework, these algorithms represent a promising yet problem-dependent pathway whose practicality remains contingent on trainability and scalability under noise and barren-plateau constraints.This review serves to complement and extend existing literature by synthesizing the most recent advancements in the field and providing a focused perspective on the persistent challenges and emerging opportunities that define the current landscape of variational quantum computing for quantum simulation.