Satyendra Singh¹, Manoj Pal² and Shobha Bharti³, ¹ Quantum University Roorkee, India, ² Shri Ram Murti Smarak College of Engineering & Technology, India, ³ Gurukula Kangri University, India

Quantum computing has become a revolutionary paradigm, providing solutions to complex computational problems that are impossible for traditional classical systems. One of its most promising uses is in modeling and simulating physical phenomena, which advances fields such as physics, chemistry, materials science, and engineering. This article offers an in-depth review of recent breakthroughs in quantum computing related to modeling and simulating physical systems. We examine the core principles of quantum algorithms, including variational quantum eigenvalue solvers (VQEs), quantum approximate optimization algorithms (QAOAs), and quantum phase estimation (QPEs), focusing on their applications to simulating molecular structures, condensed matter systems, and dynamical processes. The review also discusses improvements in quantum hardware, error correction techniques, and hybrid quantum-classical methods that have increased the simulation capabilities of current noisy intermediate-scale quantum (NISQ) devices. Moreover, it explores challenges such as scalability, decoherence, and algorithmic efficiency, along with emerging solutions to enable practical use. By reviewing the latest research, this overview highlights future directions in quantum computing, which could greatly enhance the accuracy, speed, and range of modeling complex physical systems, bridging the gap between theory and realworld application.

Quantum Computing, Quantum Simulation, VQE, NISQ.