Abstract: Quantum computing, as a forefront field in quantum technology, has made significant progress in simulating physical systems, yet it still faces technical challenges such as hardware noise and quantum errors. This review discusses the latest advancements in quantum computing for simulating physical systems, with a focus on the application of quantum-classical hybrid algorithms and error mitigation techniques, exploring their strengths and limitations across various physical systems. The review covers the simulation of molecular systems using superconducting quantum computers, many-body problems in condensed matter systems, solving equations in complex fluid dynamics, and applications in astrophysics and high-energy physics. For molecular systems, variational quantum algorithms (VQE) are widely used to solve the ground state energy of multi-electron systems, with error mitigation methods improving simulation accuracy. In condensed matter systems, quantum computing has shown high precision and efficiency in simulating strongly correlated spin models, such as the Heisenberg and Ising models, achieving unprecedented accuracy in larger spin chain simulations. In the field of fluid dynamics, research indicates that quantum-classical hybrid algorithms can accelerate the solution of the Navier-Stokes equations to some extent, providing new tools for future fluid dynamics studies. In astrophysical simulations, quantum computing has been used to study the properties of black holes and dark matter, demonstrating potential exponential acceleration, which offers new possibilities for understanding physical phenomena under extreme conditions in the universe. In high-energy physics, quantum computing shows promising applications in solving problems like the Schwinger model and has begun exploring the potential of quantum machine learning in analyzing high-energy experimental data. This review provides a comprehensive perspective on the applications of quantum computing in simulating various physical systems, and outlines future directions and technical challenges.

Key words: quantum computing, quantum simulation, physical systems, quantum algorithms

摘要： 当前量子计算作为量子科技的前沿领域，在模拟物理系统方面取得了显著进展，但仍面临硬件噪声、量子误差等技术挑战。综述了量子计算在物理系统模拟中的最新进展，聚焦于量子-经典混合算法和错误缓解技术的应用，探讨其在不同物理系统中的优势与局限性。研究内容包括基于超导量子计算机的分子体系模拟、凝聚态物理系统的多体问题模拟、复杂流体力学系统的方程求解，以及在天体物理与高能物理中的应用。针对分子体系，变分量子算法（VQE）被广泛用于求解多电子体系的基态能量，并通过错误缓解方法提升了模拟的准确性。对于凝聚态物理系统，量子计算在模拟强关联自旋模型方面展现出较高的精度和效率，特别是在更大规模的自旋链模拟中实现了前所未有的精确度。流体力学领域的研究表明，量子-经典混合算法在求解纳维-斯托克斯方程时，能够实现一定程度的加速，为未来的流体动力学研究提供了新的工具。天体物理模拟中，量子计算被用于黑洞和暗物质性质的研究，展示了潜在的指数级加速能力，为理解宇宙中极端条件下的物理现象提供了可能性。在高能物理领域，量子计算在解决施温格模型等问题中表现出良好的应用前景，并初步探索了量子机器学习在高能实验数据分析中的潜力。为量子计算在多领域物理系统模拟的应用提供了全面的视角，指出了未来的发展方向与技术挑战。

关键词: 量子计算, 量子模拟, 物理系统, 量子算法