标题： 变分量子本征值求解器在化学中的应用简介 显示英文标题

标题： An Introduction to Variational Quantum Eigensolver Applied to Chemistry

摘要： 量子力学为分子的研究引入了一个新的理论框架，通过求解应用于这些系统的薛定谔方程，可以预测性质和动力学。然而，求解这个方程计算成本高昂，这促使了各种数学框架和计算方法的发展，旨在平衡可用资源与所需的精度水平。特别是，量子计算机作为一种有前景的技术，在未来几十年内有可能更有效地解决这些问题，无论是通过减少内存、时间、能耗，$\textit{i. e.}$，减少计算复杂度还是提高精度。 这一研究领域被称为量子模拟。 鉴于当前量子计算机的技术限制，变分量子算法（VQAs），尤其是变分量子本征值求解器（VQE），作为短期内展示优于经典方法的优势的可行方法脱颖而出。这种可行性源于它们对量子门的需求较低以及实现它们所需的电路深度较小。 在这项工作中，我们展示了量子力学在分子研究中的应用，介绍了量子计算的基础知识，并通过在分子模拟中使用VQE探索了这些领域的整合。最后，我们讨论了该算法的空间和时间复杂性，强调其意义和挑战。 显示英文摘要

摘要： Quantum mechanics has introduced a new theoretical framework for the study of molecules, enabling the prediction of properties and dynamics through the solution of the Schr\"odinger equation applied to these systems. However, solving this equation is computationally expensive, which has led to the development of various mathematical frameworks and computational methods designed to balance the available resources with the desired level of accuracy. In particular, quantum computers have emerged as a promising technology with the potential to address these problems more efficiently in the coming decades, whether through reductions in memory, time, and energy consumption, $\textit{i. e.}$, reductions in computational complexity or by enhancing precision. This research field is known as Quantum Simulation. Given the current technological limitations of quantum computers, Variational Quantum Algorithms (VQAs), especially the Variational Quantum Eigensolver (VQE), stand out as a feasible approach to demonstrating advantages over classical methods in the near term. This feasibility arises from their lower demand for quantum gates and the reduced depth of the circuits required for their implementation. In this work, we present the application of quantum mechanics to the study of molecules, provide an introduction to the fundamentals of quantum computing, and explore the integration of these fields by employing the VQE in molecular simulations. Finally, we discuss the spatial and temporal complexity associated with the algorithm, highlighting its implications and challenges.