Ab initio molecular dynamics (AIMD) is a powerful tool to predict properties of molecular and condensed matter systems. However, the quality of this procedure relies on the availability of rigorous electronic structure calculations. The development of quantum processors has shown great potential for the efficient evaluation of accurate ground and excited state energies of molecular systems, opening up new avenues for molecular dynamics simulations. In this work, we address the use of variational quantum algorithms for the calculation of accurate atomic forces to be used in AIMD. In particular, we provide solutions for the alleviation of the statistical noise associated with the measurements of the expectation values of energies and forces, as well as schemes for the mitigation of the hardware noise sources (in particular, gate infidelities, qubit decoherence, and readout errors). Despite the relative large error in the calculation of the potential energy, our results show that the proposed algorithms can provide accurate MD trajectories in the microcanonical (constant energy) ensemble. Furthermore, exploiting the intrinsic noise associated to the quantum measurement process, we also propose a Langevin dynamics algorithm for the simulation of canonical, i.e., constant temperature, dynamics. Both algorithms (microcanonical and canonical) are applied to the simulation of simple molecular systems such as ${\mathrm{H}}_2$ and ${\mathrm{H}}_3^{+}$. Finally, we also provide results for the dynamics of ${\mathrm{H}}_2$ obtained with IBM quantum computer ibmq_athens.

中文翻译：

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量子计算机上的微规范和有限温度a分子动力学模拟

从头算分子动力学（AIMD）是一种强大的工具，可以预测分子和凝聚态系统的特性。但是，此过程的质量取决于严格的电子结构计算的可用性。量子处理器的发展为有效评估分子系统的精确基态和激发态能量显示出巨大潜力，为分子动力学模拟开辟了新途径。在这项工作中，我们解决了变分量子算法在AIMD中使用的精确原子力计算中的问题。特别是，我们提供了减轻与能量和力的期望值的测量值相关的统计噪声的解决方案，以及减轻硬件噪声源（尤其是门的不忠，量子位退相干和读出错误）。尽管在势能的计算中存在相对较大的误差，但我们的结果表明，所提出的算法可以在微规范（恒能）系综中提供准确的MD轨迹。此外，利用与量子测量过程相关的固有噪声，我们还提出了一种Langevin动力学算法，用于模拟规范（即恒温）动力学。两种算法（微规范和规范）都适用于简单分子系统的仿真，例如 利用与量子测量过程相关的固有噪声，我们还提出了一种Langevin动力学算法，用于模拟规范（即恒温）动力学。两种算法（微规范和规范）都适用于简单分子系统的仿真，例如 利用与量子测量过程相关的固有噪声，我们还提出了一种Langevin动力学算法，用于模拟规范（即恒温）动力学。两种算法（微规范和规范）都适用于简单分子系统的仿真，例如${\mathrm{H}}_2$ 和 ${\mathrm{H}}_3^{+}$。最后，我们还提供了动力学的结果${\mathrm{H}}_2$使用IBM量子计算机ibmq_athens获得。