Mapping out phase diagrams of quantum systems using classical simulations can be challenging or intractable due to the computational resources required to simulate even small quantum systems far away from the thermodynamic limit. We investigate using quantum computers and the variational quantum eigensolver (VQE) for this task. In contrast to the task of preparing the exact ground state using VQE, sketching phase diagrams might require less quantum resources and accuracy, because low fidelity approximations to the ground state may be enough to correctly identify different phases. We used classical numerical simulations of low-depth VQE circuits to compute order parameters for four well-studied spin and fermion models which represent a mix of 1D and 2D, and exactly-solvable and classically hard systems. We find that it is possible to predict the location of phase transitions up to reasonable accuracy using states produced by VQE even when their overlap with the true ground state is small. Further, we introduce a model-agnostic predictor of phase transitions based on the speed with which the VQE energy improves with respect to the circuit depth, and find that in some cases this is also able to predict phase transitions.

中文翻译：

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使用低深度变分量子算法绘制相图


使用经典模拟绘制量子系统的相图可能具有挑战性或棘手，因为模拟远离热力学极限的小型量子系统也需要计算资源。我们研究使用量子计算机和变分量子本征求解器（VQE）来完成这项任务。与使用 VQE 准备精确基态的任务相比，绘制相图可能需要更少的量子资源和精度，因为对基态的低保真度近似可能足以正确识别不同的相。我们使用低深度 VQE 电路的经典数值模拟来计算四个经过充分研究的自旋和费米子模型的阶次参数，这些模型代表一维和二维的混合，以及精确可解的经典硬系统。我们发现，即使相变与真实基态的重叠很小，也可以使用 VQE 产生的状态以合理的精度预测相变的位置。此外，我们根据 VQE 能量相对于电路深度提高的速度引入了与模型无关的相变预测器，并发现在某些情况下这也能够预测相变。