标题： 近似量子多体态中的有效温度 显示英文标题

标题： Effective temperature in approximate quantum many-body states

摘要： 在追求数值识别量子多体系统基态的过程中，通常采用近似量子波函数假设。 本研究关注这些近似量子多体状态在目标哈密顿量精确本征态中的谱分解。 能量谱分解可以反映量子系统与数值算法之间相互作用的复杂物理特性。 在这里，我们检查了从神经网络、张量网络和量子电路构建的各种参数化波函数假设，利用可微编程来数值近似基态和虚时演化态。 我们的发现表明，在不同的假设、优化目标和量子系统中，近似量子态的谱贡献呈现出一致的指数衰减模式，其衰减率较小，称为逆有效温度。 有效温度与假设的表达能力和准确性相关，并在学习虚时演化态时表现出相变行为。 普遍图景和独特特征表明有效温度在表征近似量子态中的重要性和潜力。 显示英文摘要

摘要： In the pursuit of numerically identifying the ground state of quantum many-body systems, approximate quantum wavefunction ansatzes are commonly employed. This study focuses on the spectral decomposition of these approximate quantum many-body states into exact eigenstates of the target Hamiltonian. The energy spectral decomposition could reflect the intricate physics at the interplay between quantum systems and numerical algorithms. Here we examine various parameterized wavefunction ansatzes constructed from neural networks, tensor networks, and quantum circuits, employing differentiable programming to numerically approximate ground states and imaginary-time evolved states. Our findings reveal a consistent exponential decay pattern in the spectral contributions of approximate quantum states across different ansatzes, optimization objectives, and quantum systems, characterized by small decay rates denoted as inverse effective temperatures. The effective temperature is related to ansatz expressiveness and accuracy and shows phase transition behaviors in learning imaginary-time evolved states. The universal picture and unique features suggest the significance and potential of the effective temperature in characterizing approximate quantum states.