论文标题
最小纠缠典型热状态的神经网络表示
Neural network representation for minimally entangled typical thermal states
论文作者
论文摘要
最小化的典型热状态（METT）是一种结构，它允许人们解决许多身体系统的量子时间演变。通过使用微弱纠缠的波函数，可以利用矩阵乘积状态形式的有效表示。我们将这些想法推广到任意变分波函数，并将其集中在限制性玻尔兹曼机器的特定情况下。假想时间的演化是使用随机重新配置（自然梯度下降）与蒙特卡洛采样结合进行的。由于时间演化发生在切线空间上，因此，希尔伯特空间中的实际路径与变化歧管上的轨迹之间的偏差可能很重要，具体取决于变异状态的内部结构和表现性。我们展示了这些差异如何转化为重新定位的温度，并证明了该方法在一个和两个空间维度中的量子自旋系统中的应用。
Minimally entangled typical thermal states (METTS) are a construction that allows one to to solve for the imaginary time evolution of quantum many body systems. By using wave functions that are weakly entangled, one can take advantage of efficient representations in the form of matrix product states. We generalize these ideas to arbitrary variational wave functions and we focus, as illustration, on the particular case of restricted Boltzmann machines. The imaginary time evolution is carried out using stochastic reconfiguration (natural gradient descent), combined with Monte Carlo sampling. Since the time evolution takes place on the tangent space, deviations between the actual path in the Hilbert space and the trajectory on the variational manifold can be important, depending on the internal structure and expressivity of the variational states. We show how these differences translate into a rescaled temperature and demonstrate the application of the method to quantum spin systems in one and two spatial dimensions.
