论文标题
用深量子神经网络求解量子主方程
Solving Quantum Master Equations with Deep Quantum Neural Networks
论文作者
论文摘要
深度量子神经网络可以通过嘈杂的中级尺度量子设备提供一种有希望的方法来实现量子学习优势。在这里，我们使用能够通用量子计算的深量子前馈神经网络来表示开放量子多体系统的混合状态，并引入了具有量子衍生物的变异方法，以求解动力学和固定状态的主方程。这种方法拥有量子网络的特殊结构，具有许多值得注意的功能，包括缺乏贫瘠的高原，返回算法的有效量子类似物，隐藏Qubits的资源储蓄重用，一般适用性，独立于维度和范围的特性和范围内的特性，以及同步物的便利实现。作为原则证明，我们将这种方法应用于一维横向场ISING和二维$ J_1-J_2 $模型，并表明它可以以所需的准确性有效地捕获其动态和固定状态。
Deep quantum neural networks may provide a promising way to achieve quantum learning advantage with noisy intermediate scale quantum devices. Here, we use deep quantum feedforward neural networks capable of universal quantum computation to represent the mixed states for open quantum many-body systems and introduce a variational method with quantum derivatives to solve the master equation for dynamics and stationary states. Owning to the special structure of the quantum networks, this approach enjoys a number of notable features, including the absence of barren plateaus, efficient quantum analogue of the backpropagation algorithm, resource-saving reuse of hidden qubits, general applicability independent of dimensionality and entanglement properties, as well as the convenient implementation of symmetries. As proof-of-principle demonstrations, we apply this approach to both one-dimensional transverse field Ising and two-dimensional $J_1-J_2$ models with dissipation, and show that it can efficiently capture their dynamics and stationary states with a desired accuracy.
