论文标题
使用张量网络，机器学习和量子计算机研究量子多体系统
Investigating Quantum Many-Body Systems with Tensor Networks, Machine Learning and Quantum Computers
论文作者
论文摘要
我们在经典和量子计算机上执行量子模拟，并建立一个机器学习框架，在该框架中，我们可以以无监督的方式绘制已知和未知量子多体系统的相图。经典模拟是在一个和两个空间维度中使用最新的张量网络方法进行的。对于一个维系统，我们使用具有许多实际优势的矩阵乘积状态（MPS），可以使用有效的密度矩阵重新归一化组（DMRG）算法进行优化。二维系统的数据是从通过假想时间演变优化的纠缠投影对状态（PEP）获得的。然后以这些模拟的可观察结果，纠缠光谱或状态向量的一部分形式的数据馈入深度学习（DL）管道中，我们执行异常检测以绘制相图。我们将此概念扩展到量子计算机，并引入量子变异异常检测。在这里，我们首先模拟基态，然后以量子机学习（QML）方式对其进行处理。模拟和QML例程均在同一设备上执行，我们在经典的模拟和IBM托管的物理量子计算机上都进行了演示。
We perform quantum simulation on classical and quantum computers and set up a machine learning framework in which we can map out phase diagrams of known and unknown quantum many-body systems in an unsupervised fashion. The classical simulations are done with state-of-the-art tensor network methods in one and two spatial dimensions. For one dimensional systems, we utilize matrix product states (MPS) that have many practical advantages and can be optimized using the efficient density matrix renormalization group (DMRG) algorithm. The data for two dimensional systems is obtained from entangled projected pair states (PEPS) optimized via imaginary time evolution. Data in form of observables, entanglement spectra, or parts of the state vectors from these simulations, is then fed into a deep learning (DL) pipeline where we perform anomaly detection to map out the phase diagram. We extend this notion to quantum computers and introduce quantum variational anomaly detection. Here, we first simulate the ground state and then process it in a quantum machine learning (QML) manner. Both simulation and QML routines are performed on the same device, which we demonstrate both in classical simulation and on a physical quantum computer hosted by IBM.
