Unifying neural-network quantum states and correlator product states via tensor networks
Unifying neural-network quantum states and correlator product states via tensor networks
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DOI：
10.1088/1751-8121/aaaaf2
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发表时间：
2018-04-03
影响因子：
2.1
通讯作者：
Clark, Stephen R.
中科院分区：
文献类型：
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作者：
Clark, Stephen R.
相关器乘积态（CPS）是量子晶格系统的一种功能强大且非常广泛的状态，其（非归一化）振幅在固定基中可以准确有效地采样。它们的工作原理是将晶格上重叠的位置簇的状态粘合在一起，称为“粘合剂”。最近，Carleo和Troyer（2017 Science 355 602）介绍了一种新型的可采样模型，称为神经网络量子态（NQS），其灵感来自机器学习中使用的受限玻尔兹曼模型。通过采用张量网络的形式主义，我们表明，NQS是一种特殊形式的CPS与新的性质。从图解的角度看，一些简单的观察变得透明。也就是说，NQS是由大尺寸的GHZ型放大器构建的CPS，使其具有独特的几何无偏性。GHZ分解子的出现也将NQS与张量的正则多进分解联系起来。NQS等价于CPS的另一个直接含义是，我们能够为广泛的范式状态制定精确的NQS表示，包括加权图状态、劳克林状态、复曲面代码状态和共振价键状态的叠加。这些例子揭示了在NQS中使用更高维隐藏单元和第二隐藏层的潜力。这项研究的主要前景是提升NQS相关算子，使他们能够增强传统的行之有效的变分蒙特卡罗方法的强相关费米子。
Correlator product states (CPS) are a powerful and very broad class of states for quantum lattice systems whose (unnormalised) amplitudes in a fixed basis can be sampled exactly and efficiently. They work by gluing together states of overlapping clusters of sites on the lattice, called correlators. Recently Carleo and Troyer (2017 Science 355 602) introduced a new type sampleable ansatz called neural-network quantum states (NQS) that are inspired by the restricted Boltzmann model used in machine learning. By employing the formalism of tensor networks we show that NQS are a special form of CPS with novel properties. Diagramatically a number of simple observations become transparent. Namely, that NQS are CPS built from extensively sized GHZ-form correlators making them uniquely unbiased geometrically. The appearance of GHZ correlators also relates NQS to canonical polyadic decompositions of tensors. Another immediate implication of the NQS equivalence to CPS is that we are able to formulate exact NQS representations for a wide range of paradigmatic states, including superpositions of weighed-graph states, the Laughlin state, toric code states, and the resonating valence bond state. These examples reveal the potential of using higher dimensional hidden units and a second hidden layer in NQS. The major outlook of this study is the elevation of NQS to correlator operators allowing them to enhance conventional well-established variational Monte Carlo approaches for strongly correlated fermions.