Sharir Or, Levine Yoav, Wies Noam, Carleo Giuseppe, Shashua Amnon
The Hebrew University of Jerusalem, Jerusalem 9190401, Israel.
Center for Computational Quantum Physics, Flatiron Institute, 162 5th Avenue, New York, New York 10010, USA.
Phys Rev Lett. 2020 Jan 17;124(2):020503. doi: 10.1103/PhysRevLett.124.020503.
Artificial neural networks were recently shown to be an efficient representation of highly entangled many-body quantum states. In practical applications, neural-network states inherit numerical schemes used in variational Monte Carlo method, most notably the use of Markov-chain Monte Carlo (MCMC) sampling to estimate quantum expectations. The local stochastic sampling in MCMC caps the potential advantages of neural networks in two ways: (i) Its intrinsic computational cost sets stringent practical limits on the width and depth of the networks, and therefore limits their expressive capacity; (ii) its difficulty in generating precise and uncorrelated samples can result in estimations of observables that are very far from their true value. Inspired by the state-of-the-art generative models used in machine learning, we propose a specialized neural-network architecture that supports efficient and exact sampling, completely circumventing the need for Markov-chain sampling. We demonstrate our approach for two-dimensional interacting spin models, showcasing the ability to obtain accurate results on larger system sizes than those currently accessible to neural-network quantum states.
人工神经网络最近被证明是高度纠缠多体量子态的一种有效表示。在实际应用中，神经网络态继承了变分蒙特卡罗方法中使用的数值方案，最显著的是使用马尔可夫链蒙特卡罗（MCMC）采样来估计量子期望值。MCMC中的局部随机采样从两个方面限制了神经网络的潜在优势：（i）其固有的计算成本对网络的宽度和深度设置了严格的实际限制，因此限制了它们的表达能力；（ii）生成精确且不相关样本的困难可能导致可观测量的估计值与它们的真实值相差甚远。受机器学习中最先进的生成模型启发，我们提出了一种专门的神经网络架构，该架构支持高效且精确的采样，完全避免了对马尔可夫链采样的需求。我们展示了针对二维相互作用自旋模型的方法，展示了在比神经网络量子态目前可处理的更大系统规模上获得准确结果的能力。
