论文标题
密度矩阵重新归一化组，张量处理单元
Density Matrix Renormalization Group with Tensor Processing Units
论文作者
论文摘要
Google的张量处理单元（TPU）是专门为加速和扩展机器学习工作负载而构建的集成电路。它们可以执行快速分布式矩阵乘法，因此可以重新用于其他计算密集型任务。在这项工作中，我们证明了使用TPU来加速和扩大密度矩阵重新归一化组（DMRG），这是一种强大的数值方法，用于计算局部量子多体汉密尔顿的基态。 DMRG尺度$ n $ as $ o（nd^3）$的成本，其中所谓的债券尺寸$ d $调节了基础矩阵产品状态（MPS）差异ansatz的表现方式。我们考虑两个空间尺寸的晶格型号，其方格的尺寸为$ 10 \ times 10 $（免费费米子）和$ 20 \ times 20 $（横向字段ISING模型），为此，所需的MPS债券维度至少可以扩展为$ \ exp（\ sqrt {n}）$。使用TPU V3 POD的一半（即$ 1，\！024 $ TPU V3内核），我们到达了一个前所未有的大债券尺寸$ d = 2^{16} = 65，\！536 $，为此优化了一个MPS Tensor大约需要2分钟。
Google's Tensor Processing Units (TPUs) are integrated circuits specifically built to accelerate and scale up machine learning workloads. They can perform fast distributed matrix multiplications and therefore be repurposed for other computationally intensive tasks. In this work we demonstrate the use of TPUs for accelerating and scaling up the density matrix renormalization group (DMRG), a powerful numerical approach to compute the ground state of a local quantum many-body Hamiltonian. The cost of DMRG scales with system size $N$ as $O(ND^3)$, where the so-called bond dimension $D$ regulates how expressive the underlying matrix product state (MPS) variational ansatz is. We consider lattice models in two spatial dimensions, with square lattices of size $10\times 10$ (free fermions) and $20\times 20$ (transverse field Ising model), for which the required MPS bond dimension is known to scale at least as $\exp(\sqrt{N})$. Using half of a TPU v3 pod (namely $1,\!024$ TPU v3 cores) we reached an unprecedentedly large bond dimension $D = 2^{16} = 65,\!536$, for which optimizing a single MPS tensor took about 2 minutes.
