Wang Yu, Luo Maxine, Reumann Matthias, Mendl Christian B
Department of Computer Science, Technical University of Munich, CIT, Boltzmannstraße 3, 85748 Garching, Germany.
Max Planck Institute of Quantum Optics, Hans-Kopfermann-Straße 1, 85748 Garching, Germany.
J Chem Theory Comput. 2025 Jul 22;21(14):6874-6886. doi: 10.1021/acs.jctc.5c00525. Epub 2025 Jul 2.
We introduce an algorithm that is simultaneously memory-efficient and low-scaling for applying ab initio molecular Hamiltonians to matrix-product states (MPS) via the tensor-hypercontraction (THC) format. These gains carry over to Krylov subspace methods, which can find low-lying eigenstates and simulate quantum time evolution while avoiding local minima and maintaining high accuracy. In our approach, the molecular Hamiltonian is represented as a sum of products of four MPOs, each with a bond dimension of only 2. Iteratively applying the MPOs to the current quantum state in MPS form, summing and recompressing the MPS leads to a scheme with the same asymptotic memory cost as the bare MPS and reduces the computational cost scaling compared to the Krylov method using a conventional MPO construction. We provide a detailed theoretical derivation of these statements and conduct supporting numerical experiments to demonstrate the advantage. Our algorithm is highly parallelizable and thus lends itself to large-scale HPC simulations.
我们介绍了一种算法，该算法通过张量超收缩（THC）格式将从头算分子哈密顿量应用于矩阵乘积态（MPS）时，同时具有内存高效和低缩放比例的特点。这些优势也适用于克里洛夫子空间方法，该方法可以找到低能本征态并模拟量子时间演化，同时避免局部最小值并保持高精度。在我们的方法中，分子哈密顿量表示为四个矩阵乘积算符（MPO）的乘积之和，每个MPO的键维度仅为2。以MPS形式将MPO迭代应用于当前量子态，对MPS进行求和和重新压缩，得到一种方案，其渐近内存成本与裸MPS相同，并且与使用传统MPO构造的克里洛夫方法相比，降低了计算成本缩放比例。我们对这些结论进行了详细的理论推导，并进行了支持性的数值实验以证明其优势。我们的算法具有高度的可并行性，因此适用于大规模的高性能计算（HPC）模拟。
