Enhanced Krylov Methods for Molecular Hamiltonians: Reduced Memory Cost and Complexity Scaling via Tensor Hypercontraction
Yu Wang, Maxine Luo, Matthias Reumann, Christian B. Mendl
TL;DR
This paper introduces a new algorithm that reduces memory and computational costs when simulating molecular systems using tensor hypercontraction and Krylov subspace methods.
Contribution
The novel contribution is a memory-efficient and low-scaling algorithm for ab initio molecular Hamiltonians using tensor-hypercontraction and matrix-product states.
Findings
The algorithm achieves the same memory cost as the bare MPS while reducing computational cost scaling.
Numerical experiments confirm the theoretical advantages of the proposed method.
The method is highly parallelizable, making it suitable for large-scale high-performance computing simulations.
Abstract
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…
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Taxonomy
TopicsQuantum many-body systems · Quantum Computing Algorithms and Architecture · Advanced NMR Techniques and Applications