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We describe an algorithm to reduce the cost of auxiliary-field quantum MonteCarlo (AFQMC) calculations for the electronic structure problem. The techniqueuses a nested low-rank factorization of the electron repulsion integral (ERI).While the cost of conventional AFQMC calculations in Gaussian bases scales as$\mathcal{O}(N^4)$ where $N$ is the size of the basis, we show thatground-state energies can be computed through tensor decomposition with reducedmemory requirements and sub-quartic scaling. The algorithm is applied tohydrogen chains and square grids, water clusters, and hexagonal BN. In allcases we observe significant memory savings and, for larger systems, reduced,sub-quartic simulation time.

Efficient ab initio auxiliary-field quantum Monte Carlo calculations in Gaussian bases via low-rank tensor decomposition