Highly correlated calculations with a polynomial cost algorithm: A study of the density matrix renormalization group

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Quantum Chemistry in the Age of Quantum Computing. (2018, unknown): “ we employ the Bravyi-Kitaev transformation, mapping the minimal-basis second-quantized Hamiltonian shown in Equation 101 to a four-qubit Hamiltonian Helec= 0I+ 1Z 1 + 2Z 2 + 3Z 3 + 4Z 1Z 2 (104) + 5Z 1Z 3 + 6Z 2Z 4 + 7X 1Z 2X 3 + 8Y 1Z 2Y 3 (105) + 9Z 1Z 2Z 3 + 10Z 1Z 3Z 4 + 11Z 2Z 3Z 4”
The density-matrix renormalization group (2004, background): “…chemical accuracy of 1 mH with errors between 4.1 and 0.2 mH, DMRG results of various groups sWhite and Martin, 1999; Daul, Ciofini, et al., 2000; Chan and Head-Gordon, 2002d are better than 0.2 mH at M,400, reaching an error of about 0.004 mH at M,900 sChan and Head-Gordon, 2002; Legeza et al.,…”
The density matrix renormalization group for ab initio quantum chemistry (2014, methodology): “basis {|αi−1〉} ⊗ {|ni〉} ⊗ {|ni+1〉} ⊗ {|αi+1〉} in which Ĥ is diagonalized changes between different micro-iterations due to the truncation of the Schmidt spectrum [68].”
Psi4 1.1: An Open-Source Electronic Structure Program Emphasizing Automation, Advanced Libraries, and Interoperability (2017, methodology): “• C HE MPS2: This library 5–7 presents a spin-adapted implementation of the density matrix renormalization group (DMRG) approach, 81,82 which is an effective way to approximate complete active space configuration interaction (CAS CI) with much larger active spaces (up to about 50 electrons in 50…”