In this paper, we discuss extending the sub-system embedding sub-algebra coupled cluster (SES-CC) formalism and the double unitary coupled cluster (DUCC) ansatz to the time domain. As we demonstrated in earlier studies, it is possible, using these formalisms, to calculate the energy of the entire system as an eigenvalue of downfolded/effective Hamiltonian in the active space, that is identifiable with the sub-system of the composite system. In these studies, we demonstrated that downfolded Hamiltonians integrate out Fermionic degrees of freedom that do not correspond to the physics encapsulated by the active space. We extend these results to the time-dependent Schrödinger equation, showing that a similar construct is possible to partition a system into a sub-system that varies slowly in time and a remaining subsystem that corresponds to fast oscillations. This time dependent formalism allows coupled cluster quantum dynamics to be extended to larger systems and for the formulation of novel quantum algorithms based on the quantum Lanczos approach, which have recently been considered in the literature.
Kowalski, Karol and Bauman, Nicholas P.. "Sub-system quantum dynamics using coupled cluster downfolding techniques." Journal of Chemical Physics, vol. 152, no. 24, Jun. 2020. https://doi.org/10.1063/5.0008436
Kowalski, Karol, & Bauman, Nicholas P. (2020). Sub-system quantum dynamics using coupled cluster downfolding techniques. Journal of Chemical Physics, 152(24). https://doi.org/10.1063/5.0008436
Kowalski, Karol, and Bauman, Nicholas P., "Sub-system quantum dynamics using coupled cluster downfolding techniques," Journal of Chemical Physics 152, no. 24 (2020), https://doi.org/10.1063/5.0008436
@article{osti_1646832,
author = {Kowalski, Karol and Bauman, Nicholas P.},
title = {Sub-system quantum dynamics using coupled cluster downfolding techniques},
annote = {In this paper, we discuss extending the sub-system embedding sub-algebra coupled cluster (SES-CC) formalism and the double unitary coupled cluster (DUCC) ansatz to the time domain. As we demonstrated in earlier studies, it is possible, using these formalisms, to calculate the energy of the entire system as an eigenvalue of downfolded/effective Hamiltonian in the active space, that is identifiable with the sub-system of the composite system. In these studies, we demonstrated that downfolded Hamiltonians integrate out Fermionic degrees of freedom that do not correspond to the physics encapsulated by the active space. We extend these results to the time-dependent Schrödinger equation, showing that a similar construct is possible to partition a system into a sub-system that varies slowly in time and a remaining subsystem that corresponds to fast oscillations. This time dependent formalism allows coupled cluster quantum dynamics to be extended to larger systems and for the formulation of novel quantum algorithms based on the quantum Lanczos approach, which have recently been considered in the literature.},
doi = {10.1063/5.0008436},
url = {https://www.osti.gov/biblio/1646832},
journal = {Journal of Chemical Physics},
number = {24},
volume = {152},
place = {United States},
year = {2020},
month = {06}}
Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, Vol. 454, Issue 1969https://doi.org/10.1098/rspa.1998.0164