Quantum Embedding Method for the Simulation of Strongly Correlated Systems on Quantum Computers

TL;DR

The projection-based embedding method for combining the variational quantum eigensolver (VQE) algorithm, although not limited to, with density functional theory (DFT) is employed and is shown to be a promising approach for simulating systems with a strongly correlated fragment on a quantum computer.

Abstract

Quantum computing has emerged as a promising platform for simulating strongly correlated systems in chemistry, for which the standard quantum chemistry methods are either qualitatively inaccurate or too expensive. However, due to the hardware limitations of the available noisy near-term quantum devices, their application is currently limited only to small chemical systems. One way for extending the range of applicability can be achieved within the quantum embedding approach. Herein, we employ the projection-based embedding method for combining the variational quantum eigensolver (VQE) algorithm, although not limited to, with density functional theory (DFT). The developed VQE-in-DFT method is then implemented efficiently on a real quantum device and employed for simulating the triple bond breaking process in butyronitrile. The results presented herein show that the developed method is a promising approach for simulating systems with a strongly correlated fragment on a quantum computer. The developments as well as the accompanying implementation will benefit many different chemical areas including the computer aided drug design as well as the study of metalloenzymes with a strongly correlated fragment.

Figures (3)

• Figure 1: Schematic depiction of the steps performed in this work.
• Figure 2: Potential energy surface (upper panels) for the triple C-N bond dissociation in CH$_3$CH$_2$CH$_2$CN calculated with different WF-in-PBE/STO-3G methods and two active spaces, AS(4,4) (left column) and AS(6,6) (right column). The middle panels show the error for a respective embedding method relative to the reference FCI-in-PBE method. The lowest panels indicate the number of CNOT gates (solid magenta line) and number of q-ADAPT-in-PBE iterations (dashed magenta line).
• Figure 3: Potential energy surface (upper panel) for the triple C-N bond dissociation in CH$_3$CH$_2$CH$_2$CN calculated with the FCI-in-PBE (black curve), q-ADAPT-in-PBE (magenta line), and ibm_cairo-in-PBE (dark green line) methods in the AS(4,4) active space. The shaded green area indicates the standard deviation between 10 independent experiment repetitions and the dark green line corresponds to the average value. The lower panel shows the error for the ibm_cairo-in-PBE method relative to the reference FCI-in-PBE method.