Quantum-Classical Hybrid Algorithm for the Simulation of All-Electron Correlation

• URL: http://arxiv.org/abs/2106.11972v1
• Date: Tue, 22 Jun 2021 18:00:00 GMT
• Title: Quantum-Classical Hybrid Algorithm for the Simulation of All-Electron Correlation
• Authors: Jan-Niklas Boyn, Aleksandr O. Lykhin, Scott E. Smart, Laura Gagliardi and David A. Mazziotti
• Abstract summary: We present a novel hybrid-classical algorithm that computes a molecule's all-electron energy and properties on the classical computer. We demonstrate the ability of the quantum-classical hybrid algorithms to achieve chemically relevant results and accuracy on currently available quantum computers.
• Score: 58.720142291102135
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: While the treatment of chemically relevant systems containing hundreds or even thousands of electrons remains beyond the reach of quantum devices, the development of quantum-classical hybrid algorithms to resolve electronic correlation presents a promising pathway toward a quantum advantage in the computation of molecular electronic structure. Such hybrid algorithms treat the exponentially scaling part of the calculation -- the static (multireference) correlation -- on the quantum computer and the non-exponentially scaling part -- the dynamic correlation -- on the classical computer. While a variety of such algorithms have been proposed, due to the dependence on the wave function of most classical methods for dynamic correlation, the development of easy-to-use classical post-processing implementations has been limited. Here we present a novel hybrid-classical algorithm that computes a molecule's all-electron energy and properties on the classical computer from a critically important simulation of the static correlation on the quantum computer. Significantly, for the all-electron calculations we circumvent the wave function by using density-matrix methods that only require input of the statically correlated two-electron reduced density matrix (2-RDM), which can be efficiently measured in the quantum simulation. Although the algorithm is completely general, we test it with two classical 2-RDM methods, the anti-Hermitian contracted Schr\"odinger equation (ACSE) theory and multiconfiguration pair-density functional theory (MC-PDFT), using the recently developed quantum ACSE method for the simulation of the statically correlated 2-RDM. We obtain experimental accuracy for the relative energies of all three benzyne isomers and thereby, demonstrate the ability of the quantum-classical hybrid algorithms to achieve chemically relevant results and accuracy on currently available quantum computers.

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