Classification of electronic structures and state preparation for quantum computation of reaction chemistry

TL;DR

This paper investigates the challenges of preparing initial quantum states for reaction chemistry simulations, introduces a new classification of electronic structures based on orbital entanglement, and highlights the advantages of quantum phase estimation algorithms.

Contribution

It presents a novel classification scheme for electronic structures and demonstrates the feasibility of initializing guiding states for quantum chemical simulations.

Findings

Class-1 molecules are dominated by few determinants and are easier for traditional methods.

Class-2 molecules are multi-configurational and pose challenges for classical approaches.

Quantum algorithms can effectively initialize states for complex multi-configurational molecules.

Abstract

Quantum computation for chemical problems will require the construction of guiding states with sufficient overlap with a target state. Since easily available and initializable mean-field states are characterized by an overlap that is reduced for multi-configurational electronic structures and even vanishes with growing system size, we here investigate the severity of state preparation for reaction chemistry. We emphasize weaknesses in current traditional approaches (even for weakly correlated molecules) and highlight the advantage of quantum phase estimation algorithms. An important result is the introduction of a new classification scheme for electronic structures based on orbital entanglement information. We identify two categories of multi-configurational molecules. Whereas class-1 molecules are dominated by very few determinants and often found in reaction chemistry, class-2 molecules do not allow one to single out a reasonably sized number of important determinants. The latter are particularly hard for traditional approaches and an ultimate target for quantum computation. Some open-shell iron-sulfur clusters belong to class 2. We discuss the role of the molecular orbital basis set and show that true class-2 molecules remain in this class independent of the choice of the orbital basis, with the iron-molybdenum cofactor of nitrogenase being a prototypical example. We stress that class-2 molecules can be build in a systematic fashion from open-shell centers or unsaturated carbon atoms. Our key result is that it will always be possible to initialize a guiding state for chemical reaction chemistry in the ground state based on initial low-cost approximate electronic structure information, which is facilitated by the finite size of the atomistic structures to be considered.