Constrained variational quantum eigensolver: Quantum computer search engine in the Fock space

TL;DR

This paper introduces a constrained variational quantum eigensolver (VQE) that directs the quantum search to specific electronic states, overcoming limitations of traditional VQE in electronic structure calculations.

Contribution

The authors develop a constrained VQE method that incorporates physical constraints without extra quantum resources, enabling targeted electronic state calculations.

Findings

Successfully simulated specific electronic states of H₂ and H₂O

Demonstrated the method on Rigetti's 19Q-Acorn quantum processor

Achieved accurate state targeting without additional quantum overhead

Abstract

Variational quantum eigensolver (VQE) is an efficient computational method promising chemical accuracy in electronic structure calculations on a universal-gate quantum computer. However, such a simple task as computing the electronic energy of a hydrogen molecular cation, H$_2^+$, is not possible for a general VQE protocol because the calculation will invariably collapse to a lower energy of the corresponding neutral form, H$_2$. The origin of the problem is that VQE effectively performs an unconstrained energy optimization in the Fock space of the original electronic problem. We show how this can be avoided by introducing necessary constraints directing VQE to the electronic state of interest. The proposed constrained VQE can find an electronic state with a certain number of electrons, spin, or any other property. The new algorithm does not require any additional quantum resources. We demonstrate performance of the constrained VQE by simulating various states of H$_2$ and H$_2$O on Rigetti Computing Inc's 19Q-Acorn quantum processor.