Constrained Variational Quantum Eigensolver: Quantum Computer Search Engine in the Fock Space.

Area of Science:

• Quantum computing
• Computational chemistry
• Electronic structure theory

Background:

• Variational quantum eigensolver (VQE) is a promising quantum algorithm for electronic structure calculations.
• Standard VQE struggles with problems like calculating H2+ energy due to unconstrained optimization in Fock space, leading to collapse into lower energy states (e.g., H2).

Purpose of the Study:

• To develop a constrained VQE (cVQE) algorithm to accurately compute electronic states of interest.
• To address the issue of energy state collapse in VQE and remove unphysical kinks in potential energy surfaces (PESs).

Main Methods:

• Introduction of constraints into the VQE optimization process to guide the calculation towards the desired electronic state.
• Demonstration of cVQE by simulating potential energy surfaces (PESs) for H2 and H2O molecules.
• Implementation and testing on Rigetti Computing Inc.'s 19Q-Acorn quantum processor.

Main Results:

• The constrained VQE successfully computes the electronic energy for states like H2+, avoiding collapse to neutral states.
• The cVQE algorithm naturally eliminates unphysical kinks in potential energy surfaces, a common issue in standard VQE.
• Accurate PESs for H2 and H2O were simulated on a real quantum processor.

Conclusions:

• Constrained VQE is an effective method for accurate electronic structure calculations on quantum computers.
• The developed algorithm enhances the reliability and efficiency of quantum chemistry simulations by enforcing necessary constraints.
• cVQE offers a pathway to more robust quantum computations for molecular systems.