Probability Distribution Analysis of the Cascaded Variational Quantum Eigensolver

TL;DR

This paper introduces a process for selecting guiding states in the cascaded variational quantum eigensolver to improve accuracy and resource efficiency, demonstrated on a bimolecular reaction using NISQ quantum computers.

Contribution

It presents a trapezoidal-state preparation method for guiding state selection in CVQE, optimizing accuracy and resource use based on probability distribution analysis.

Findings

Effective guiding state selection improves solution accuracy.

Resource-efficient CVQE solutions are achievable with the proposed method.

Demonstrated on a bimolecular reaction using NISQ hardware.

Abstract

The cascaded variational quantum eigensolver (CVQE) circumvents the need for iterative communication between the quantum and classical processing units that is necessary in the conventional VQE algorithm. While CVQE offers complete freedom to choose the guiding state as input, not all guiding states suffice for solution accuracy, as well as resource efficiency. Our work presents a process based on trapezoidal-state preparation for selecting guiding states that yield accurate many-electron ground-state solutions with minimal resource consumption. By analyzing the state probability distributions at different stages of the CVQE calculations, we determine the optimal guiding-state parameters for given resource constraints. We demonstrate the process by comparing electronic energies along the minimal-energy path for a prototypical bimolecular reaction, $\mathrm{H}_2 + \mathrm{H}_2^+ \rightarrow \mathrm{H}_3^+ + \mathrm{H}$, using Noisy Intermediate-Scale Quantum (NISQ) computing.