Adiabatic-Inspired Hybrid Quantum-Classical Methods for Molecular Ground State Preparation

TL;DR

This paper introduces a new hybrid quantum-classical algorithm inspired by adiabatic processes for more efficient molecular ground state preparation, benchmarking it against existing methods and demonstrating its advantages in quantum chemistry applications.

Contribution

The paper presents a novel G-AQC-PQC hybrid algorithm that combines adiabatic-inspired initialization with classical optimization, improving efficiency over traditional VQE methods.

Findings

G-AQC-PQC outperforms conventional VQE in accuracy.

Adiabatically-inspired methods show advantages in near-term quantum chemistry.

The framework unifies existing adiabatic-inspired quantum algorithms.

Abstract

Quantum computing promises to efficiently and accurately solve many important problems in quantum chemistry which elude classical solvers, such as the electronic structure problem of highly correlated materials. Two leading methods in solving the ground state problem are the Variational Quantum Eigensolver (VQE) and Adiabatic Quantum Computing (AQC) algorithms. VQE often struggles with convergence due to the energy landscape being highly non-convex and the existence of barren plateaux, and implementing AQC is beyond the capabilities of current quantum devices as it requires deep circuits. Adiabatically-inspired algorithms aim to fill this gap. In this paper, we first present a unifying framework for these algorithms and then benchmark the following methods: the Adiabatically Assisted VQE (AAVQE) (Garcia-Saez and Latorre (2018)), the Variational Adiabatic Quantum Computing (VAQC) (Harwood et al (2022)), and the Adiabatic Quantum Computing with Parametrized Quantum Circuits (AQC-PQC) (Kolotouros et al (2025)) algorithms. Second, we introduce a novel hybrid approach termed G-AQC-PQC, which generalizes the AQC-PQC method, and combines adiabatic-inspired initialization with the low-memory BFGS optimizer, reducing the quantum computational cost of the method. Third, we compare the accuracy of the methods for chemistry applications using the beryllium hydride molecule (BeH$_2$). We compare the approaches across a number of different choices (ans\"atze types, depth, discretization steps, initial Hamiltonian, adiabatic schedules and method used). Our results show that the G-AQC-PQC outperforms conventional VQE. We further discuss limitations such as the zero-gradient problem and identify regimes where adiabatically-inspired methods offer a tangible advantage for near-term quantum chemistry applications.