Towards the Practical Application of Near-Term Quantum Computers in Quantum Chemistry Simulations: A Problem Decomposition Approach

TL;DR

This paper proposes a hybrid quantum-classical framework using problem decomposition techniques to enable practical quantum chemistry simulations on near-term quantum devices, focusing on molecular systems and their conformations.

Contribution

It introduces a novel hybrid approach combining classical decomposition and quantum simulation, evaluating three PD techniques for near-term quantum chemistry applications.

Findings

PD techniques differentiate molecular conformations effectively.

Sampling error impacts the predictive accuracy of quantum simulations.

The framework advances the feasibility of simulating larger molecules on near-term quantum hardware.

Abstract

With the aim of establishing a framework to efficiently perform the practical application of quantum chemistry simulation on near-term quantum devices, we envision a hybrid quantum--classical framework for leveraging problem decomposition (PD) techniques in quantum chemistry. Specifically, we use PD techniques to decompose a target molecular system into smaller subsystems requiring fewer computational resources. In our framework, there are two levels of hybridization. At the first level, we use a classical algorithm to decompose a target molecule into subsystems, and utilize a quantum algorithm to simulate the quantum nature of the subsystems. The second level is in the quantum algorithm. We consider the quantum--classical variational algorithm that iterates between an expectation estimation using a quantum device and a parameter optimization using a classical device. We investigate three popular PD techniques for our hybrid approach: the fragment molecular-orbital (FMO) method, the divide-and-conquer (DC) technique, and the density matrix embedding theory (DMET). We examine the efficacy of these techniques in correctly differentiating conformations of simple alkane molecules. In particular, we consider the ratio between the number of qubits for PD and that of the full system; the mean absolute deviation; and the Pearson correlation coefficient and Spearman's rank correlation coefficient. Sampling error is introduced when expectation values are measured on the quantum device. Therefore, we study how this error affects the predictive performance of PD techniques. The present study is our first step to opening up the possibility of using quantum chemistry simulations at a scale close to the size of molecules relevant to industry on near-term quantum hardware.