Coupled Cluster Downfolding Theory in Simulations of Chemical Systems on Quantum Hardware

TL;DR

This paper presents a hybrid quantum-classical approach using coupled-cluster downfolding to simulate chemical systems efficiently on current quantum hardware, aiming to bridge the gap to fault-tolerant quantum computing.

Contribution

It introduces a method to evaluate downfolded Hamiltonians in active spaces and compute energies with quantum algorithms, enhancing accuracy and feasibility for NISQ devices.

Findings

Achieved accurate correlation energies with hundreds of orbitals downfolded.

Demonstrated the method's potential to adapt problem size to quantum hardware constraints.

Bridged the gap between NISQ devices and future fault-tolerant quantum computers.

Abstract

The practical application of quantum technologies to chemical problems faces significant challenges, particularly in the treatment of realistic basis sets and the accurate inclusion of electron correlation effects. A direct approach to these problems is currently infeasible due to limitations in the number of logical qubits, their fidelity, and the shallow circuit depths supported by existing hardware; all of which hinder simulations at the required level of accuracy. A promising alternative is hybrid quantum-classical computing, where classical resources are used to construct effective Hamiltonians characterized by dimensions that conform to the constraints of current quantum devices. In this paper, we demonstrate the performance of a hybrid approach: coupled-cluster downfolded Hamiltonians are first evaluated in reduced-dimensionality active spaces, and the corresponding ground-state energies are subsequently computed using quantum algorithms. Our comprehensive analysis explores the achievable accuracy in recovering correlation energies when hundreds of orbitals are downfolded into a problem size tractable by today's quantum hardware. We argue that such flexible hybrid algorithms, where problem size can be tailored to available quantum resources, can serve as a bridge between noisy intermediate-scale quantum (NISQ) devices and future fault-tolerant quantum computers, marking a step toward the early realization of quantum advantage in chemistry.