A qubit-ADAPT Implementation for H$_2$ Molecules using an Explicitly Correlated Basis

TL;DR

This paper demonstrates a quantum algorithm combining ADAPT with an explicitly correlated basis for H₂ molecules, achieving chemical accuracy with short quantum circuits suitable for near-term quantum devices.

Contribution

It introduces a first-quantized ADAPT approach using explicitly correlated basis functions, enhancing quantum efficiency for molecular simulations.

Findings

Short quantum circuits achieve chemical accuracy (< 1.6 mHa).

Method competes with second quantized approaches like Unitary Coupled Cluster.

Classical simulations validate the effectiveness of the approach.

Abstract

With the recent advances in the development of devices capable of performing quantum computations, a growing interest in finding near-term applications has emerged in many areas of science. In the era of non-fault tolerant quantum devices, algorithms that only require comparably short circuits accompanied by high repetition rates are considered to be a promising approach for assisting classical machines with finding solution on computationally hard problems. The ADAPT approach previously introduced in Nat. Commun. 10, 3007 (2019) extends the class of variational quantum eigensolver (VQE) algorithms with dynamically growing ans\"atze in order to find approximations to ground and excited state energies of molecules. In this work, the ADAPT algorithm has been combined with a first-quantized formulation for the hydrogen molecule in the Born-Oppenheimer approximation, employing the explicitly correlated basis functions introduced in J. Chem. Phys. 43, 2429 (1965). By the virtue of their explicit electronic correlation properties, it is shown in classically performed simulations that relatively short circuits yield chemical accuracy ($< 1.6$ mHa) for ground and excited state potential curves that can compete with second quantized approaches such as Unitary Coupled Cluster.