The generative quantum eigensolver (GQE) and its application for ground state search

TL;DR

The paper introduces the generative quantum eigensolver (GQE), a novel quantum algorithm that uses classical generative models to find ground states, demonstrating its effectiveness on molecular systems and real hardware.

Contribution

It develops a transformer-based GQE framework, called GPT-QE, which is outside the variational paradigm and shows promising results in quantum chemistry applications.

Findings

Surpassed CCSD in nitrogen molecule dissociation

Approached chemical accuracy in simulations

Demonstrated on real quantum hardware

Abstract

We introduce the generative quantum eigensolver (GQE), a new quantum computational framework that operates outside the variational quantum algorithm paradigm by applying classical generative models to quantum simulation. The GQE algorithm optimizes a classical generative model to produce quantum circuits with desired properties. Here, we develop a transformer-based implementation, which we name the generative pre-trained transformer-based (GPT) quantum eigensolver (GPT-QE). We show a proof-of-concept of training and pretraining of GPT-QE applied to electronic structure Hamiltonians, and demonstrate its ability illustrated by surpassing coupled cluster singles and doubles (CCSD) for the strong bond dissociation of the nitrogen molecule and approaching chemical accuracy. We also demonstrate the method on real quantum hardware.