Simultaneous determination of multiple low-lying energy levels on a superconducting quantum processor

TL;DR

This paper reports the experimental implementation of the ancilla-entangled variational quantum eigensolver (AEVQE) on a superconducting quantum platform, successfully determining low-lying energy levels of molecules and models, and analyzing factors affecting its performance.

Contribution

It demonstrates the first experimental realization of AEVQE on a superconducting platform for complex quantum systems, providing insights into its effectiveness and comparison with other VQE methods.

Findings

Successfully determined energy levels of H$_2$ and TFIMs

Observed phase transition in TFIMs from magnetization data

Compared performance of AEVQE with ancilla-free VQE algorithms

Abstract

Determining the ground and low-lying excited states is critical in numerous scenarios. Recent work has proposed the ancilla-entangled variational quantum eigensolver (AEVQE) that utilizes entanglement between ancilla and physical qubits to simultaneously tagert multiple low-lying energy levels. In this work, we report the experimental implementation of the AEVQE on a superconducting quantum cloud platform, demonstrating the full procedure of solving the low-lying energy levels of the H$_2$ molecule and the transverse-field Ising models (TFIMs). We obtain the potential energy curves of H$_2$ and show an indication of the ferromagnetic to paramagnetic phase transition in the TFIMs from the average absolute magnetization. Moreover, we investigate multiple factors that affect the algorithmic performance and provide a comparison with ancilla-free VQE algorithms. Our work demonstrates the experimental feasibility of the AEVQE algorithm and offers a guidance for the VQE approach in solving realistic problems on publicly-accessible quantum platforms.