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

Huili Zhang1, Yibin Guo1,2,3, Guanglei Xu2, Yulong Feng1, Jingning Zhang1,*, Hai-feng Yu1,4,†, and S.P. Zhao1,2

  • *Contact author: zhangjn@baqis.ac.cn
  • †Contact author: hfyu@baqis.ac.cn
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Phys. Rev. Applied 25, 034066 – Published 19 March, 2026

DOI: https://doi.org/10.1103/j3d6-wr9v

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 target multiple low-lying energy levels. In this work, we report the implementation of the AEVQE on a superconducting quantum cloud platform, demonstrating the full procedure of solving the low-lying energy levels of the H2 molecule and the transverse-field Ising models (TFIMs). We obtain the potential energy curves of H2 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 feasibility of the AEVQE algorithm and offers guidance for the VQE approach in solving realistic problems on publicly accessible quantum platforms.

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Phys. Rev. Applied 25, 034066– Published 19 March, 2026
  • Received 20 July 2025
  • Revised 26 January 2026
  • Accepted 23 February 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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