Multilevel variational spectroscopy using a programmable quantum simulator

Energy spectroscopy is a powerful tool with diverse applications across various disciplines. Variational quantum-classical algorithms based on programmable digital quantum simulators have emerged as promising approaches for conducting spectroscopy on various models using a single device, despite facing significant quantum and classical resource overheads. Here, we experimentally demonstrate multilevel variational spectroscopy for fundamental many-body Hamiltonians using a superconducting digital quantum simulator. By exploiting symmetries and the subspace search method, we achieve full spectroscopy for a four-qubit Heisenberg spin chain, yielding an average energy deviation as small as 0.13 from the theoretical values, assuming unity coupling strength. Our method, when extended to eight-qubit Heisenberg and transverse-field Ising Hamiltonians, successfully determines the three lowest-energy levels. In achieving the above, we introduce a circuit-agnostic compilation method that enhances the robustness of our simulator against signal crosstalk. Our study highlights the combination of the subspace search method and symmetry-assisted resource efficiency in variational quantum algorithms and lays the foundation for practical spectroscopy on near-term quantum simulators, with potential applications in quantum chemistry and condensed matter physics. Published by the American Physical Society 2024