Tangent Space Excitation Ansatz for Quantum Circuits

Computing the excitation spectra of quantum many-body systems on noisy quantum devices is a promising avenue to demonstrate the practical utility of current quantum processors, especially as we move toward the ``megaquop'' regime. For this task, here we introduce a \textit{tangent-space excitation ansatz} for quantum circuits, motivated by the quasi-particle picture of many-body systems and the structural similarity between quantum circuits and classical tensor networks. Increasing the circuit depth by one layer to construct the tangent space around the variational optimum of a parametrized quantum circuit, we show that a large number of low-energy states can be accurately captured. We demonstrate this ansatz using various models in both one and two spatial dimensions, including the challenging kagome Heisenberg antiferromagnet. We further provide evidence that this approach, implementable using Hadamard test, is stable in the presence of measurement noise and scalable to large system size.