Tangent Space Excitation Ansatz for Quantum Circuits

Computing excitation spectra of quantum many-body systems is a promising avenue to demonstrate the practical utility of current noisy quantum devices, especially as we move toward the "megaquop" regime. For this task, here we introduce a tangent space excitation ansatz for quantum circuits, motivated by the quasiparticle picture of many-body systems and the structural similarity between quantum circuits and tensor networks. Increasing circuit depth by one layer to construct tangent space around the variational optimum of a parametrized quantum circuit, we show that massive low-energy single-particle states can be captured. Our ansatz relies on a distinct mechanism from that of the excitation ansatz in a matrix product state and projected entangled-pair state, and avoids intrinsic limitations of the latter. Comparing our approach with existing quantum excited-state algorithms, we find that with similar computational cost, both the number of excited states and accuracy are significantly improved. We demonstrate our ansatz in both one and two dimensions, and further show that this approach, implementable using the Hadamard test, is scalable and suitable for current quantum processors.