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arXiv · 2203.12372

Effective calculation of the Green's function in the time domain on near-term quantum processors

Francesco Libbi·Jacopo Rizzo·Francesco Tacchino·Nicola Marzari·Ivano Tavernelli
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Abstract

We propose an improved quantum algorithm to calculate the Green's function through real-time propagation, and use it to compute the retarded Green's function for the 2-, 3- and 4-site Hubbard models. This novel protocol significantly reduces the number of controlled operations when compared to those previously suggested in literature. Such reduction is quite remarkable when considering the 2-site Hubbard model, for which we show that it is possible to obtain the exact time propagation of the $|N\pm 1\rangle$ states by exponentiating one single Pauli component of the Hamiltonian, allowing us to perform the calculations on an actual superconducting quantum processor.

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Francesco Libbi, Jacopo Rizzo, Francesco Tacchino, Nicola Marzari, Ivano Tavernelli. 2022-03-23. Effective calculation of the Green's function in the time domain on near-term quantum processors. https://doi.org/10.1103/physrevresearch.4.043038

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