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

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 $|N\pm 1⟩$ 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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Cited by in corpus (16)

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• Adaptive variational quantum computing approaches for Green's functions and nonlinear susceptibilities
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• Efficient Berry Phase Calculation via Adaptive Variational Quantum Computing Approach
• Utilizing Quantum Processor for the Analysis of Strongly Correlated Materials
• Quantum Algorithm for Green's Functions Measurements in the Fermi-Hubbard Model
• Digital quantum simulation of squeezed states via enhanced bosonic encoding in a superconducting quantum processor
• Qudit-native measurement protocol for dynamical correlations using Hadamard tests