Quantum Fourier analysis for multivariate functions and applications to a class of Schrödinger-type partial differential equations

@article{GarcaMolina2022QuantumFA,
  title={Quantum Fourier analysis for multivariate functions and applications to a class of Schr{\"o}dinger-type partial differential equations},
  author={Paula Garc{\'i}a-Molina and Javier Rodr{\'i}guez-Mediavilla and Juan Jos{\'e} Garc{\'i}a-Ripoll},
  journal={Physical Review A},
  year={2022}
}
In this work, we develop a highly efficient representation of functions and differential operators based on Fourier analysis. Using this representation, we create a variational hybrid quantum algorithm to solve static, Schrödinger-type, Hamiltonian partial differential equations (PDEs), using space-efficient variational circuits, including the symmetries of the problem, and global and gradient-based optimizers. We use this algorithm to benchmark the performance of the representation techniques… 
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