Even More Efficient Quantum Computations of Chemistry Through Tensor Hypercontraction

@article{Lee2021EvenME,
  title={Even More Efficient Quantum Computations of Chemistry Through Tensor Hypercontraction},
  author={Joonho Lee and Dominic W. Berry and Craig Gidney and William J. Huggins and Jarrod R. McClean and Nathan Wiebe and Ryan Babbush},
  journal={PRX Quantum},
  year={2021}
}
We describe quantum circuits with only $\widetilde{\cal O}(N)$ Toffoli complexity that block encode the spectra of quantum chemistry Hamiltonians in a basis of $N$ arbitrary (e.g., molecular) orbitals. With ${\cal O}(\lambda / \epsilon)$ repetitions of these circuits one can use phase estimation to sample in the molecular eigenbasis, where $\lambda$ is the 1-norm of Hamiltonian coefficients and $\epsilon$ is the target precision. This is the lowest complexity that has been shown for quantum… 

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