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Toward Density Functional Theory on Quantum Computers?

by Bruno Senjean, Saad Yalouz, Matthieu Saubanère

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Submission summary

Authors (as registered SciPost users): Matthieu Saubanere · Bruno Senjean · Saad Yalouz
Submission information
Preprint Link:  (pdf)
Date accepted: 2022-12-22
Date submitted: 2022-11-22 09:49
Submitted by: Senjean, Bruno
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Quantum Physics
Approaches: Theoretical, Computational


Quantum Chemistry and Physics have been pinpointed as killer applications for quantum computers, and quantum algorithms have been designed to solve the Schr\"odinger equation with the wavefunction formalism. It is yet limited to small systems, as their size is limited by the number of qubits available. Computations on large systems rely mainly on mean-field-type approaches such as density functional theory, for which no quantum advantage has been envisioned so far. In this work, we question this a priori by proposing a counter-intuitive mapping from the non-interacting to an auxiliary interacting Hamiltonian that may provide the desired advantage.

Author comments upon resubmission

We would like to resubmit a corrected version of our manuscript entitled "Toward Density Functional Theory on Quantum Computers?".
We thank the referees for their meaningful comments that helped to improve the manuscript significantly.

Sincerely Yours,
Bruno Senjean, Saad Yalouz and Matthieu Saubanère.

List of changes

- “is orthonormal” has been added below Eq. 15, as well as the following paragraph in the Method section: “As our algorithm is designed for an orthonormal basis set, we used the Löwdin symmetric orthonormalization of the atomic orbitals to get a basis of orthonormal atomic orbitals. In principle, this step will be circumvented by using already orthonormal basis sets such as plane waves or Daubechies wavelets. They usually require much more basis functions but this is not a problem for Q-DFT as they are mapped on only log2(N) qubits”
- On page 5, "expected" changed to "originally hoped"
- On page 6, "Consequently, hardware efficient ansatz..." changed to "Consequently, a hardware efficient ansatz..."
- On page 12: "...number of interacting pseudo-orbital..." changed to "...number of interacting pseudo-orbitals..."

Published as SciPost Phys. 14, 055 (2023)

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