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Determining the N-representability of transition reduced density matrices.

Gustavo E Massaccesi1,2, Pablo Capuzzi3,4, Ofelia B Oña5

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This study introduces a novel method to solve the N-representability problem for transition reduced density matrices (RDMs) in quantum systems. The approach embeds smaller RDMs into larger ones, enabling accurate RDM purification and wave function reconstruction.

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Area of Science:

  • Quantum Chemistry
  • Electronic Structure Theory
  • Computational Physics

Background:

  • The N-representability problem for reduced density matrices (RDMs) is a critical challenge in accurately describing quantum systems.
  • Transition RDMs are essential for understanding molecular properties and dynamics, but their N-representability is complex.
  • Existing methods often struggle with the accurate determination of transition RDMs.

Purpose of the Study:

  • To develop a practical method for determining the N-representability of transition reduced density matrices (RDMs).
  • To embed a p-body transition RDM into a (p+1)-body RDM for an (N+1)-particle system.
  • To enable the purification of transition RDMs and reconstruction of wave functions.

Main Methods:

  • Embedding a p-body transition RDM into a (p+1)-body RDM of an (N+1)-particle system.
  • Applying a unitary evolution algorithm based on an adaptive derivative-assembled pseudo-Trotter variational quantum algorithm.
  • Minimizing the distance between projected (p+1)-body RDMs and a target RDM via unitary transformations.

Main Results:

  • Successfully demonstrated a method to determine the N-representability of transition RDMs.
  • Enabled the purification of transition RDMs, correcting and refining their accuracy.
  • Reconstructed approximate wave functions involved in quantum transitions.
  • Validated the approach through numerical simulations on systems like H3.

Conclusions:

  • The proposed embedding and unitary evolution approach provides an effective strategy for N-representability of transition RDMs.
  • This methodology enhances the accuracy of transition density matrices and wave function reconstruction.
  • The validated approach offers a robust and accurate solution for fundamental challenges in electronic structure theory.