Equivalence and Divergence of Imaginary-Time Evolution and Gradient Descent for Gaussian Variational States

Yash Palan

Equivalence and Divergence of Imaginary-Time Evolution and Gradient Descent for Gaussian Variational States

Quantum Physics 2025-11-11 v1 Other Condensed Matter

Authors: Yash Palan

Abstract

Imaginary-time evolution (ITE) is one of the most widely used numerical techniques for obtaining ground states of many-body Hamiltonians. In this work, we compare ITE with gradient descent (GD) within the framework of Gaussian wavefunction ansatze. We show that while ITE and GD are formally equivalent for fermionic systems, GD exhibits consistently faster convergence for bosonic systems, challenging the common assumption of their complete equivalence.

Keywords

imaginary-time evolution gradient descent Gaussian variational states fermionic systems bosonic systems

Cite

@article{arxiv.2511.06364,
  title  = {Equivalence and Divergence of Imaginary-Time Evolution and Gradient Descent for Gaussian Variational States},
  author = {Yash Palan},
  journal= {arXiv preprint arXiv:2511.06364},
  year   = {2025}
}

Comments

5 pages, 2 figures

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