Augmenting Imaginary-Time Evolution with Local Geometric Information
Abstract
Imaginary-time evolution (ITE) underpins a broad family of algorithms for ground-state preparation in quantum simulation and quantum many-body physics. In these methods, convergence is governed by the energy variance of the instantaneous state, causing the flow to approach the ground state only asymptotically. We introduce an augmented imaginary-time evolution (AITE) framework that replaces the standard gradient flow on the energy landscape with a geometrically informed descent along locally optimal directions, which are identified by exploiting the higher-order statistical structure of the instantaneous energy distribution. The resulting flow strictly outperforms standard ITE throughout the entire evolution and exhibits two qualitatively distinct regimes: a superlinear convergence regime, followed by an extinction regime in which the energy error vanishes exactly at a finite value of the imaginary-time flow parameter, in contrast to the asymptotic exponential decay of ITE. Standard ITE is recovered in the zero-skewness limit of AITE, implying that the acceleration extends naturally across the broader ITE algorithmic family.
Related
- svPITE: A Python package for the state-vector-based probabilistic imaginary-time evolution algorithm
- svPITE: A Python package for the state-vector-based probabilistic imaginary-time evolution algorithm
- Quantum Imaginary Time Evolution on an Infinite 1D Chain
- Probabilistic imaginary-time evolution via compiled diagonal representations
- Gaussian continuous tensor network states: short-distance properties and imaginary-time evolution
BibTeX
@misc{benavidesriveros2026augmenting,
title = {{Augmenting Imaginary-Time Evolution with Local Geometric Information}},
author = {Carlos L. Benavides-Riveros and Prachi Sharma and Pietropaolo Frisoni and Fedor Šimkovic IV},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.23934},
eprint = {2606.23934},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.23934},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Augmenting Imaginary-Time Evolution with Local Geometric Information
AU - Carlos L. Benavides-Riveros
AU - Prachi Sharma
AU - Pietropaolo Frisoni
AU - Fedor Šimkovic IV
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2606.23934
UR - https://arxiv.org/abs/2606.23934
AB - Imaginary-time evolution (ITE) underpins a broad family of algorithms for ground-state preparation in quantum simulation and quantum many-body physics. In these methods, convergence is governed by the energy variance of the instantaneous state, causing the flow to approach the ground state only asymptotically. We introduce an augmented imaginary-time evolution (AITE) framework that replaces the standard gradient flow on the energy landscape with a geometrically informed descent along locally optimal directions, which are identified by exploiting the higher-order statistical structure of the instantaneous energy distribution. The resulting flow strictly outperforms standard ITE throughout the entire evolution and exhibits two qualitatively distinct regimes: a superlinear convergence regime, followed by an extinction regime in which the energy error vanishes exactly at a finite value of the imaginary-time flow parameter, in contrast to the asymptotic exponential decay of ITE. Standard ITE is recovered in the zero-skewness limit of AITE, implying that the acceleration extends naturally across the broader ITE algorithmic family.
ER -