Augmenting Imaginary-Time Evolution with Local Geometric Information
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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 imaginary time, in sharp 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.