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arXiv · 2504.01065

Role of Riemannian geometry in double-bracket quantum imaginary-time evolution

René Zander·Raphael Seidel·Li Xiaoyue·Marek Gluza
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Abstract

Double-bracket quantum imaginary-time evolution (DB-QITE) is a quantum algorithm which coherently implements steps in the Riemannian steepest-descent direction for the energy cost function. DB-QITE is derived from Brockett's double-bracket flow which exhibits saddle points where gradients vanish. In this work, we perform numerical simulations of DB-QITE and describe signatures of transitioning through the vicinity of such saddle points. We provide an explicit gate count analysis using quantum compilation programmed in Qrisp.

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René Zander, Raphael Seidel, Li Xiaoyue, Marek Gluza. 2025-04-01. Role of Riemannian geometry in double-bracket quantum imaginary-time evolution. https://doi.org/10.1007/978-3-032-03924-8_11

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