Hybrid Real-Imaginary Time Evolution for Low-Depth Hamiltonian Simulation in Quantum Optimization
Abstract
Counterdiabatic (CD) driving is a powerful technique for accelerating adiabatic quantum computing. However, it becomes self-limiting in complex optimizations like the Sherrington-Kirkpatrick model: long evolution times needed to traverse crossings force the CD strength to scale as , causing it to vanish before convergence and wasting the quantum resources invested in its implementation. We break this trade-off with a Hybrid adaptive variational quantum dynamics simulation (HAVQDS). HAVQDS combines adaptive real-time evolution for circuit compression with imaginary-time steps that suppress excitations at no extra gate cost. For the SK model (6--14 qubits), HAVQDS achieves higher approximation ratios than adiabatic or CD approaches, while reducing CNOT counts by 1--2 orders of magnitude, enabling high-fidelity quantum optimization.
Cite
@article{arxiv.2511.06280,
title = {Hybrid Real-Imaginary Time Evolution for Low-Depth Hamiltonian Simulation in Quantum Optimization},
author = {Fei Li and Xiao-Wei Li},
journal= {arXiv preprint arXiv:2511.06280},
year = {2026}
}