Qudit-ADAPT-VQE: an adaptive variational algorithm with counterdiabatic-inspired improvements for qudits

Abstract:Variational quantum algorithms based on qudits have attracted significant attention in recent years. However, as in their qubit-based counterparts, challenges such as barren plateaus and the design of efficient ansatz remain major obstacles. In this work, we propose to address these issues through a qudit implementation of the ADAPT-VQE algorithm, which constructs the ansatz iteratively. Specifically, we introduce an operator pool inspired by adiabatic evolution enhanced with counterdiabatic driving for ansatz construction and employ it to solve Max 3-Cut. We show that the warm-start strategy inherent to ADAPT-VQE, together with an ansatz construction based on counterdiabatic operators, achieves higher accuracy and lower native gates implementation than approaches on fixed ansatz. Furthermore, we show that, in qudit-based quantum computing, ADAPT-VQE with a counterdiabatic operator pool can navigate rough optimization landscapes with local traps through the burrowing mechanism, suggesting robustness against barren plateau effects and providing a scalable framework for variational quantum algorithms with qudits.

arXiv:2608.14981 [quant-ph]

(or arXiv:2608.14981v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2608.14981 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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