AI 中文总结
本研究提出量子位版ADAPT-VQE算法，引入受逆绝热驱动启发的算子池，在求解最大3割问题时精度更高、原生门成本更低，且能应对优化空间局部陷阱，为量子位变分量子算法提供可扩展框架。
AI 中文摘要
基于量子位（qudit）的变分量子算法近年来受到广泛关注，但与基于量子比特（qubit）的同类算法类似，贫瘠高原（barren plateaus）及高效拟设（ansatz）的设计等挑战仍是主要障碍。本研究提出通过量子位（qudit）实现ADAPT-VQE算法来解决这些问题，该算法可迭代构建拟设。具体而言，我们引入受绝热演化启发且经逆绝热驱动（counterdiabatic driving）增强的算子池用于拟设构建，并将其应用于求解最大3割（Max 3-Cut）问题。结果表明，ADAPT-VQE固有的热启动（warm-start）策略，结合基于逆绝热算子的拟设构建，相比固定拟设的方法实现了更高的精度和更低的原生门（native gates）实现成本。此外，我们还表明，在基于量子位（qudit）的量子计算中，配备逆绝热算子池的ADAPT-VQE可通过隧穿机制（burrowing mechanism）跨越带有局部陷阱的粗糙优化空间，这表明其对贫瘠高原效应具有鲁棒性，并为基于量子位（qudit）的变分量子算法提供了可扩展框架。
英文摘要
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.
Comments14 pages, 6 figures
