发表机构
Universität Hamburg; University of Tennessee, Chattanooga（汉堡大学; 田纳西大学查塔努加分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究对比混合qudit-qubit与纯qubit实现，发现前者资源需求大幅降低（qutrit约180倍、ququint约2220倍），并揭示算法产生多体纠缠，增加经典模拟难度。
AI 中文摘要
最近，文献[1]提出了一种混合qudit-qubit算法，用于以多项式量子优势求解整数规划问题。在本工作中，我们研究该算法[1]，通过与其纯qubit实现进行对比资源分析，并探索纠缠结构以评估算法的经典可模拟性，从而理解qudit（d维量子系统）的作用。资源分析部分从逻辑门数量和容错物理资源（包括非Clifford门）两方面进行。与纯qubit模拟相比，混合qudit-qubit实现具有更紧凑的酉算子结构，这降低了逻辑和容错资源需求。以两个示例问题为例，一个使用qutrit（d=3），另一个使用ququint（d=5），在简化的容错资源模型下，与各自的纯qubit实现相比，总资源数量分别减少了约180倍和约2220倍。在纠缠研究方面，观察到类体积律的熵增长和多体纠缠特征，导致算法经典模拟的难度增加。该算法即使对于二次问题也能产生协同的三体纠缠，表明算法结构本身可以在系统中生成与问题无关的高阶纠缠。
英文摘要
Recently, a hybrid qudit-qubit algorithm [1] was presented for solving the integer programming problem with a polynomial quantum advantage. In this work, we investigate the algorithm [1] to understand the role of qudits ($d$-dimensional quantum system) by conducting a comparative resource analysis with its qubit-only implementation and the classical simulability of the algorithm by exploring the entanglement structure. The resource analysis part is performed in terms of logical gate counts, and fault-tolerant physical resources, including non-Clifford gates. The hybrid qudit-qubit implementation has a more compact structure of the unitary operators as opposed to its qubit-only simulation which reduces the logical and fault-tolerant resource requirements. Two example problems, one with qutrits ($d=3$) and the other with ququint ($d=5$), when contrasted with their qubit-only implementation, within a simplified fault-tolerant resource model, showed $\sim 180 \times $ and $\sim 2220\times$ fewer total resource count, respectively. For the entanglement study, volume-law-like entropy growth and signatures of multi-partite entanglement is observed leading to increasing difficulty in the classical simulation of the algorithm. The algorithm generates synergistic tri-partite entanglement even for a quadratic problem, revealing that the algorithmic structure itself can generate higher-order entanglement in the system independent of the problem.
Comments22 pages, 6 figures, 3 tables
