探索 qutrit 在图着色量子优化中的潜力
Exploring the Potential of Qutrits for Quantum Optimization of Graph Coloring
AI总结：
本文针对图 3-着色问题提出基于 qutrit 的 QAOA 编码与电路，并通过无噪声仿真证明其在精度、 qudit 数量和电路深度上相对 qubit 编码的优势。
摘要：
近期的硬件演示和电路编译进展，使得在近期设备上使用高维系统（qudit）进行量子计算成为一种颇具吸引力的可能。有些问题采用 qudit 而非 qubit 会具有更自然或更优的编码。本文通过使用 qutrit 表述图 3-着色这一具有实际应用的著名难题，并利用量子近似优化算法（QAOA）求解，来探索这种潜力。文中构建了基于 qutrit 的成本哈密顿量和混合器哈密顿量，并使用 qutrit 门构造相应的量子电路。我们使用 PennyLane 进行无噪声仿真，将该表述与基于 qubit 的 QAOA 进行比较，并分析求解质量和所需资源。初步结果表明，在一组相当的超参数下，qutrit 编码能找到更准确的解，使用的 qudit 数量减少一半，并且每层电路深度明显小于高效的 qubit 编码。本工作表明，qutrit 可能有助于在近期设备上求解某些问题，但仍需进一步研究以评估其在噪声环境中的潜力。
英文摘要：
Recent hardware demonstrations and advances in circuit compilation have made quantum computing with higher-dimensional systems (qudits) on near-term devices an attractive possibility. Some problems have more natural or optimal encodings using qudits over qubits. We explore this potential by formulating graph 3-coloring, a well-known and difficult problem with practical applications, using qutrits, and solve it using the quantum approximate optimization algorithm (QAOA). Qutrit-based cost and mixer Hamiltonians are constructed along with appropriate quantum circuits using qutrit gates. We run noiseless simulations using PennyLane to compare the formulation against qubit-based QAOA, and analyze the solution quality and resources required. Preliminary results show that the qutrit encoding finds more accurate solutions with a comparable set of hyperparameters, uses half as many qudits, and has a notably smaller circuit depth per layer than an efficient qubit encoding. This work suggests that qutrits may be useful in solving some problems on near-term devices, however further work is required to assess their potential in a noisy environment.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
