发表机构
Graduate School of Engineering Science, The University of Osaka; Graduate School of Informatics, Kyoto University; Center for Quantum Information and Quantum Biology, The University of Osaka; Center for Quantum Computing, RIKEN（大阪大学工学研究科; 京都大学情报学府; 大阪大学量子信息与量子生物学中心; 理化学研究所量子计算中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究通过经典模拟指导设计浅层电路，利用Heisenberg参数迁移和Schrieffer-Wolff门，为二维Hubbard模型实现低深度初态制备，显著提升基态保真度，并估计$10\ imes10$晶格制备成本约$10^5$个$T$门。
AI 中文摘要
基态能量估计的量子算法需要与基态具有不可忽略保真度的初态。在经典模拟的指导下，我们为二维半填充Hubbard模型设计了浅层电路，首先制备近似的Heisenberg基态，然后应用直接从Schrieffer-Wolff（SW）生成元导出的电荷涨落门。对于Heisenberg模型，我们展示了从$4\ imes4$晶格到高达$10\ imes10$晶格的有效参数迁移，无需进一步优化。我们通过张量网络模拟、变分蒙特卡洛参考态以及基态能量和单重态间隙的估计，获得了基态保真度的有前景下界。精确的$4\ imes4$计算表明，SW门显著提高了嵌入Heisenberg态的Hubbard基态保真度。成功的Heisenberg参数迁移支持使用这些小编晶格结果来设计超出经典模拟范围的大型晶格上的浅层Hubbard电路。对于$10\ imes10$晶格，估计的制备成本约为$10^5$个$T$门，包括Clifford+$T$合成，这完全处于megaquop机制内。这些结果为强关联系统的低成本初态制备提供了一条途径。
英文摘要
Quantum algorithms for ground-state energy estimation require initial states with non-negligible fidelity to the ground state. Guided by classical simulations, we design shallow circuits for the two-dimensional half-filled Hubbard model by first preparing an approximate Heisenberg ground state and then applying charge-fluctuation gates derived directly from the Schrieffer-Wolff (SW) generator. For the Heisenberg model, we demonstrate effective parameter transfer from a $4\times4$ lattice to lattices up to $10\times10$ without further optimization. We obtain promising lower bounds on the ground-state fidelity using tensor-network simulations, variational Monte Carlo reference states, and estimates of the ground-state energy and singlet gap. Exact $4\times4$ calculations show that the SW gates substantially improve the Hubbard ground-state fidelity of the embedded Heisenberg state. The successful Heisenberg parameter transfer supports the use of these small-lattice results to design shallow Hubbard circuits on larger lattices beyond the reach of classical simulations. For a $10\times10$ lattice, the estimated preparation cost is on the order of $10^5$ $T$ gates, including Clifford+$T$ synthesis, which is well within the megaquop regime. These results offer a route to low-cost initial-state preparation for ground-starongly correlated systems.
Comments15 pages, 6 figures, 5 tables
