AI 中文总结
本研究针对QCD量子模拟乘积公式法门成本过高的问题，通过优化指数化哈密顿量分解，将二阶乘积公式的T门成本降低近10^14倍，推动QCD量子模拟迈向现实可行。
AI 中文摘要
自Byrnes和Yamamoto的开创性工作[PRA 73, 022328 (2006)]以来，用于模拟量子色动力学（QCD）的量子算法已逐步成熟。哈密顿量模拟最常用的策略涉及乘积公式分解。然而，Byrnes和Yamamoto将乘积公式方法应用于SU($N_c$)格点规范理论时，每个Trotter步的门复杂度为$O(Λ^{8(N_c^2-1)})$，其中$Λ$是电（即不可约表示）基中的玻色子截断。Kan和Nam的一项开创性工作[arXiv:2107.12769 (2021)]大幅改善了这一不理想的成本，报告了$O\big(Λ\text{polylog}(Λ)\big)$的标度关系，但仍需要数量多到不切实际的量子门。在此，我们阐明了这一高成本估算背后的原因之一，并表明可以从Kan和Nam的每个Trotter步成本估算中去除大小为$O(2^{4(N_c^2-1)})$的因子。我们具体证明，通过使用我们过去工作中开发的方法[PRD 112, 014508 (2025); Quantum 7, 1213 (2023)]，指数化哈密顿量分解——这是应用乘积公式算法的必要步骤——可以比之前认为的高效得多地执行。我们的方法将使用二阶乘积公式的QCD模拟的T门成本估算降低了近$10^{14}$倍，且与模拟参数和规模无关。我们聚焦于电基下的模拟，进一步将我们的结果与其他方法进行了对比：Ciavarella、Klco和Savage的局域多重态基方法[PRD 103, 094501 (2021)]，以及Rhodes、Kreshchuk和Pathak的近最优算法[PRX Quantum 5, 040347 (2024)]。这项工作凸显了持续的算法改进对于将QCD的量子模拟成本降至现实量子计算机可及范围的重要性。
英文摘要
Quantum algorithms for simulating quantum chromodynamics (QCD) have matured steadily since the pioneering work of Byrnes and Yamamoto [PRA 73, 022328 (2006)]. The most popular strategies for Hamiltonian simulation involve product-formula decompositions. However, the application of product-formula methods to SU($N_c$) lattice gauge theories by Byrnes and Yamamoto leads to $O(Λ^{8(N_c^2-1)})$ gate complexity per Trotter step, where $Λ$ is the bosonic cutoff in the electric (i.e., irreducible-representation) basis. A seminal work by Kan and Nam [arXiv:2107.12769 (2021)] significantly improves over such an undesirable cost and reports an $O\big(Λ\text{polylog}(Λ)\big)$ scaling, yet it still calls for an unrealistically large number of quantum gates. Here, we illuminate one of the reasons behind this high cost estimate and show that a factor of size $O(2^{4(N_c^2-1)})$ can be removed from the per-Trotter-step cost estimate by Kan and Nam. We specifically show that, by using methods developed in our past works [PRD 112, 014508 (2025); Quantum 7, 1213 (2023)], exponentiated-Hamiltonian decomposition---a necessary step in the application of product-formula algorithms---can be performed far more efficiently than previously thought. Our method reduces the T-gate cost estimate of QCD simulations using a second-order product formula by a factor of nearly $10^{14}$, independent of simulation parameters and sizes. Focusing on simulations in the electric basis, we further contrast our results with other methods: the local-multiplet basis approach of Ciavarella, Klco, and Savage [PRD 103, 094501 (2021)] and the near-optimal algorithm of Rhodes, Kreshchuk, and Pathak [PRX Quantum 5, 040347 (2024)]. This work highlights the importance of continued algorithmic improvement to bringing the quantum-simulation cost of QCD within reach of realistic quantum computers.
Comments16 pages + bibliography, 3 figures
