Matsuta Takuro, Furue Ryo
Faculty of Environmental Earth Science, Hokkaido University, Hokkaido, Japan.
JAMSTEC, Yokohama, Japan.
PLoS One. 2025 Jun 26;20(6):e0326303. doi: 10.1371/journal.pone.0326303. eCollection 2025.
Recent advancements in quantum computing suggest the potential to revolutionize computational algorithms across various scientific domains including oceanography and atmospheric science. The field is still relatively young and quantum computation is so different from classical computation that suitable frameworks to represent oceanic and atmospheric dynamics are yet to be explored. Quantum annealing (QA), one of the major paradigms, focuses on combinatorial optimization tasks. Given its potential to excel in NP-hard problems, QA may significantly accelerate the calculation of ocean and atmospheric systems described by the Navier-Stokes equations in the future. In this paper, we apply both QA and simulated annealing (SA), its classical counterpart, to a simplified ocean model known as the Stommel problem. We use the Stommel problem, which is not an NP problem and therefore does not benefit from QA today, just as an example, a first step in exploring QA for more intricate problems governed by the Navier-Stokes equations. We cast the linear partial differential equation governing the Stommel model into an optimization problem by the least-squares method and discretize the cost function in two ways: finite difference and truncated basis expansion. In either case, SA successfully reproduces the expected solution when appropriate parameters are chosen. In contrast, QA using the D-Wave quantum annealing machine fails to obtain good solutions for some cases owing to hardware limitations; in particular, the highly limited connectivity graph of the machine limits the size of the solvable problems, at least under currently available algorithms. Either expanding the machine's connectivity graph or improving the graph-embedding algorithms would probably be necessary for quantum annealing machines to be usable for oceanic and atmospheric dynamics problems.
量子计算领域的最新进展表明，它有潜力彻底改变包括海洋学和大气科学在内的各种科学领域的计算算法。该领域仍相对年轻，且量子计算与经典计算差异极大，因此尚未探索出适合表示海洋和大气动力学的框架。量子退火（QA）作为主要范例之一，专注于组合优化任务。鉴于其在解决NP难问题方面的潜力，量子退火未来可能会显著加速由纳维 - 斯托克斯方程描述的海洋和大气系统的计算。在本文中，我们将量子退火及其经典对应算法模拟退火（SA）应用于一个名为斯托默尔问题的简化海洋模型。我们以斯托默尔问题为例，它并非NP问题，所以目前无法从量子退火中受益，这只是探索量子退火应用于由纳维 - 斯托克斯方程控制的更复杂问题的第一步。我们通过最小二乘法将控制斯托默尔模型的线性偏微分方程转化为一个优化问题，并以两种方式离散成本函数：有限差分法和截断基展开法。在任何一种情况下，当选择合适的参数时，模拟退火都能成功重现预期解。相比之下，由于硬件限制，使用D-Wave量子退火机的量子退火在某些情况下无法获得良好的解；特别是，该机器的连接图高度受限，限制了可解问题的规模，至少在当前可用算法下是这样。对于量子退火机能够用于解决海洋和大气动力学问题而言，可能需要扩大机器的连接图或改进图嵌入算法。
