AI 中文总结
本研究开发了用于求解线性微分方程的连续变量量子退火公式，通过将微分方程映射为与玻色量子退火兼容的目标函数，数值模拟显示其可复现二阶线性微分方程的解析解，有望避免基于量子比特实现的离散化开销。
AI 中文摘要
现有大多数量子退火方法针对基于量子比特（qubit）的架构设计，将其应用于连续变量优化问题时需对变量进行离散化，这会产生大量量子比特开销。近期已提出基于玻色系统的连续变量量子退火作为替代框架，其中每个优化变量直接编码于玻色模式（如腔模）。本研究开发了用于求解线性微分方程的连续变量量子退火公式，通过将解的确定过程重铸为连续变量优化问题，可将微分方程映射为与玻色量子退火兼容的目标函数。对二阶线性微分方程的数值模拟表明，在所考虑的条件下，该公式能复现对应的解析解。这些结果为求解微分方程提供了一条潜在途径，可避免基于量子比特的实现所固有的离散化开销。
英文摘要
Most existing quantum annealing approaches are formulated for qubit-based architectures. Consequently, applying them to continuous-variable optimization problems requires discretizing the variables, which can incur substantial qubit overhead. Continuous-variable quantum annealing based on bosonic systems has recently been proposed as an alternative framework, in which each optimization variable is directly encoded in a bosonic mode, such as a cavity mode. In this work, we develop a continuous-variable quantum annealing formulation for solving linear differential equations. By recasting the determination of the solution as a continuous-variable optimization problem, the differential equation can be mapped onto an objective function compatible with bosonic quantum annealing. Numerical simulations of second-order linear differential equations demonstrate that, under the conditions considered, the proposed formulation reproduces the corresponding analytical solutions. These results establish a potential route toward solving differential equations without the discretization overhead inherent in qubit-based implementations.
