AI 中文总结
该研究提出基于LCU的量子格气算法，实现了Burgers方程的无条件成功量子模拟，其时间步可无概率失效级联，为非线性偏微分方程求解提供了新的量子算法方案。
AI 中文摘要
近期提出的求解线性与非线性偏微分方程的量子算法大多依赖非幺正操作，这类操作通常以概率方式实现，需要后选择，从而增加了计算成本。我们证明量子格气算法可实现非线性的无条件成功量子模拟，据我们所知，这是首个时间步可在无概率失效情况下级联的Burgers方程量子算法。核心思路是利用幺正组合（LCU）框架中量子测量的随机性与经典格气算法固有随机性之间的对应关系。通过这种方式，我们确定了可采用该时间推进形式的概率经典算法的一般性质，并以另一应用实例说明该方法。
英文摘要
Most recently proposed quantum algorithms for solving linear and nonlinear partial differential equations rely on non-unitary operations. These operations are typically implemented probabilistically, requiring postselection and thus increasing the computational cost. We show that quantum lattice gas algorithms enable unconditionally successful quantum simulation of nonlinearities, yielding, to our knowledge, the first quantum algorithm for Burgers equation whose time steps can be concatenated without probabilistic failure. The key idea is to exploit the correspondence between the stochasticity of quantum measurement in the linear combination of unitaries framework and the intrinsic randomness of the classical lattice gas algorithm. In doing so, we identify general properties that characterize probabilistic classical algorithms amenable to this time-marching formulation, and illustrate the approach with an additional application.
