We propose a simple method for simulating a general class of non-unitary dynamics as a linear combination of Hamiltonian simulation (LCHS) problems. LCHS does not rely on converting the problem into a dilated linear system problem, or on the spectral mapping theorem. The latter is the mathematical foundation of many quantum algorithms for solving a wide variety of tasks involving non-unitary processes, such as the quantum singular value transformation (QSVT). The LCHS method can achieve optimal cost in terms of state preparation. We also demonstrate an application for open quantum dynamics simulation using the complex absorbing potential method with near-optimal dependence on all parameters.

翻译：我们提出一种简单方法，将一类广义非幺正动力学模拟问题表述为哈密顿模拟的线性组合（LCHS）。LCHS方法既不依赖将问题转化为扩张线性系统问题，也不依赖于谱映射定理——后者是许多处理非幺正过程的量子算法（如量子奇异值变换QSVT）的数学基础。该方法可在态制备代价方面达到最优，同时我们通过复吸收势方法展示了其在开放量子动力学模拟中的应用，实现了对所有参数的近最优依赖关系。