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：我们提出一种简捷方法，将一类通用的非幺正动力学过程表示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展线性系统问题，也不依赖谱映射定理——后者是许多涉及非幺正过程的量子算法（如量子奇异值变换QSVT）的数学基石。该线性组合方法能在态制备方面实现最优代价。我们同时展示了其在开放量子动力学模拟中的应用：通过复吸收势方法，该方法在所有参数上均具有近最优依赖性。