论文标题
在模拟随机过程中的量子优势
Quantum advantage in simulating stochastic processes
论文作者
论文摘要
我们研究了通过量子动力学模拟经典随机过程的问题，并介绍了三种情况，其中出现了记忆或时间量子优势。首先，通过引入和分析随机矩阵的嵌入性问题的量子版本，我们表明无量子无内存动态可以模拟必要需要内存的经典过程。其次，通过将随机过程的时空成本$ p $扩展到量子域，我们证明了模拟$ p $的量子成本优于经典成本的优势。第三，我们证明，具有量子控件的马尔可夫主方程可访问的一组经典状态大于可通过经典控件访问的那些集合，例如，在冷却协议中具有潜在的优势。
We investigate the problem of simulating classical stochastic processes through quantum dynamics, and present three scenarios where memory or time quantum advantages arise. First, by introducing and analysing a quantum version of the embeddability problem for stochastic matrices, we show that quantum memoryless dynamics can simulate classical processes that necessarily require memory. Second, by extending the notion of space-time cost of a stochastic process $P$ to the quantum domain, we prove an advantage of the quantum cost of simulating $P$ over the classical cost. Third, we demonstrate that the set of classical states accessible via Markovian master equations with quantum controls is larger than the set of those accessible with classical controls, leading, e.g., to a potential advantage in cooling protocols.
