Quantum Cellular Automata

经典元胞自动机是一种非常通用的工具，用于模拟复杂的分布式系统。他们的量子模拟最近引起了人们的关注，因为这种结构特别适合于由许多相等成分组成的晶格系统进行量子计算，这些成分可能不容易单独解决。这样的系统现在正在实现（参见项目El， E2），因此有一个直接的需要来评估分布式晶格系统的潜力。然而，与经典情况相反，量子元胞自动机的一般形式并不是那么容易描述的，特别是在承认可逆和不可逆进化的情况下。在这个项目中，量子元胞自动机将以自下而上的方法研究简单自动机（如量子行走）的详细特性，以及自上而下的方法研究一般自动机的结构，从第一原理开始分析。

Classical cellular automata are a very versatile tool for simulating complex distributed systems. Their quantum analogue has come into focus more recently, because this architecture is especially suited to allow quantum computation by a lattice system of many equal constituents, which are, perhaps, not easily addressed individually. Such systems are now getting realized (see projects El, E2), so there is a direct need to assess the potential of distributed lattice systems.In contrast to the classical case, however, the general form of a quantum cellular automaton is not so easy to describe, especially when both reversible and irreversible evolutions are admitted. In this project quantum cellular automata will be studied both in a bottom-up approach of investigating detailed properties of simple automata such as quantum walks, and a top-down approach, in which the structure of general automata is analyzed from first principles.