Quantum Cellular Automata - Usage of The Term

Usage of The Term

In the context of models of computation or of physical systems, quantum cellular automaton refers to the merger of elements of both (1) the study of cellular automata in conventional computer science and (2) the study of quantum information processing. In particular, the following are features of models of quantum cellular automata:

• The computation is considered to come about by parallel operation of multiple computing devices, or cells. The cells are usually taken to be identical, finite-dimensional quantum systems (e.g. each cell is a qubit);
• Each cell has a neighborhood of other cells. Altogether these form a network of cells, which is usually taken to be regular (e.g. the cells are arranged as a lattice with or without periodic boundary conditions);
• The evolution of all of the cells has a number of physics-like symmetries. Locality is one: the next state of a cell depends only on its current state and that of its neighbours. Homogeneity is another: the evolution acts the same everywhere, and is independent of time;
• The state space of the cells, and the operations performed on them, should be motivated by principles of quantum mechanics.

Another feature that is often considered important for a model of quantum cellular automata is that it should be universal for quantum computation (i.e. that it can efficiently simulate quantum Turing machines, some arbitrary quantum circuit or simply all other quantum cellular automata.

Models which have been proposed recently impose further conditions, e.g. that quantum cellular automata should be reversible and/or locally unitary, and have an easily determined global transition function from the rule for updating individual cells. Recent results show that these properties can be derived axiomatically, from the symmetries of the global evolution.