An Introduction to Quantum Cellular Automata

Computer scientists have invented a plethora of fascinating machines to study. They are called computational models, and they come in many strange and varied shapes: Turing machines, register machines, circuits, finite automata, and many more. When people began wondering what the computational potential of quantum physics was, they needed quantum-computational models, and the most straightforward way to get these was to take one of the old, classical computational models and modify it with quantum weirdness. As could be expected, this game of “quantization” (putting ‘Q’s in front of things) has become a commonplace part of quantum computer science. Some quantized models have attained more prominence than others. For instance, the quantum circuit model has become standard for discussing issues of computational complexity, and the importance of Turing machines as a basis for classical computation has carried over to an interest in quantum Turing machines. But alternatives certainly exist, and each provides a new, interesting perspective on how computation works in a quantum universe. In this report, I will discuss the quantum cellular automaton (QCA), a model which is exciting not only for its simple and elegant structure, but also for its “physical” flavor. Quantum cellular automata were physically inspired, and can thus shed light on the behavior of physical systems, and conversely, they carry the hope of providing a physical implementation of quantum computation. Furthermore, just as a large class of classical computational models have convergent capabilities, making the concepts of “computable” and “efficient” much more universal than would be expected, quantum cellular automata appear to fit in with the rest of the quantum computational models: they are quantum-computationally universal. As such, quantum cellular automata encompass the whole universe of quantum computation, and one can be sure that studying them will shed light on the entirety of the field.