Quantum computational webs

We introduce the notion of quantum computational webs: These are quantum states universal for measurement-based computation which can be built up from a collection of simple primitives. The primitive elements - reminiscent of building blocks in a construction kit - are (i) states on a one-dimensional chain of systems ("computational quantum wires") with the power to process one logical qubit and (ii) suitable couplings which connect the wires to a computationally universal "web". All elements are preparable by nearest-neighbor interactions in a single pass - a type of operation well-suited for a number of physical architectures. We provide a complete classification of qubit wires. This is first instance where a physically well-motivated class of universal resources can be fully understood. Finally, we sketch possible realizations in superlattices, and explore the power of coupling mechanisms based on Ising or exchange-interactions.