  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.
