Schemes for parallel quantum computation without local control of qubits

Typical quantum computing schemes require transformations (gates) to be targeted at specific elements (qubits). In many physical systems, direct targeting is difficult to achieve; an alternative is to encode local gates into globally applied transformations. Here we demonstrate the minimum physical requirements for such an approach: a one-dimensional array composed of two alternating "types" of two-state system. Each system need be sensitive only to the net state of its nearest neighbors, i.e. the number in state "up arrow" minus the number in "down arrow." Additionally, we show that all such arrays can perform quite general parallel operations. A broad range of physical systems and interactions is suitable: we highlight two examples.