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 $“\uparrow ”$ minus the number in $“\downarrow .”$ 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.

• Received 29 March 1999

DOI:https://doi.org/10.1103/PhysRevA.61.020301