Macroscopic quantum computation using Bose-Einstein condensates

We analyze quantum computation using quantum information stored on two component Bose-Einstein condensates (BECs). We construct a general framework for quantum algorithms to be executed using the collective states of the BECs. The use of BECs allows for an increase of energy scales via bosonic enhancement, resulting in two-qubit gate operations that can be performed at a time reduced by a factor of $N$, where $N$ is the number of bosons in the BEC. We illustrate the scheme by an application to Grover's algorithm, and discuss possible experimental implementations and decoherence effects.