  We interpret quantum computing as a geometric evolution process by
reformulating finite quantum systems via Connes' noncommutative geometry. In
this formulation, quantum states are represented as noncommutative connections,
while gauge transformations on the connections play a role of unitary quantum
operations. Thereby, a geometrical model for quantum computation is presented,
which is equivalent to the quantum circuit model. This result shows a geometric
way of realizing quantum computing and as such, provides an alternative
proposal of building a quantum computer.
