  In this paper, we study the quantum computation realized by an
interaction-free measurement (IFM). Using Kwiat et al.'s interferometer, we
construct a two-qubit quantum gate that changes one particle's trajectory
according to whether or not the other particle exists in the interferometer. We
propose a method for distinguishing Bell-basis vectors, each of which consists
of a pair of an electron and a positron, by this gate. (This is called the
Bell-basis measurement.) This method succeeds with probability 1 in the limit
of $N \to \infty$, where N is the number of beam splitters in the
interferometer. Moreover, we can carry out a controlled-NOT gate operation by
the above Bell-basis measurement and the method proposed by Gottesman and
Chuang. Therefore, we can prepare a universal set of quantum gates by the IFM.
This means that we can execute any quantum algorithm by the IFM.
