  A quantum circuit is generalized to a nonunitary one whose constituents are
nonunitary gates operated by quantum measurement. It is shown that a specific
type of one-qubit nonunitary gates, the controlled-NOT gate, as well as all
one-qubit unitary gates constitute a universal set of gates for the nonunitary
quantum circuit, without the necessity of introducing ancilla qubits. A
reversing measurement scheme is used to improve the probability of successful
nonunitary gate operation. A quantum NAND gate and Abrams-Lloyd's nonlinear
gate are analyzed as examples. Our nonunitary circuit can be used to reduce the
qubit overhead needed to ensure fault-tolerant quantum computation.
