A linear-size quantum circuit for addition with no ancillary qubits
We construct a quantum circuit for addition of two n-bit binary numbers that uses no ancillary qubits. The circuit is based on the ripple-carry approach. The depth and size of the circuit are O(n). This is an affirmative answer to the question of Kutin [1] as to whether a linear-depth quantum circuit for addition can be constructed without ancillary qubits using the ripple-carry approach. We also construct quantum circuits for addition modulo 2(n), subtraction, and comparison that use no ancillary qubits by modifying the circuit for addition.
quantum circuits addition ancillary qubits