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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 Kutin 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 2ⁿ, subtraction, and comparison that use no ancillary qubits by modifying the circuit for addition.
Takahashi et al. (Thu,) studied this question.
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