A Higher radix architecture for quantum carry-lookahead adder

Abstract

Abstract In this paper, we propose an efficient quantum carry-lookahead adder based on the higher radix structure. For the addition of two n-bit numbers, our adder uses $$O(n)-O(\frac{n}{r})$$ O ( n ) - O ( n r ) qubits and $$O(n)+O(\frac{n}{r})$$ O ( n ) + O ( n r ) T gates to get the correct answer in T-depth $$O(r)+O(\log {\frac{n}{r}})$$ O ( r ) + O ( log n r ) , where r is the radix. Quantum carry-lookahead adder has already attracted some attention because of its low T-depth. Our work further reduces the overall cost by introducing a higher radix layer. By analyzing the performance in T-depth, T-count, and qubit count, it is shown that the proposed adder is superior to existing quantum carry-lookahead adders. Even compared to the Draper out-of-place adder which is very compact and efficient, our adder is still better in terms of T-count.