A Delay-Efficient Implementation of Quantum Carry Select Adders

Quantum addition is a crucial operation for the implementation of quantum algorithms. For this reason, many researchers focused their attention on the design of quantum adders. The two main schemes for adders are the Ripple Carry Adder (RCA), which is considered slow because its execution time depends on the length of the operands, and the Carry Look-ahead Adder, which can reduce the execution time anticipating the computation of the carry, but is more complex and expensive in terms of quantum cost. A good alternative to the slow ripple carry adder and the complex carry-lookahead adder is represented by the Carry Select Adder (CSA), which divides the addition execution into subgroups of qubits and exploits the simplicity of the RCA. In this work, we propose a new quantum version of the CSA, based on an efficient realization of the RCA, chosen among the possible RCAs proposed in the literature. To this end, we show how to design the quantum CSA blocks and how to concatenate them to produce the result. The proposed quantum CSA has been simulated on the DDSIM tool of Munich Quantum Toolkit (MQT) to check its correctness, and the performance has been analyzed using the three conventional parameters for quantum circuits: number of qubits, quantum cost and delay. For each of these parameters, a formula is given as a function of the size of the operand length and the number of blocks in the quantum CSA. The CSA proposed shows a speedup variable from 2.5 to 6 for operands up to 64 qubits and a block size that goes from 2 to n/2.