Efficient Construction of a Control Modular Adder on a Carry-Lookahead Adder Using Relative-phase Toffoli Gates

Understand

Control modular addition is a core arithmetic function, and we must consider the computational cost for actual quantum computers to realize efficient implementation.

• To achieve a low computational cost in a control modular adder, we focus on minimizing KQ, defined by the product of the number of qubits and the depth of the circuit.
• In this paper, we construct an efficient control modular adder with small KQ by using relative-phase Toffoli gates in two major types of quantum computers: Fault-Tolerant Quantum Computers (FTQ) on the Logical layer and Noisy Intermediate-Scale Quantum Computers (NISQ).
• We give a more efficient construction compared to Van Meter and Itoh's, based on a carry-lookahead adder.