Fast quantum modular exponentiation architecture for Shor's factoring algorithm

We present a novel and efficient, in terms of circuit depth, design for Shor’s quantum factorization algorithm. The circuit effectively utilizes a diverse set of adders based on the Quantum Fourier transform (QFT) Draper’s adders to build more complex arithmetic blocks: quantum multiplier/accumulators by constants and quantum dividers by constants. These arithmetic blocks are effectively architected into a quantum modular multiplier which is the fundamental block for the modular exponentiation circuit, the most computational intensive part of Shor’s algorithm. The proposed modular exponentiation circuit has a depth of about 2000n2 and requires 9n + 2 qubits, where n is the number of bits of the classic number to be factored. The total quantum cost of the proposed design is 1600n3. The circuit depth can be further decreased by more than three times if the approximate QFT implementation of each adder unit is exploited.